Sierpinski carpet
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Produce a graphical or ASCII-art representation of a Sierpinski carpet of order N.
For example, the Sierpinski carpet of order 3 should look like this:
########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
The use of the # character is not rigidly required for ASCII art.
The important requirement is the placement of whitespace and non-whitespace characters.
- Related task
11l
F sierpinski_carpet(n)
V carpet = [String(‘#’)]
L 1..n
carpet = carpet.map(x -> x‘’x‘’x)
[+] carpet.map(x -> x‘’x.replace(‘#’, ‘ ’)‘’x)
[+] carpet.map(x -> x‘’x‘’x)
R carpet.join("\n")
print(sierpinski_carpet(3))Action!
BYTE FUNC InCarpet(BYTE x,y)
DO
IF x MOD 3=1 AND y MOD 3=1 THEN
RETURN (0)
FI
x==/3 y==/3
UNTIL x=0 AND y=0
OD
RETURN (1)
PROC DrawCarpet(INT x0 BYTE y0,depth)
BYTE i,x,y,size
size=1
FOR i=1 TO depth
DO size==*3 OD
FOR y=0 TO size-1
DO
FOR x=0 TO size-1
DO
IF InCarpet(x,y) THEN
Plot(x0+2*x,y0+2*y)
Plot(x0+2*x+1,y0+2*y)
Plot(x0+2*x+1,y0+2*y+1)
Plot(x0+2*x,y0+2*y+1)
FI
OD
OD
RETURN
PROC Main()
BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6
Graphics(8+16)
Color=1
COLOR1=$0C
COLOR2=$02
DrawCarpet(79,15,4)
DO UNTIL CH#$FF OD
CH=$FF
RETURN- Output:
Screenshot from Atari 8-bit computer
Ada
with Ada.Text_Io; use Ada.Text_Io;
procedure Sierpinski_Carpet is
subtype Index_Type is Integer range 1..81;
type Pattern_Array is array(Index_Type range <>, Index_Type range <>) of Boolean;
Pattern : Pattern_Array(1..81,1..81) := (Others =>(others => true));
procedure Clear_Center(P : in out Pattern_Array; X1 : Index_Type; X2 : Index_Type;
Y1 : Index_Type; Y2 : Index_Type) is
Xfirst : Index_Type;
Xlast : Index_Type;
Yfirst : Index_Type;
Ylast : Index_Type;
Diff : Integer;
begin
Xfirst :=(X2 - X1 + 1) / 3 + X1;
Diff := Xfirst - X1;
Xlast := Xfirst + Diff;
Yfirst := (Y2 - Y1) / 3 + Y1;
YLast := YFirst + Diff;
for I in XFirst..XLast loop
for J in YFirst..YLast loop
P(I, J) := False;
end loop;
end loop;
end Clear_Center;
procedure Print(P : Pattern_Array) is
begin
for I in P'range(1) loop
for J in P'range(2) loop
if P(I,J) then
Put('*');
else
Put(' ');
end if;
end loop;
New_Line;
end loop;
end Print;
procedure Divide_Square(P : in out Pattern_Array; Order : Positive) is
Factor : Natural := 0;
X1, X2 : Index_Type;
Y1, Y2 : Index_Type;
Division : Index_Type;
Num_Sections : Index_Type;
begin
while Factor < Order loop
Num_Sections := 3**Factor;
Factor := Factor + 1;
X1 := P'First;
Division := P'Last / Num_Sections;
X2 := Division;
Y1 := X1;
Y2 := X2;
loop
loop
Clear_Center(P, X1, X2, Y1, Y2);
exit when X2 = P'Last;
X1 := X2;
X2 := X2 + Division;
end loop;
exit when Y2 = P'Last;
Y1 := Y2;
Y2 := Y2 + Division;
X1 := P'First;
X2 := Division;
end loop;
end loop;
end Divide_Square;
begin
Divide_Square(Pattern, 3);
Print(Pattern);
end Sierpinski_Carpet;
ALGOL 68
PROC in carpet = (INT in x, in y)BOOL: (
INT x := in x, y := in y;
BOOL out;
DO
IF x = 0 OR y = 0 THEN
out := TRUE; GO TO stop iteration
ELIF x MOD 3 = 1 AND y MOD 3 = 1 THEN
out := FALSE; GO TO stop iteration
FI;
x %:= 3;
y %:= 3
OD;
stop iteration: out
);
PROC carpet = (INT n)VOID:
FOR i TO 3 ** n DO
FOR j TO 3 ** n DO
IF in carpet(i-1, j-1) THEN
print("* ")
ELSE
print(" ")
FI
OD;
print(new line)
OD;
carpet(3)ALGOL W
As with the first C sample, uses pairs of characters for each point to give a squarer appreaence.
begin
for depth := 3 do begin
integer dim;
dim := 1;
for i := 0 until depth - 1 do dim := dim * 3;
for i := 0 until dim - 1 do begin
for j := 0 until dim - 1 do begin
integer d;
d := dim div 3;
while d not = 0
and not ( ( i rem ( d * 3 ) ) div d = 1 and ( j rem ( d * 3 ) ) div d = 1 )
do d := d div 3;
writeon( if d not = 0 then " " else "##" )
end for_j;
write()
end for_i;
write()
end for_depth
end.- Output:
###################################################### ## #### #### #### #### #### #### #### #### ## ###################################################### ###### ############ ############ ###### ## ## ## #### ## ## #### ## ## ## ###### ############ ############ ###### ###################################################### ## #### #### #### #### #### #### #### #### ## ###################################################### ################## ################## ## #### #### ## ## #### #### ## ################## ################## ###### ###### ###### ###### ## ## ## ## ## ## ## ## ###### ###### ###### ###### ################## ################## ## #### #### ## ## #### #### ## ################## ################## ###################################################### ## #### #### #### #### #### #### #### #### ## ###################################################### ###### ############ ############ ###### ## ## ## #### ## ## #### ## ## ## ###### ############ ############ ###### ###################################################### ## #### #### #### #### #### #### #### #### ## ######################################################
APL
carpet←{{⊃⍪/,⌿3 3⍴4 0 4\⊂⍵}⍣⍵⊢⍪'#'}
- Output:
carpet 0
#
carpet 1
###
# #
###
carpet 2
#########
# ## ## #
#########
### ###
# # # #
### ###
#########
# ## ## #
#########
carpet 3
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
######### #########
# ## ## # # ## ## #
######### #########
### ### ### ###
# # # # # # # #
### ### ### ###
######### #########
# ## ## # # ## ## #
######### #########
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
AppleScript
Functional
(ES5 Functional version)
----------------------- CARPET MODEL ---------------------
-- sierpinskiCarpet :: Int -> [[Bool]]
on sierpinskiCarpet(n)
-- rowStates :: Int -> [Bool]
script rowStates
on |λ|(x, _, xs)
-- cellState :: Int -> Bool
script cellState
-- inCarpet :: Int -> Int -> Bool
on inCarpet(x, y)
if (0 = x or 0 = y) then
true
else
not ((1 = x mod 3) and ¬
(1 = y mod 3)) and ¬
inCarpet(x div 3, y div 3)
end if
end inCarpet
on |λ|(y)
inCarpet(x, y)
end |λ|
end script
map(cellState, xs)
end |λ|
end script
map(rowStates, enumFromTo(0, (3 ^ n) - 1))
end sierpinskiCarpet
--------------------------- TEST -------------------------
on run
-- Carpets of orders 1, 2, 3
set strCarpets to ¬
intercalate(linefeed & linefeed, ¬
map(showCarpet, enumFromTo(1, 3)))
set the clipboard to strCarpets
return strCarpets
end run
---------------------- CARPET DISPLAY --------------------
-- showCarpet :: Int -> String
on showCarpet(n)
-- showRow :: [Bool] -> String
script showRow
-- showBool :: Bool -> String
script showBool
on |λ|(bool)
if bool then
character id 9608
else
" "
end if
end |λ|
end script
on |λ|(xs)
intercalate("", map(my showBool, xs))
end |λ|
end script
intercalate(linefeed, map(showRow, sierpinskiCarpet(n)))
end showCarpet
-------------------- GENERIC FUNCTIONS -------------------
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set xs to {}
repeat with i from m to n
set end of xs to i
end repeat
xs
else
{}
end if
end enumFromTo
-- intercalate :: Text -> [Text] -> Text
on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
- Output:
███ █ █ ███ █████████ █ ██ ██ █ █████████ ███ ███ █ █ █ █ ███ ███ █████████ █ ██ ██ █ █████████ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████ ███ ██████ ██████ ███ █ █ █ ██ █ █ ██ █ █ █ ███ ██████ ██████ ███ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████ █████████ █████████ █ ██ ██ █ █ ██ ██ █ █████████ █████████ ███ ███ ███ ███ █ █ █ █ █ █ █ █ ███ ███ ███ ███ █████████ █████████ █ ██ ██ █ █ ██ ██ █ █████████ █████████ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████ ███ ██████ ██████ ███ █ █ █ ██ █ █ ██ █ █ █ ███ ██████ ██████ ███ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████
Or, defining the Sierpinski carpet weave more simply in terms of generic abstractions like zipWith and concatMap:
-- weave :: [String] -> [String]
on weave(xs)
script thread
property f : zipWith(my append)
on |λ|(x)
f's |λ|(f's |λ|(xs, x), xs)
end |λ|
end script
script blank
on |λ|(x)
replicate(length of x, space)
end |λ|
end script
concatMap(thread, {xs, map(blank, xs), xs})
end weave
-- TEST ---------------------------------------------------
on run
-- sierpinksi :: Int -> String
script sierpinski
on |λ|(n)
unlines(item n of take(n, ¬
iterate(weave, {character id 9608})))
end |λ|
end script
sierpinski's |λ|(3)
end run
-- GENERIC ABSTRACTIONS -----------------------------------
-- Append two lists.
-- append (++) :: [a] -> [a] -> [a]
-- append (++) :: String -> String -> String
on append(xs, ys)
xs & ys
end append
-- concatMap :: (a -> [b]) -> [a] -> [b]
on concatMap(f, xs)
set lng to length of xs
set acc to {}
tell mReturn(f)
repeat with i from 1 to lng
set acc to acc & |λ|(item i of xs, i, xs)
end repeat
end tell
return acc
end concatMap
-- iterate :: (a -> a) -> a -> Gen [a]
on iterate(f, x)
script
property v : missing value
property g : mReturn(f)'s |λ|
on |λ|()
if missing value is v then
set v to x
else
set v to g(v)
end if
return v
end |λ|
end script
end iterate
-- length :: [a] -> Int
on |length|(xs)
set c to class of xs
if list is c or string is c then
length of xs
else
(2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite)
end if
end |length|
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min
-- replicate :: Int -> String -> String
on replicate(n, s)
set out to ""
if n < 1 then return out
set dbl to s
repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate
-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set c to class of xs
if list is c then
if 0 < n then
items 1 thru min(n, length of xs) of xs
else
{}
end if
else if string is c then
if 0 < n then
text 1 thru min(n, length of xs) of xs
else
""
end if
else if script is c then
set ys to {}
repeat with i from 1 to n
set v to xs's |λ|()
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
else
missing value
end if
end take
-- unlines :: [String] -> String
on unlines(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f)
script
on |λ|(xs, ys)
set lng to min(|length|(xs), |length|(ys))
if 1 > lng then return {}
set xs_ to take(lng, xs) -- Allow for non-finite
set ys_ to take(lng, ys) -- generators like cycle etc
set lst to {}
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs_, item i of ys_)
end repeat
return lst
end tell
end |λ|
end script
end zipWith
- Output:
█████████ █ ██ ██ █ █████████ ███ ███ █ █ █ █ ███ ███ █████████ █ ██ ██ █ █████████
Simple
on SierpinskiCarpet(n, char)
if (n < 0) then return {}
script o
property lst1 : {char}
property lst2 : missing value
end script
set gap to space
repeat with k from 0 to (n - 1)
copy o's lst1 to o's lst2
repeat with i from 1 to (3 ^ k)
set str to o's lst1's item i
set o's lst1's item i to str & str & str
set o's lst2's item i to str & gap & str
end repeat
set o's lst1 to o's lst1 & o's lst2 & o's lst1
set gap to gap & gap & gap
end repeat
return join(o's lst1, linefeed)
end SierpinskiCarpet
on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join
return SierpinskiCarpet(3, "#")
- Output:
########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
Arturo
inCarpet?: function [x,y][
X: x
Y: y
while [true][
if or? zero? X
zero? Y -> return true
if and? 1 = X % 3
1 = Y % 3 -> return false
X: X / 3
Y: Y / 3
]
]
carpet: function [n][
loop 0..dec 3^n 'i [
loop 0..dec 3^n 'j [
prints (inCarpet? i j)? -> "# "
-> " "
]
print ""
]
]
carpet 3
- Output:
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
Asymptote
path across(path p, real node) {
return
point(p, node + 1/3) + point(p, node - 1/3) - point(p, node);
}
path corner_subquad(path p, real node) {
return
point(p, node) --
point(p, node + 1/3) --
across(p, node) --
point(p, node - 1/3) --
cycle;
}
path noncorner_subquad(path p, real node1, real node2) {
return
point(p, node1 + 1/3) --
across(p, node1) --
across(p, node2) --
point(p, node2 - 1/3) --
cycle;
}
void carpet(path p, int order) {
if (order == 0)
fill(p);
else {
for (real node : sequence(0, 3)) {
carpet(corner_subquad(p, node), order - 1);
carpet(noncorner_subquad(p, node, node + 1), order - 1);
}
}
}
path q =
// A square
unitsquare
// An oblong rhombus
// (0, 0) -- (5, 3) -- (0, 6) -- (-5, 3) -- cycle
// A trapezoid
// (0, 0) -- (4, 2) -- (6, 2) -- (10, 0) -- cycle
// A less regular quadrilateral
// (0, 0) -- (4, 1) -- (9, -4) -- (1, -1) -- cycle
// A concave shape
// (0, 0) -- (5, 3) -- (10, 0) -- (5, 1) -- cycle
;
size(9 inches, 6 inches);
carpet(q, 5);
AutoHotkey
ahk discussion
Loop 4
MsgBox % Carpet(A_Index)
Carpet(n) {
Loop % 3**n {
x := A_Index-1
Loop % 3**n
t .= Dot(x,A_Index-1)
t .= "`n"
}
Return t
}
Dot(x,y) {
While x>0 && y>0
If (mod(x,3)=1 && mod(y,3)=1)
Return " "
Else x //= 3, y //= 3
Return "."
}
AWK
# WSC.AWK - Waclaw Sierpinski's carpet contributed by Dan Nielsen
#
# syntax: GAWK -f WSC.AWK [-v o={a|A}{b|B}] [-v X=anychar] iterations
#
# -v o=ab default
# a|A loose weave | tight weave
# b|B don't show | show how the carpet is built
# -v X=? Carpet is built with X's. The character assigned to X replaces all X's.
#
# iterations
# The number of iterations. The default is 0 which produces one carpet.
#
# what is the difference between a loose weave and a tight weave:
# loose tight
# X X X X X X X X X XXXXXXXXX
# X X X X X X X XX XX X
# X X X X X X X X X XXXXXXXXX
# X X X X X X XXX XXX
# X X X X X X X X
# X X X X X X XXX XXX
# X X X X X X X X X XXXXXXXXX
# X X X X X X X XX XX X
# X X X X X X X X X XXXXXXXXX
#
# examples:
# GAWK -f WSC.AWK 2
# GAWK -f WSC.AWK -v o=Ab -v X=# 2
# GAWK -f WSC.AWK -v o=Ab -v X=\xDB 2
#
BEGIN {
optns = (o == "") ? "ab" : o
n = ARGV[1] + 0 # iterations
if (n !~ /^[0-9]+$/) { exit(1) }
seed = (optns ~ /A/) ? "XXX,X X,XXX" : "X X X ,X X ,X X X " # tight/loose weave
leng = row = split(seed,A,",") # seed the array
for (i=1; i<=n; i++) { # build carpet
for (a=1; a<=3; a++) {
row = 0
for (b=1; b<=3; b++) {
for (c=1; c<=leng; c++) {
row++
tmp = (a == 2 && b == 2) ? sprintf("%*s",length(A[c]),"") : A[c]
B[row] = B[row] tmp
}
if (optns ~ /B/) { # show how the carpet is built
if (max_row < row+0) { max_row = row }
for (r=1; r<=max_row; r++) {
printf("i=%d row=%02d a=%d b=%d '%s'\n",i,r,a,b,B[r])
}
print("")
}
}
}
leng = row
for (j=1; j<=row; j++) { A[j] = B[j] } # re-seed the array
for (j in B) { delete B[j] } # delete work array
}
for (j=1; j<=row; j++) { # print carpet
if (X != "") { gsub(/X/,substr(X,1,1),A[j]) }
sub(/ +$/,"",A[j])
printf("%s\n",A[j])
}
exit(0)
}
- Sample:
GAWK -f WSC.AWK 1 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X GAWK -f WSC.AWK -v o=A 1 XXXXXXXXX X XX XX X XXXXXXXXX XXX XXX X X X X XXX XXX XXXXXXXXX X XX XX X XXXXXXXXX
BASIC
Applesoft BASIC
100 HGR
110 POKE 49234,0
120 DEF FN M(X) = X - INT (D * 3) * INT (X / INT (D * 3))
130 DE = 4
140 DI = 3 ^ DE * 3
150 FOR I = 0 TO DI - 1
160 FOR J = 0 TO DI - 1
170 FOR D = DI / 3 TO 0 STEP 0
180 IF INT ( FN M(I) / D) = 1 AND INT ( FN M(J) / D) = 1 THEN 200BREAK
190 D = INT (D / 3): NEXT D
200 HCOLOR= 3 * (D = 0)
210 HPLOT J,I
220 NEXT J
230 NEXT IBASIC256
function in_carpet(x, y)
while x <> 0 and y <> 0
if(x mod 3) = 1 and (y mod 3) = 1 then return False
y = int(y / 3): x = int(x / 3)
end while
return True
end function
Subroutine carpet(n)
k = (3^n)-1
for i = 0 to k
for j = 0 to k
if in_carpet(i, j) then print("#"); else print(" ");
next j
print
next i
end subroutine
for k = 0 to 3
print "N = "; k
call carpet(k)
print
next k
endBBC BASIC
Order% = 3
side% = 3^Order%
VDU 23,22,8*side%;8*side%;64,64,16,128
FOR Y% = 0 TO side%-1
FOR X% = 0 TO side%-1
IF FNincarpet(X%,Y%) PLOT X%*16,Y%*16+15
NEXT
NEXT Y%
REPEAT WAIT 1 : UNTIL FALSE
END
DEF FNincarpet(X%,Y%)
REPEAT
IF X% MOD 3 = 1 IF Y% MOD 3 = 1 THEN = FALSE
X% DIV= 3
Y% DIV= 3
UNTIL X%=0 AND Y%=0
= TRUE
Commodore BASIC
100 PRINT CHR$(147); CHR$(18); "**** SIERPINSKI CARPET ****"
110 PRINT
120 INPUT "ORDER"; O$
130 O = VAL(O$)
140 IF O < 1 THEN 120
150 PRINT
160 SZ = 3 ↑ O
170 FOR Y = 0 TO SZ - 1
180 :FOR X = 0 TO SZ - 1
190 : CH$ = "#"
200 : X1 = X
210 : Y1 = Y
220 : IF (X1 = 0) OR (Y1 = 0) THEN 290
230 : X3 = X1 - 3 * INT(X1 / 3)
240 : Y3 = Y1 - 3 * INT(Y1 / 3)
250 : IF (X3 = 1) AND (Y3 = 1) THEN CH$ = " ": GOTO 290
260 : X1 = INT(X1 / 3)
270 : Y1 = INT(Y1 / 3)
280 : GOTO 220
290 : PRINT CH$;
300 :NEXT X
310 PRINT
320 NEXT Y
- Output:
All of the Commodore 8-bits have a 25-line display, so orders 3 and up scroll the top of the carpet off the screen. Orders 4+ additionally require at least 81 columns, and even a PET or C128 maxes out at 80. So we'll settle for an order-2 demonstration:
**** SIERPINSKI CARPET **** ORDER? 2 ######### # ## ## # ######### ### ### # # # # ### ### ######### # ## ## # ######### READY.
You can get a more graphical display by replacing the "#" with CHR$(18)+CHR$(186)+CHR$(146); for maximum portability it should also output a CHR$(142) at some earlier point, maybe by adding it to the otherwise-empty PRINT statement on line 110. Then the filled-in squares become mostly-solid blocks with narrow gaps along their right and bottom edges so you can still count them when adjacent.
FreeBASIC
ASCII version
Function in_carpet(x As Uinteger, y As Uinteger) As Boolean
While x <> 0 And y <> 0
If(x Mod 3) = 1 And (y Mod 3) = 1 Then Return False
y = y \ 3: x = x \ 3
Wend
Return True
End Function
Sub carpet(n As Uinteger)
Dim As Uinteger i, j, k = (3^n)-1
For i = 0 To k
For j = 0 To k
If in_carpet(i, j) Then Print("#"); Else Print(" ");
Next j
Print
Next i
End Sub
For k As Byte = 0 To 4
Print !"\nN ="; k
carpet(k)
Next k
Sleep
Graphic version
Screenres 500, 545, 8
Windowtitle "Sierpinski Carpet"
Cls
Color 1, 15
Sub carpet (x As Integer, y As Integer, size As Integer, order As Integer)
Dim As Integer ix, iy, isize, iorder, side, newX, newY
ix = x: iy = y: isize = size: iorder = order
Line (ix, iy)-(ix + isize - 1, iy + isize - 1), 1, BF
side = Int(isize / 3)
newX = ix + side
newY = iy + side
Line (newX, newY)-(newX + side - 1, newY + side - 1), 15, BF
iorder -= 1
If iorder >= 0 Then
carpet(newX - side, newY - side + 1, side, iorder)
carpet(newX, newY - side + 1, side, iorder)
carpet(newX + side, newY - side + 1, side, iorder)
carpet(newX + side, newY, side, iorder)
carpet(newX + side, newY + side, side, iorder)
carpet(newX, newY + side, side, iorder)
carpet(newX - side, newY + side, side, iorder)
carpet(newX - side, newY, side, iorder)
End If
End Sub
carpet(5, 20, 243, 0)
carpet(253, 20, 243, 1)
carpet(5, 293, 243, 2)
carpet(253, 293, 243, 3)
Sleep
IS-BASIC
100 PROGRAM "Sierpins.bas"
110 LET O=3
120 LET SZ=3^O
130 FOR Y=0 TO SZ-1
140 FOR X=0 TO SZ-1
150 LET CH$=CHR$(159)
160 LET X1=X:LET Y1=Y
170 DO UNTIL X1=0
180 IF MOD(X1,3)=1 AND MOD(Y1,3)=1 THEN LET CH$=" ":EXIT DO
190 LET X1=INT(X1/3):LET Y1=INT(Y1/3)
200 LOOP
210 PRINT CH$;
220 NEXT
230 PRINT
240 NEXTLiberty BASIC
NoMainWin
WindowWidth = 508
WindowHeight = 575
Open "Sierpinski Carpets" For Graphics_nsb_nf As #g
#g "Down; TrapClose [halt]"
'labels
#g "Place 90 15;\Order 0"
#g "Place 340 15;\Order 1"
#g "Place 90 286;\Order 2"
#g "Place 340 286;\Order 3"
'carpets
Call carpet 5, 20, 243, 0
Call carpet 253, 20, 243, 1
Call carpet 5, 293, 243, 2
Call carpet 253, 293, 243, 3
#g "Flush"
Wait
[halt]
Close #g
End
Sub carpet x, y, size, order
#g "Color 0 0 128; BackColor 0 0 128"
#g "Place ";x;" ";y
#g "BoxFilled ";x+size-1;" ";y+size-1
#g "Color white; BackColor white"
side = Int(size/3)
newX = x+side
newY = y+side
#g "Place ";newX;" ";newY
#g "BoxFilled ";newX+side-1;" ";newY+side-1
order = order - 1
If order > -1 Then
Call carpet newX-side, newY-side+1, side, order
Call carpet newX, newY-side+1, side, order
Call carpet newX+side, newY-side+1, side, order
Call carpet newX+side, newY, side, order
Call carpet newX+side, newY+side, side, order
Call carpet newX, newY+side, side, order
Call carpet newX-side, newY+side, side, order
Call carpet newX-side, newY, side, order
End If
End SubMinimal BASIC
Adapted to text mode. In some systems the screen scrolls for an order greater than 2.
10 REM Sierpinski carpet
20 REM R - order; S - size.
30 LET R = 3
40 LET S = 3^R
50 FOR I = 0 TO S-1
60 FOR J = 0 TO S-1
70 LET X = J
80 LET Y = I
90 GOSUB 500
100 IF C = 1 THEN 130
110 PRINT " ";
120 GOTO 140
130 PRINT "*";
140 NEXT J
150 PRINT
160 NEXT I
170 END
490 REM Is (X,Y) in the carpet? Returns C = 0 (no) or C = 1 (yes).
500 LET C = 0
510 X3 = INT(X/3)
520 Y3 = INT(Y/3)
530 REM If (X mod 3 = 1) and (Y mod 3 = 1) then return
540 IF (X-X3*3)*(Y-Y3*3) = 1 THEN 600
550 LET X = X3
560 LET Y = Y3
570 IF X > 0 THEN 510
580 IF Y > 0 THEN 510
590 LET C = 1
600 RETURN
Nascom BASIC
10 REM Sierpinski carpet
20 CLS
30 LET RDR=3
40 LET S=3^RDR
50 FOR I=0 TO S-1
60 FOR J=0 TO S-1
70 LET X=J
80 LET Y=I
90 GOSUB 300
100 IF C THEN SET(J,I)
110 NEXT J
120 NEXT I
130 REM ** Set up machine code INKEY$ command
140 IF PEEK(1)<>0 THEN RESTORE 410
150 DOKE 4100,3328:FOR A=3328 TO 3342 STEP 2
160 READ B:DOKE A,B:NEXT A
170 SCREEN 1,15
180 PRINT "Hit any key to exit.";
190 A=USR(0):IF A<0 THEN 190
200 CLS
210 END
290 REM ** Is (X,Y) in the carpet?
295 REM Returns C=0 (no) or C=1 (yes).
300 LET C=0
310 XD3=INT(X/3):YD3=INT(Y/3)
320 IF X-XD3*3=1 AND Y-YD3*3=1 THEN RETURN
330 LET X=XD3
340 LET Y=YD3
350 IF X>0 OR Y>0 THEN GOTO 310
360 LET C=1
370 RETURN
395 REM ** Data for machine code INKEY$
400 DATA 25055,1080,-53,536,-20665,3370,-5664,0
410 DATA 27085,14336,-13564,6399,18178,10927
420 DATA -8179,233
PureBasic
Procedure in_carpet(x,y)
While x>0 And y>0
If x%3=1 And y%3=1
ProcedureReturn #False
EndIf
y/3: x/3
Wend
ProcedureReturn #True
EndProcedure
Procedure carpet(n)
Define i, j, l=Pow(3,n)-1
For i=0 To l
For j=0 To l
If in_carpet(i,j)
Print("#")
Else
Print(" ")
EndIf
Next
PrintN("")
Next
EndProcedure
QB64
_Title "Sierpinski Carpet"
Screen _NewImage(500, 545, 8)
Cls , 15: Color 1, 15
'labels
_PrintString (96, 8), "Order 0"
_PrintString (345, 8), "Order 1"
_PrintString (96, 280), "Order 3"
_PrintString (345, 280), "Order 4"
'carpets
Call carpet(5, 20, 243, 0)
Call carpet(253, 20, 243, 1)
Call carpet(5, 293, 243, 2)
Call carpet(253, 293, 243, 3)
Sleep
System
Sub carpet (x As Integer, y As Integer, size As Integer, order As Integer)
Dim As Integer ix, iy, isize, iorder, side, newX, newY
ix = x: iy = y: isize = size: iorder = order
Line (ix, iy)-(ix + isize - 1, iy + isize - 1), 1, BF
side = Int(isize / 3)
newX = ix + side
newY = iy + side
Line (newX, newY)-(newX + side - 1, newY + side - 1), 15, BF
iorder = iorder - 1
If iorder >= 0 Then
Call carpet(newX - side, newY - side + 1, side, iorder)
Call carpet(newX, newY - side + 1, side, iorder)
Call carpet(newX + side, newY - side + 1, side, iorder)
Call carpet(newX + side, newY, side, iorder)
Call carpet(newX + side, newY + side, side, iorder)
Call carpet(newX, newY + side, side, iorder)
Call carpet(newX - side, newY + side, side, iorder)
Call carpet(newX - side, newY, side, iorder)
End If
End SubQuite BASIC
In Quite BASIC, the point on the lower left on the canvas is 0, 0.
10 REM Sierpinski carpet
20 CLS
30 LET R = 3
40 LET S = 1
50 FOR P = 1 TO R
60 LET S = 3 * S
70 NEXT P
80 REM Now S (size) is 3 to the power of R (order)
90 FOR I = 0 TO S - 1
100 FOR J = 0 TO S - 1
110 LET X = J
120 LET Y = I
130 GOSUB 300
140 IF C = 1 THEN PLOT J, I, "white"
150 NEXT J
160 NEXT I
170 END
300 REM Subroutine -- Is (X,Y) in the carpet?
310 REM Returns C = 0 (no) or C = 1 (yes).
320 LET C = 0
330 IF X % 3 = 1 AND Y % 3 = 1 THEN RETURN
340 LET X = FLOOR(X / 3)
350 LET Y = FLOOR(Y / 3)
360 IF X > 0 OR Y > 0 THEN GOTO 330
370 LET C = 1
380 RETURN
Sinclair ZX81 BASIC
Works with the unexpanded (1k RAM) ZX81. A screenshot of the output is here.
10 LET O=3
20 LET S=3**O
30 FOR I=0 TO S-1
40 FOR J=0 TO S-1
50 LET X=J
60 LET Y=I
70 GOSUB 120
80 IF C THEN PLOT J,I
90 NEXT J
100 NEXT I
110 GOTO 190
120 LET C=0
130 IF X-INT (X/3)*3=1 AND Y-INT (Y/3)*3=1 THEN RETURN
140 LET X=INT (X/3)
150 LET Y=INT (Y/3)
160 IF X>0 OR Y>0 THEN GOTO 130
170 LET C=1
180 RETURN
Tiny BASIC
In some systems the screen scrolls for an order greater than 2.
10 REM SIERPINSKI CARPET
20 REM R - ORDER; S - SIZE.
30 LET R=3
40 LET S=1
50 LET P=1
60 IF P>R THEN GOTO 100
70 LET S=3*S
80 LET P=P+1
90 GOTO 60
100 REM NOW S IS 3 TO THE POWER OF R
110 LET I=0
120 LET J=0
130 LET X=J
140 LET Y=I
150 GOSUB 500
160 IF C=1 THEN GOTO 190
170 PRINT " ";
180 GOTO 200
190 PRINT "*";
200 LET J=J+1
210 IF J=S THEN GOTO 230
220 GOTO 130
230 PRINT
240 LET I=I+1
250 IF I=S THEN GOTO 270
260 GOTO 120
270 END
490 REM IS (X,Y) IN THE CARPET? RETURNS C = 0 (NO) OR C = 1 (YES).
500 LET C=0
510 W=X/3
520 Z=Y/3
530 IF X-W*3=1 IF Y-Z*3=1 THEN RETURN
540 LET X=W
550 LET Y=Z
560 IF X>0 THEN GOTO 510
570 IF Y>0 THEN GOTO 510
580 LET C=1
590 RETURN
- Output:
*************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * *************************** ********* ********* * ** ** * * ** ** * ********* ********* *** *** *** *** * * * * * * * * *** *** *** *** ********* ********* * ** ** * * ** ** * ********* ********* *************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * ***************************
uBasic/4tH
Input "Carpet order: ";n
l = (3^n) - 1
For i = 0 To l
For j = 0 To l
Push i,j
Gosub 100
If Pop() Then
Print "#";
Else
Print " ";
EndIf
Next
Print
Next
End
100 y = Pop(): x = Pop() : Push 1
Do While (x > 0) * (y > 0)
If (x % 3 = 1) * (y % 3 = 1) Then
Push (Pop() - 1)
Break
EndIf
y = y / 3
x = x / 3
Loop
Return
VBA
Const Order = 4
Function InCarpet(ByVal x As Integer, ByVal y As Integer)
Do While x <> 0 And y <> 0
If x Mod 3 = 1 And y Mod 3 = 1 Then
InCarpet = " "
Exit Function
End If
x = x \ 3
y = y \ 3
Loop
InCarpet = "#"
End Function
Public Sub sierpinski_carpet()
Dim i As Integer, j As Integer
For i = 0 To 3 ^ Order - 1
For j = 0 To 3 ^ Order - 1
Debug.Print InCarpet(i, j);
Next j
Debug.Print
Next i
End Sub
- Output:
################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ### ### ### ###### ### ### ###### ### ### ### # # # # # # # ## # # # # # # ## # # # # # # # ### ### ### ###### ### ### ###### ### ### ### ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ### ###### ###### ### ### ###### ###### ### # # # ## # # ## # # # # # # ## # # ## # # # ### ###### ###### ### ### ###### ###### ### ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ######### ######### ######### ######### # ## ## # # ## ## # # ## ## # # ## ## # ######### ######### ######### ######### ### ### ### ### ### ### ### ### # # # # # # # # # # # # # # # # ### ### ### ### ### ### ### ### ######### ######### ######### ######### # ## ## # # ## ## # # ## ## # # ## ## # ######### ######### ######### ######### ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ### ###### ###### ### ### ###### ###### ### # # # ## # # ## # # # # # # ## # # ## # # # ### ###### ###### ### ### ###### ###### ### ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ### ### ### ###### ### ### ###### ### ### ### # # # # # # # ## # # # # # # ## # # # # # # # ### ### ### ###### ### ### ###### ### ### ### ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # #################################################################################
VBScript
Function InCarpet(i,j)
If i > 0 And j > 0 Then
Do While i > 0 And j > 0
If i Mod 3 = 1 And j Mod 3 = 1 Then
InCarpet = " "
Exit Do
Else
InCarpet = "#"
End If
i = Int(i / 3)
j = Int(j / 3)
Loop
Else
InCarpet = "#"
End If
End Function
Function Carpet(n)
k = 3^n - 1
x2 = 0
y2 = 0
For y = 0 To k
For x = 0 To k
x2 = x
y2 = y
WScript.StdOut.Write InCarpet(x2,y2)
Next
WScript.StdOut.WriteBlankLines(1)
Next
End Function
Carpet(WScript.Arguments(0))
- Output:
F:\VBScript>cscript /nologo RosettaCode-Sierpinski_Carpet.vbs 3 ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
Yabasic
sub sp$(n)
local i, s$
for i = 1 to n
s$ = s$ + " "
next i
return s$
end sub
sub replace$(s$, cf$, cr$)
local i, p
do
i = instr(s$, cf$, p)
if not i break
mid$(s$, i, 1) = cr$
p = i
loop
return s$
end sub
sub foreach$(carpet$, p$, m)
local n, i, t$(1)
n = token(carpet$, t$(), ",")
for i = 1 to n
switch(m)
case 0: p$ = p$ + "," + t$(i) + t$(i) + t$(i) : break
case 1: p$ = p$ + "," + t$(i) + sp$(len(t$(i))) + t$(i) : break
default: error "Method not found!" : break
end switch
next i
return p$
end sub
sub sierpinskiCarpet$(n)
local carpet$, next$, i
carpet$ = "@"
for i = 1 to n
next$ = foreach$(carpet$, "")
next$ = foreach$(carpet$, next$, 1)
carpet$ = foreach$(carpet$, next$)
next i
return carpet$
end sub
print replace$(sierpinskiCarpet$(3), ",", "\n")Befunge
The order, N, is specified by the first number on the stack. The upper limit is implementation dependent and is determined by the interpreter's cell size.
311>*#3\>#-:#1_$:00p00g-#@_010p0>:20p10g30v
>p>40p"#"30g40g*!#v_$48*30g3%1-v^ >$55+,1v>
0 ^p03/3g03/3g04$_v#!*!-1%3g04!<^_^#- g00 <
^3g01p02:0p01_@#-g>#0,#02#:0#+g#11#g+#0:#<^
BQN
_decode is a base conversion idiom from BQNcrate.
Carpet1 works based on the following condition:
Consider a coordinate grid in base 3. The holes in the carpet occur where
1) a trit in the x-coordinate is 1, and
2) the trit in the same position in the y-coordinate is also 1.
_decode ← {⌽𝕗|⌊∘÷⟜𝕗⍟(↕1+·⌊𝕗⋆⁼1⌈⊢)}
Carpet ← { # 2D Array method using ∾.
{∾(3‿3⥊4≠↕9)⊏⟨(≢𝕩)⥊0,𝕩⟩}⍟(𝕩-1) 1‿1⥊1
}
Carpet1 ← { # base conversion method, works in a single step.
¬{∨´𝕨∧○((-𝕨⌈○≠𝕩)⊸↑)𝕩}⌜˜2|3 _decode¨↕3⋆𝕩-1
}
•Show " #"⊏˜Carpet 4
•Show (Carpet ≡ Carpet1) 4
┌─
╵"###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
######### #########
# ## ## # # ## ## #
######### #########
### ### ### ###
# # # # # # # #
### ### ### ###
######### #########
# ## ## # # ## ## #
######### #########
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################"
┘
1
Brainf***
Double the first two prints for squarer output.
input order and print the associated Sierpinski carpet
orders over 5 require larger cell sizes
+++>>+[[-]>[-],[+[-----------[>[-]++++++[<------>-]<--<<[->>++++++++++<<]>>[-<<+
>>]<+>]]]<]<<[>>+<<-]+>[>>[-]>[-]<<<<[>>>>+<<<<-]>>>>[<<[<<+>>>+<-]>[<+>-]>-]<<<
-]>[-]<<[>+>+<<-]>>[<<+>>-]<[<[>>+>+<<<-]>>>[<<<+>>>-]<[<[>>+>>>+<<<<<-]>>[<<+>>
-]<[>>+>>>+<<<<<-]>>[<<+>>-]>>->-<<<<+[[>+>+<<-]>[<+>-]>[>[>>+>+<<<-]>>>[<<<+>>>
-]+++<[->-[>+>>]>[+[-<+>]>+>>]<<<<<]>[-]>>[-]<->+<[>-]>[<<<+>>>->]<<[-]<<<[>>+>+
<<<-]>>>[<<<+>>>-]+++<[->-[>+>>]>[+[-<+>]>+>>]<<<<<]>[-]>>[-]<->+<[>-]>[<<<+>>>-
>]<<[-]<<<[>[>+<-]<-]>[-]>[<<+>>-]<<[>>++++[<++++++++>-]<.[-]<<[-]<[-]<<<->>>>>-
]<<<-]<<[>+>+<<-]>[<+>-]>[>[>>+<<-]>>>+++<[->-[>+>>]>[+[-<+>]>+>>]<<<<<]>[-]>[-]
>[<<<<<+>>>>>-]<<<+++<[->-[>+>>]>[+[-<+>]>+>>]<<<<<]>[-]>[-]>[<<<+>>>-]<<<<[>>+>
+<<<-]>>>[<<<+>>>-]<<[>>+>+<<<-]>>>[<<<+>>>-]<<[>[>+<-]<-]>[-]+>[[-]<->]<[->+<]>
[<<+>>-]<<[>>+++++[<+++++++>-]<.[-]<<[-]<[-]<<<->>>>>-]<<<-]<<]<-]++++++++++.[-]
<-]- Output:
########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
C
If you write coordinates of any point on the carpet in base 3, the pixel is blank if and only if any matching pair of digits are (1, 1).
#include <stdio.h>
int main()
{
int i, j, dim, d;
int depth = 3;
for (i = 0, dim = 1; i < depth; i++, dim *= 3);
for (i = 0; i < dim; i++) {
for (j = 0; j < dim; j++) {
for (d = dim / 3; d; d /= 3)
if ((i % (d * 3)) / d == 1 && (j % (d * 3)) / d == 1)
break;
printf(d ? " " : "##");
}
printf("\n");
}
return 0;
}
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
typedef struct sCarpet {
int dim; // dimension
char *data; // character data
char **rows; // pointers to data rows
} *Carpet;
/* Clones a tile into larger carpet, or blank if center */
void TileCarpet( Carpet d, int r, int c, Carpet tile )
{
int y0 = tile->dim*r;
int x0 = tile->dim*c;
int k,m;
if ((r==1) && (c==1)) {
for(k=0; k < tile->dim; k++) {
for (m=0; m < tile->dim; m++) {
d->rows[y0+k][x0+m] = ' ';
}
}
}
else {
for(k=0; k < tile->dim; k++) {
for (m=0; m < tile->dim; m++) {
d->rows[y0+k][x0+m] = tile->rows[k][m];
}
}
}
}
/* define a 1x1 starting carpet */
static char s1[]= "#";
static char *r1[] = {s1};
static struct sCarpet single = { 1, s1, r1};
Carpet Sierpinski( int n )
{
Carpet carpet;
Carpet subCarpet;
int row,col, rb;
int spc_rqrd;
subCarpet = (n > 1) ? Sierpinski(n-1) : &single;
carpet = malloc(sizeof(struct sCarpet));
carpet->dim = 3*subCarpet->dim;
spc_rqrd = (2*subCarpet->dim) * (carpet->dim);
carpet->data = malloc(spc_rqrd*sizeof(char));
carpet->rows = malloc( carpet->dim*sizeof(char *));
for (row=0; row<subCarpet->dim; row++) {
carpet->rows[row] = carpet->data + row*carpet->dim;
rb = row+subCarpet->dim;
carpet->rows[rb] = carpet->data + rb*carpet->dim;
rb = row+2*subCarpet->dim;
carpet->rows[rb] = carpet->data + row*carpet->dim;
}
for (col=0; col < 3; col++) {
/* 2 rows of tiles to copy - third group points to same data a first */
for (row=0; row < 2; row++)
TileCarpet( carpet, row, col, subCarpet );
}
if (subCarpet != &single ) {
free(subCarpet->rows);
free(subCarpet->data);
free(subCarpet);
}
return carpet;
}
void CarpetPrint( FILE *fout, Carpet carp)
{
char obuf[730];
int row;
for (row=0; row < carp->dim; row++) {
strncpy(obuf, carp->rows[row], carp->dim);
fprintf(fout, "%s\n", obuf);
}
fprintf(fout,"\n");
}
int main(int argc, char *argv[])
{
// FILE *f = fopen("sierp.txt","w");
CarpetPrint(stdout, Sierpinski(3));
// fclose(f);
return 0;
}
Recursive version:
#include <stdio.h>
#include <stdlib.h>
typedef struct _PartialGrid{
char** base;
int xbegin, xend, ybegin, yend; // yend strictly not used
} PartialGrid;
void sierpinski_hollow(PartialGrid G){
int len = G.xend - G.xbegin+1;
int unit = len/3;
for(int i = G.xbegin+unit; i <G.xbegin+2*unit;i++){
for(int j = G.ybegin+unit; j <G.ybegin+2*unit;j++){
G.base[j][i] = ' ';
}}
}
void sierpinski(PartialGrid G, int iterations){
if(iterations==0)
return;
if((iterations)==1){
sierpinski_hollow(G);
sierpinski(G,0);
}
sierpinski_hollow(G);
for(int i=0;i<3;i++){
for(int j=0;j<3;j++){
int length = G.xend-G.xbegin+1;
int unit = length/3;
PartialGrid q = {G.base, G.xbegin + i*unit, G.xbegin+(i+1)*unit-1,
G.ybegin+j*unit, G.ybegin+(j+1)*unit-1};
sierpinski(q, iterations-1);
}
}
}
int intpow(int base, int expo){
if(expo==0){
return 1;
}
return base*intpow(base,expo-1);
}
int allocate_grid(char*** g, int n, const char sep){
int size = intpow(3,n+1);
*g = (char**)calloc(size, sizeof(char*));
if(*g==NULL)
return -1;
for(int i = 0; i < size; ++i){
(*g)[i] = (char*)calloc(size, sizeof(char));
if((*g)[i] == NULL)
return -1;
for(int j = 0; j < size; j++){
(*g)[i][j] = sep;
}
}
return size;
}
void print_grid(char** b, int size){
for(int i = 0; i < size; i++){
printf("%s\n",b[i]);
}
}
int main(){
int n = 3;
char** basegrid;
int size = allocate_grid(&basegrid, n, '#');
if(size == -1)
return 1; //bad alloc
PartialGrid b = {basegrid, 0, size-1, 0, size-1};
sierpinski(b, n);
print_grid(basegrid, size);
free(basegrid);
return 0;
}
C#
using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
static List<string> NextCarpet(List<string> carpet)
{
return carpet.Select(x => x + x + x)
.Concat(carpet.Select(x => x + x.Replace('#', ' ') + x))
.Concat(carpet.Select(x => x + x + x)).ToList();
}
static List<string> SierpinskiCarpet(int n)
{
return Enumerable.Range(1, n).Aggregate(new List<string> { "#" }, (carpet, _) => NextCarpet(carpet));
}
static void Main(string[] args)
{
foreach (string s in SierpinskiCarpet(3))
Console.WriteLine(s);
}
}
C++
Performance focused variant (about 7x faster than the div/mod solutions at AMD Ryzen 7 4800H)
// contributed to rosettacode.org by Peter Helcmanovsky
// BCT = Binary-Coded Ternary: pairs of bits form one digit [0,1,2] (0b11 is invalid digit)
#include <cstdint>
#include <cstdlib>
#include <cstdio>
static constexpr int32_t bct_low_bits = 0x55555555;
static int32_t bct_decrement(int32_t v) {
--v; // either valid BCT (v-1), or block of bottom 0b00 digits becomes invalid 0b11
return v ^ (v & (v>>1) & bct_low_bits); // fix all 0b11 to 0b10 (digit "2")
}
int main (int argc, char *argv[])
{
// parse N from first argument, if no argument, use 3 as default value
const int32_t n = (1 < argc) ? std::atoi(argv[1]) : 3;
// check for valid N (0..9) - 16 requires 33 bits for BCT form 1<<(n*2) => hard limit
if (n < 0 || 9 < n) { // but N=9 already produces 370MB output
std::printf("N out of range (use 0..9): %ld\n", long(n));
return 1;
}
const int32_t size_bct = 1<<(n*2); // 3**n in BCT form (initial value for loops)
// draw the carpet, two nested loops counting down in BCT form of values
int32_t y = size_bct;
do { // all lines loop
y = bct_decrement(y); // --Y (in BCT)
int32_t x = size_bct;
do { // line loop
x = bct_decrement(x); // --X (in BCT)
// check if x has ternary digit "1" at same position(s) as y -> output space (hole)
std::putchar((x & y & bct_low_bits) ? ' ' : '#');
} while (0 < x);
std::putchar('\n');
} while (0 < y);
return 0;
}
#include <windows.h>
#include <math.h>
//--------------------------------------------------------------------------------------------------
const int BMP_SIZE = 738;
//--------------------------------------------------------------------------------------------------
class Sierpinski
{
public:
void draw( HDC wdc, int wid, int hei, int ord )
{
_wdc = wdc;
_ord = wid / static_cast<int>( pow( 3.0, ord ) );
drawIt( 0, 0, wid, hei );
}
void setHWND( HWND hwnd ) { _hwnd = hwnd; }
private:
void drawIt( int x, int y, int wid, int hei )
{
if( wid < _ord || hei < _ord ) return;
int w = wid / 3, h = hei / 3;
RECT rc;
SetRect( &rc, x + w, y + h, x + w + w, y + h + h );
FillRect( _wdc, &rc, static_cast<HBRUSH>( GetStockObject( BLACK_BRUSH ) ) );
for( int a = 0; a < 3; a++ )
for( int b = 0; b < 3; b++ )
{
if( a == 1 && b == 1 ) continue;
drawIt( x + b * w, y + a * h, w, h );
}
}
HWND _hwnd;
HDC _wdc;
int _ord;
};
//--------------------------------------------------------------------------------------------------
class wnd
{
public:
wnd() { _inst = this; }
int wnd::Run( HINSTANCE hInst )
{
_hInst = hInst;
_hwnd = InitAll();
_carpet.setHWND( _hwnd );
ShowWindow( _hwnd, SW_SHOW );
UpdateWindow( _hwnd );
MSG msg;
ZeroMemory( &msg, sizeof( msg ) );
while( msg.message != WM_QUIT )
{
if( PeekMessage( &msg, NULL, 0, 0, PM_REMOVE ) != 0 )
{
TranslateMessage( &msg );
DispatchMessage( &msg );
}
}
return UnregisterClass( "_SIERPINSKI_", _hInst );
}
private:
void wnd::doPaint( HDC dc ) { _carpet.draw( dc, BMP_SIZE, BMP_SIZE, 5 ); }
static int WINAPI wnd::WndProc( HWND hWnd, UINT msg, WPARAM wParam, LPARAM lParam )
{
switch( msg )
{
case WM_DESTROY: PostQuitMessage( 0 ); break;
case WM_PAINT:
{
PAINTSTRUCT ps;
HDC dc = BeginPaint( hWnd, &ps );
_inst->doPaint( dc );
EndPaint( hWnd, &ps );
}
default:
return DefWindowProc( hWnd, msg, wParam, lParam );
}
return 0;
}
HWND InitAll()
{
WNDCLASSEX wcex;
ZeroMemory( &wcex, sizeof( wcex ) );
wcex.cbSize = sizeof( WNDCLASSEX );
wcex.style = CS_HREDRAW | CS_VREDRAW;
wcex.lpfnWndProc = ( WNDPROC )WndProc;
wcex.hInstance = _hInst;
wcex.hCursor = LoadCursor( NULL, IDC_ARROW );
wcex.hbrBackground = ( HBRUSH )( COLOR_WINDOW + 1 );
wcex.lpszClassName = "_SIERPINSKI_";
RegisterClassEx( &wcex );
RECT rc = { 0, 0, BMP_SIZE, BMP_SIZE };
AdjustWindowRect( &rc, WS_SYSMENU | WS_CAPTION, FALSE );
int w = rc.right - rc.left,
h = rc.bottom - rc.top;
return CreateWindow( "_SIERPINSKI_", ".: Sierpinski carpet -- PJorente :.", WS_SYSMENU, CW_USEDEFAULT, 0, w, h, NULL, NULL, _hInst, NULL );
}
static wnd* _inst;
HINSTANCE _hInst;
HWND _hwnd;
Sierpinski _carpet;
};
wnd* wnd::_inst = 0;
//--------------------------------------------------------------------------------------------------
int APIENTRY _tWinMain( HINSTANCE hInstance, HINSTANCE hPrevInstance, LPTSTR lpCmdLine, int nCmdShow )
{
wnd myWnd;
return myWnd.Run( hInstance );
}
//--------------------------------------------------------------------------------------------------
Clojure
(ns example
(:require [clojure.contrib.math :as math]))
(defn in-carpet? [x y]
(loop [x x, y y]
(cond
(or (zero? x) (zero? y)) true
(and (= 1 (mod x 3)) (= 1 (mod y 3))) false
:else (recur (quot x 3) (quot y 3)))))
(defn carpet [n]
(apply str
(interpose
\newline
(for [x (range (math/expt 3 n))]
(apply str
(for [y (range (math/expt 3 n))]
(if (in-carpet? x y) "*" " ")))))))
(println (carpet 3))
Common Lisp
This solution works by printing a square of # except where both of the coordinates of a cell contain a 1 in the same digit position in base 3. For example, the central empty square has a 1 in the highest base-3 digit of all its cells, and the smallest empty squares have 1s in the lowest base-3 digit.
(defun print-carpet (order)
(let ((size (expt 3 order)))
(flet ((trinary (x) (format nil "~3,vR" order x))
(ones (a b) (and (eql a #\1) (eql b #\1))))
(loop for i below size do
(fresh-line)
(loop for j below size do
(princ (if (some #'ones (trinary i) (trinary j))
" "
"#")))))))
Crystal
def sierpinski_carpet(n)
carpet = ["#"]
n.times do
carpet = carpet.map { |x| x + x + x } +
carpet.map { |x| x + x.tr("#"," ") + x } +
carpet.map { |x| x + x + x }
end
carpet
end
5.times{ |i| puts "\nN=#{i}"; sierpinski_carpet(i).each { |row| puts row } }
- Output:
N=0 # N=1 ### # # ### N=2 ######### # ## ## # ######### ### ### # # # # ### ### ######### # ## ## # ######### N=3 ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### N=4 ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ### ### ### ###### ### ### ###### ### ### ### # # # # # # # ## # # # # # # ## # # # # # # # ### ### ### ###### ### ### ###### ### ### ### ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ### ###### ###### ### ### ###### ###### ### # # # ## # # ## # # # # # # ## # # ## # # # ### ###### ###### ### ### ###### ###### ### ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ######### ######### ######### ######### # ## ## # # ## ## # # ## ## # # ## ## # ######### ######### ######### ######### ### ### ### ### ### ### ### ### # # # # # # # # # # # # # # # # ### ### ### ### ### ### ### ### ######### ######### ######### ######### # ## ## # # ## ## # # ## ## # # ## ## # ######### ######### ######### ######### ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ### ###### ###### ### ### ###### ###### ### # # # ## # # ## # # # # # # ## # # ## # # # ### ###### ###### ### ### ###### ###### ### ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ### ### ### ###### ### ### ###### ### ### ### # # # # # # # ## # # # # # # ## # # # # # # # ### ### ### ###### ### ### ###### ### ### ### ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # #################################################################################
D
import std.stdio, std.string, std.algorithm, std.array;
auto sierpinskiCarpet(in int n) pure nothrow @safe {
auto r = ["#"];
foreach (immutable _; 0 .. n) {
const p = r.map!q{a ~ a ~ a}.array;
r = p ~ r.map!q{a ~ a.replace("#", " ") ~ a}.array ~ p;
}
return r.join('\n');
}
void main() {
3.sierpinskiCarpet.writeln;
}
More functional style:
import std.stdio, std.algorithm, std.range, std.functional;
auto nextCarpet(in string[] c) pure nothrow {
/*immutable*/ const b = c.map!q{a ~ a ~ a}.array;
return b ~ c.map!q{a ~ a.replace("#", " ") ~ a}.array ~ b;
}
void main() {
["#"]
.recurrence!((a, n) => a[n - 1].nextCarpet)
.dropExactly(3)
.front
.binaryReverseArgs!writefln("%-(%s\n%)");
}
A more direct and efficient version:
import std.stdio, std.array;
char[][] sierpinskiCarpet(in size_t n) pure nothrow @safe {
auto mat = uninitializedArray!(typeof(return))(3 ^^ n, 3 ^^ n);
foreach (immutable r, row; mat) {
row[] = '#';
foreach (immutable c, ref cell; row) {
size_t r2 = r, c2 = c;
while (r2 && c2) {
if (r2 % 3 == 1 && c2 % 3 == 1) {
cell = ' ';
break;
}
r2 /= 3;
c2 /= 3;
}
}
}
return mat;
}
void main() {
writefln("%-(%s\n%)", 3.sierpinskiCarpet);
7.sierpinskiCarpet.length.writeln;
}
Delphi
See Pascal.
DWScript
function InCarpet(x, y : Integer) : Boolean;
begin
while (x<>0) and (y<>0) do begin
if ((x mod 3)=1) and ((y mod 3)=1) then
Exit(False);
x := x div 3;
y := y div 3;
end;
Result := True;
end;
procedure Carpet(n : Integer);
var
i, j, p : Integer;
begin
p := Round(IntPower(3, n));
for i:=0 to p-1 do begin
for j:=0 to p-1 do begin
if InCarpet(i, j) then
Print('#')
else Print(' ');
end;
PrintLn('');
end;
end;
Carpet(3);
E
def inCarpet(var x, var y) {
while (x > 0 && y > 0) {
if (x %% 3 <=> 1 && y %% 3 <=> 1) {
return false
}
x //= 3
y //= 3
}
return true
}
def carpet(order) {
for y in 0..!(3**order) {
for x in 0..!(3**order) {
print(inCarpet(x, y).pick("#", " "))
}
println()
}
}EasyLang
proc carp x y sz . .
move x - sz / 2 y - sz / 2
rect sz sz
if sz > 0.5
h = sz / 3
carp x - sz y - sz h
carp x - sz y h
carp x - sz y + sz h
carp x + sz y - sz h
carp x + sz y h
carp x + sz y + sz h
carp x y - sz h
carp x y + sz h
.
.
background 000
clear
color 633
carp 50 50 100 / 3
Elixir
defmodule RC do
def sierpinski_carpet(n), do: sierpinski_carpet(n, ["#"])
def sierpinski_carpet(0, carpet), do: carpet
def sierpinski_carpet(n, carpet) do
new_carpet = Enum.map(carpet, fn x -> x <> x <> x end) ++
Enum.map(carpet, fn x -> x <> String.replace(x, "#", " ") <> x end) ++
Enum.map(carpet, fn x -> x <> x <> x end)
sierpinski_carpet(n-1, new_carpet)
end
end
Enum.each(0..3, fn n ->
IO.puts "\nN=#{n}"
Enum.each(RC.sierpinski_carpet(n), fn line -> IO.puts line end)
end)
- Output:
N=0 # N=1 ### # # ### N=2 ######### # ## ## # ######### ### ### # # # # ### ### ######### # ## ## # ######### N=3 ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
Erlang
% Implemented by Arjun Sunel
-module(carpet).
-export([main/0]).
main() ->
sierpinski_carpet(3).
sierpinski_carpet(N) ->
lists: foreach(fun(X) -> lists: foreach(fun(Y) -> carpet(X,Y) end,lists:seq(0,trunc(math:pow(3,N))-1)), io:format("\n") end, lists:seq(0,trunc(math:pow(3,N))-1)).
carpet(X,Y) ->
if
X=:=0 ; Y=:=0 ->
io:format("*");
(X rem 3)=:=1, (Y rem 3) =:=1 ->
io:format(" ");
true ->
carpet(X div 3, Y div 3)
end.
- Output:
*************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * *************************** ********* ********* * ** ** * * ** ** * ********* ********* *** *** *** *** * * * * * * * * *** *** *** *** ********* ********* * ** ** * * ** ** * ********* ********* *************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * *************************** ok
ERRE
PROGRAM SIERP_CARPET
! for rosettacode.org
!$INTEGER
BEGIN
OPEN("O",1,"OUT.PRN")
PRINT(CHR$(12);) !CLS
DEPTH=3
DIMM=1
FOR I=0 TO DEPTH-1 DO
DIMM=DIMM*3
END FOR
FOR I=0 TO DIMM-1 DO
FOR J=0 TO DIMM-1 DO
D=DIMM DIV 3
REPEAT
EXIT IF ((I MOD (D*3)) DIV D=1 AND (J MOD (D*3)) DIV D=1)
D=D DIV 3
UNTIL NOT(D>0)
IF D>0 THEN PRINT(#1," ";) ELSE PRINT(#1,"##";) END IF
END FOR
PRINT(#1,)
END FOR
! PRINT(#1,CHR$(12);) for printer only!
CLOSE(1)
END PROGRAMOutput is redirected to file OUT.PRN: you can change this to SCRN: to screen or "LPTx:" for a parallel printer. Output taken from OUT.PRN file:
- Output:
###################################################### ## #### #### #### #### #### #### #### #### ## ###################################################### ###### ############ ############ ###### ## ## ## #### ## ## #### ## ## ## ###### ############ ############ ###### ###################################################### ## #### #### #### #### #### #### #### #### ## ###################################################### ################## ################## ## #### #### ## ## #### #### ## ################## ################## ###### ###### ###### ###### ## ## ## ## ## ## ## ## ###### ###### ###### ###### ################## ################## ## #### #### ## ## #### #### ## ################## ################## ###################################################### ## #### #### #### #### #### #### #### #### ## ###################################################### ###### ############ ############ ###### ## ## ## #### ## ## #### ## ## ## ###### ############ ############ ###### ###################################################### ## #### #### #### #### #### #### #### #### ## ######################################################
Euphoria
include std/math.e
integer order = 4
function InCarpet(atom x, atom y)
while 1 do
if x = 0 or y = 0 then
return 1
elsif floor(mod(x,3)) = 1 and floor(mod(y,3)) = 1 then
return 0
end if
x /= 3
y /= 3
end while
end function
for i = 0 to power(3,order)-1 do
for j = 0 to power(3,order)-1 do
if InCarpet(i,j) = 1 then
puts(1,"#")
else
puts(1," ")
end if
end for
puts(1,'\n')
end forExcel
LAMBDA
Binding the names SIERPCARPET, SIERPWEAVE, and SHOWBLOCKS to the following lambda expressions in the Name Manager of the Excel WorkBook:
(See LAMBDA: The ultimate Excel worksheet function)
SHOWBLOCKS
=LAMBDA(xs,
IF(0 <> xs, "█", " ")
)
SIERPCARPET
=LAMBDA(n,
APPLYN(n)(
SIERPWEAVE
)(1)
)
SIERPWEAVE
=LAMBDA(xs,
LET(
triple, REPLICATECOLS(3)(xs),
gap, LAMBDA(x, IF(x, 0, 0))(xs),
middle, APPENDCOLS(
APPENDCOLS(xs)(gap)
)(xs),
APPENDROWS(
APPENDROWS(triple)(middle)
)(triple)
)
)
and also assuming the following generic bindings in the Name Manager for the WorkBook:
APPENDCOLS
=LAMBDA(xs,
LAMBDA(ys,
LET(
nx, COLUMNS(xs),
ny, COLUMNS(ys),
colIndexes, SEQUENCE(1, nx + ny),
rowIndexes, SEQUENCE(MAX(ROWS(xs), ROWS(ys))),
IFERROR(
IF(nx < colIndexes,
INDEX(ys, rowIndexes, colIndexes - nx),
INDEX(xs, rowIndexes, colIndexes)
),
NA()
)
)
)
)
APPENDROWS
=LAMBDA(xs,
LAMBDA(ys,
LET(
nx, ROWS(xs),
rowIndexes, SEQUENCE(nx + ROWS(ys)),
colIndexes, SEQUENCE(
1,
MAX(COLUMNS(xs), COLUMNS(ys))
),
IFERROR(
IF(rowIndexes <= nx,
INDEX(xs, rowIndexes, colIndexes),
INDEX(ys, rowIndexes - nx, colIndexes)
),
NA()
)
)
)
)
APPLYN
=LAMBDA(n,
LAMBDA(f,
LAMBDA(x,
IF(0 < n,
APPLYN(n - 1)(f)(
f(x)
),
x
)
)
)
)
REPLICATECOLS
=LAMBDA(n,
LAMBDA(xs,
LET(
nCols, COLUMNS(xs),
h, n * nCols,
ixs, SEQUENCE(ROWS(xs), h, 0, 1),
INDEX(
xs,
1 + QUOTIENT(ixs, h),
1 + MOD(ixs, nCols)
)
)
)
)
- Output:
| fx | =SHOWBLOCKS(SIERPCARPET(A2)) | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | H | I | J | K | ||
| 1 | Level | Sierpinski carpet | ||||||||||
| 2 | 0 | █ | ||||||||||
| 3 | ||||||||||||
| 4 | 1 | █ | █ | █ | ||||||||
| 5 | █ | █ | ||||||||||
| 6 | █ | █ | █ | |||||||||
| 7 | ||||||||||||
| 8 | 2 | █ | █ | █ | █ | █ | █ | █ | █ | █ | ||
| 9 | █ | █ | █ | █ | █ | █ | ||||||
| 10 | █ | █ | █ | █ | █ | █ | █ | █ | █ | |||
| 11 | █ | █ | █ | █ | █ | █ | ||||||
| 12 | █ | █ | █ | █ | ||||||||
| 13 | █ | █ | █ | █ | █ | █ | ||||||
| 14 | █ | █ | █ | █ | █ | █ | █ | █ | █ | |||
| 15 | █ | █ | █ | █ | █ | █ | ||||||
| 16 | █ | █ | █ | █ | █ | █ | █ | █ | █ | |||
| 17 | ||||||||||||
F#
open System
let blank x = new String(' ', String.length x)
let nextCarpet carpet =
List.map (fun x -> x + x + x) carpet @
List.map (fun x -> x + (blank x) + x) carpet @
List.map (fun x -> x + x + x) carpet
let rec sierpinskiCarpet n =
let rec aux n carpet =
if n = 0 then carpet
else aux (n-1) (nextCarpet carpet)
aux n ["#"]
List.iter (printfn "%s") (sierpinskiCarpet 3)
Factor
The order n sierpinski carpet is the Kronecker product of order n-1 and order 1.
USING: kernel math math.matrices prettyprint ;
: sierpinski ( n -- )
1 - { { 1 1 1 } { 1 0 1 } { 1 1 1 } } swap over [ kron ]
curry times [ 1 = "#" " " ? ] matrix-map simple-table. ;
3 sierpinski
Fan
**
** Generates a square Sierpinski gasket
**
class SierpinskiCarpet
{
public static Bool inCarpet(Int x, Int y){
while(x!=0 && y!=0){
if (x % 3 == 1 && y % 3 == 1)
return false;
x /= 3;
y /= 3;
}
return true;
}
static Int pow(Int n, Int exp)
{
rslt := 1
exp.times { rslt *= n }
return rslt
}
public static Void carpet(Int n){
for(i := 0; i < pow(3, n); i++){
buf := StrBuf()
for(j := 0; j < pow(3, n); j++){
if( inCarpet(i, j))
buf.add("*");
else
buf.add(" ");
}
echo(buf);
}
}
Void main()
{
carpet(4)
}
}
Fennel
(fn in-carpet? [x y]
(if
(or (= 0 x) (= 0 y)) true
(and (= 1 (% x 3)) (= 1 (% y 3))) false
(in-carpet? (// x 3) (// y 3))))
(fn make-carpet [size]
(for [y 0 (- (^ 3 size) 1)]
(for [x 0 (- (^ 3 size) 1)]
(if (in-carpet? x y)
(io.write "#")
(io.write " ")))
(io.write "\n")))
(for [i 0 3]
(make-carpet i)
(print))
Forth
\ Generates a square Sierpinski gasket
: 1? over 3 mod 1 = ; ( n1 n2 -- n1 n2 f)
: 3/ 3 / swap ; ( n1 n2 -- n2/3 n1)
\ is this cell in the carpet?
: incarpet ( n1 n2 -- f)
begin over over or while 1? 1? and if 2drop false exit then 3/ 3/ repeat
2drop true \ return true if in the carpet
;
\ draw a carpet of n size
: carpet ( n --)
1 swap 0 ?do 3 * loop dup \ calculate power of 3
0 ?do dup 0 ?do i j incarpet if [char] # else bl then emit loop cr loop
drop \ evaluate every cell in the carpet
;
cr 4 carpet
Fortran
program Sierpinski_carpet
implicit none
call carpet(4)
contains
function In_carpet(a, b)
logical :: in_carpet
integer, intent(in) :: a, b
integer :: x, y
x = a ; y = b
do
if(x == 0 .or. y == 0) then
In_carpet = .true.
return
else if(mod(x, 3) == 1 .and. mod(y, 3) == 1) then
In_carpet = .false.
return
end if
x = x / 3
y = y / 3
end do
end function
subroutine Carpet(n)
integer, intent(in) :: n
integer :: i, j
do i = 0, 3**n - 1
do j = 0, 3**n - 1
if(In_carpet(i, j)) then
write(*, "(a)", advance="no") "#"
else
write(*, "(a)", advance="no") " "
end if
end do
write(*,*)
end do
end subroutine Carpet
end program Sierpinski_carpet
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
It can be done using an L-system. There are generic functions written in Fōrmulæ to compute an L-system in the page L-system.
The program that creates a Sierpiński carpet is:
Gnuplot
Version #1.
- Note
- Find plotff.gp file-function for load command here on RC Brownian tree page.
- dat-files are PARI/GP generated output files. See this page below.
## SCff.gp 1/14/17 aev
## Plotting Sierpinski carpet fractal.
## dat-files are PARI/GP generated output files:
## http://rosettacode.org/wiki/Sierpinski_carpet#PARI.2FGP
#cd 'C:\gnupData'
##SC5
clr = '"green"'
filename = "SC5gp1"
ttl = "Sierpinski carpet fractal, v.#1"
load "plotff.gp"
- Output:
1. All SCff.gp commands. 2. All plotted png-files: SC5gp1.png (for now)
Plotting a Sierpinski carpet fractal: versions #2 and #3
plotscf.gp and plotscf1.gp file-functions for the load command are the only possible imitation of the fine functions in the gnuplot.
- plotscf.gp
## plotscf.gp 12/7/16 aev
## Plotting a Sierpinski carpet fractal to the png-file.
## Note: assign variables: ord (order), clr (color), filename and ttl (before using load command).
## ord (order) # a.k.a. level - defines size of fractal (also number of dots).
reset
set terminal png font arial 12 size 640,640
ofn=filename.".png"
set output ofn
unset border; unset xtics; unset ytics; unset key;
set title ttl font "Arial:Bold,12"
set xrange [0:1]; set yrange [0:1];
sc(n, x, y, d) = n >= ord ? \
sprintf('set object rect from %f,%f to %f,%f fc rgb @clr fs solid;', x, y, x+d, y+d) : \
sc(n+1, x, y, d/3) . sc(n+1, x+d/3, y, d/3) . \
sc(n+1, x+2*d/3, y, d/3) . sc(n+1, x, y+d/3, d/3) . \
sc(n+1, x+2*d/3, y+d/3, d/3) . sc(n+1, x, y+2*d/3, d/3) . \
sc(n+1, x+d/3, y+2*d/3, d/3) . sc(n+1, x+2*d/3, y+2*d /3, d/3);
eval(sc(0, 0.0, 0.0, 1.0))
plot -100
set output
- plotscf1.gp
## plotscf1.gp 12/7/16 aev
## Plotting a Sierpinski carpet fractal to the png-file.
## Note: assign variables: ord (order, just for title), clr (color), filename and ttl (before using load command).
## In this version order is always 5.
reset
set terminal png font arial 12 size 640,640
ofn=filename.".png"
set output ofn
unset border; unset xtics; unset ytics; unset key;
set title ttl font "Arial:Bold,12"
o=3
sqr(x,y) = abs(x + y) + abs(x - y) - o
f(x) = o*abs(x) - o
c0(x,y) = abs(x + y) + abs(x - y) - 1
c1(x,y) = c0(o*x,f(y)) * c0(f(x),o*y) * c0(f(x),f(y))
c2(x,y) = c1(o*x,f(y)) * c1(f(x),o*y) * c1(f(x),f(y))
c3(x,y) = c2(o*x,f(y)) * c2(f(x),o*y) * c2(f(x),f(y))
c4(x,y) = c3(o*x,f(y)) * c3(f(x),o*y) * c3(f(x),f(y))
sc(x,y) = sqr(x,y)>0 || c0(x,y)*c1(x,y)*c2(x,y)*c3(x,y)*c4(x,y)<0 ? 0:1
set xrange [-1.5:1.5]; set yrange [-1.5:1.5];
set pm3d map;
set palette model RGB defined (0 "white", 1 @clr);
set size ratio -1
smp=640; set samples smp; set isosamples smp;
unset colorbox
splot sc(x,y)
set output
- Plotting v.#2 and v.#3
## pSCF.gp 12/7/16 aev
## Plotting Sierpinski carpet fractals.
## Note: assign variables: ord (order), clr (color), filename and ttl (before using load command).
## ord (order) # a.k.a. level - defines size of fractal (also number of dots).
#cd 'C:\gnupData'
##SCF21
ord=3; clr = '"red"';
filename = "SCF21gp"; ttl = "Sierpinski carpet fractal #21, ord ".ord;
load "plotscf.gp"
##SCF22
ord=5; clr = '"brown"';
filename = "SCF22gp"; ttl = "Sierpinski carpet fractal #22, ord ".ord;
load "plotscf.gp"
##SCF31
ord=5; clr = '"navy"';
filename = "SCF31gp"; ttl = "Sierpinski carpet fractal #31, ord ".ord;
load "plotscf1.gp"
- Output:
1. All pSCF.gp file commands. 2. 3 plotted png-files: SCF21gp, SCF22gp and SCF31gp
Go
Variable "grain" shown set to "#" here, but it's fun to experiment with other values. "|", ". ", "[]", "___", "██", "░░"...
package main
import (
"fmt"
"strings"
"unicode/utf8"
)
var order = 3
var grain = "#"
func main() {
carpet := []string{grain}
for ; order > 0; order-- {
// repeat expression allows for multiple character
// grain and for multi-byte UTF-8 characters.
hole := strings.Repeat(" ", utf8.RuneCountInString(carpet[0]))
middle := make([]string, len(carpet))
for i, s := range carpet {
middle[i] = s + hole + s
carpet[i] = strings.Repeat(s, 3)
}
carpet = append(append(carpet, middle...), carpet...)
}
for _, r := range carpet {
fmt.Println(r)
}
}
Groovy
Solution, uses list-indexing of base 3 string representation:
def base3 = { BigInteger i -> i.toString(3) }
def sierpinskiCarpet = { int order ->
StringBuffer sb = new StringBuffer()
def positions = 0..<(3**order)
def digits = 0..<([order,1].max())
positions.each { i ->
String i3 = base3(i).padLeft(order, '0')
positions.each { j ->
String j3 = base3(j).padLeft(order, '0')
sb << (digits.any{ i3[it] == '1' && j3[it] == '1' } ? ' ' : order.toString().padRight(2) )
}
sb << '\n'
}
sb.toString()
}
Test Program:
(0..4).each { println sierpinskiCarpet(it) }
- Output:
0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 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4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Haskell
inCarpet :: Int -> Int -> Bool
inCarpet 0 _ = True
inCarpet _ 0 = True
inCarpet x y = not ((xr == 1) && (yr == 1)) && inCarpet xq yq
where ((xq, xr), (yq, yr)) = (x `divMod` 3, y `divMod` 3)
carpet :: Int -> [String]
carpet n = map
(zipWith
(\x y -> if inCarpet x y then '#' else ' ')
[0..3^n-1]
. repeat)
[0..3^n-1]
printCarpet :: Int -> IO ()
printCarpet = mapM_ putStrLn . carpet
nextCarpet :: [String] -> [String]
nextCarpet carpet = border ++ map f carpet ++ border
where border = map (concat . replicate 3) carpet
f x = x ++ map (const ' ') x ++ x
sierpinskiCarpet :: Int -> [String]
sierpinskiCarpet n = iterate nextCarpet ["#"] !! n
main :: IO ()
main = mapM_ putStrLn $ sierpinskiCarpet 3
Seems not very different from version above,
main :: IO ()
main = putStr . unlines . (!!3) $ iterate next ["#"]
next :: [String] -> [String]
next block =
block ! block ! block
++
block ! center ! block
++
block ! block ! block
where
(!) = zipWith (++)
center = map (map $ const ' ') block
which we could also read as:
carpet :: Int -> String
carpet = unlines . (iterate weave ["██"] !!)
weave :: [String] -> [String]
weave xs =
let f = zipWith (<>)
g = flip f
in concatMap
(g xs . f xs)
[ xs,
fmap (const ' ') <$> xs,
xs
]
main :: IO ()
main = mapM_ (putStrLn . carpet) [0 .. 2]
Or more applicatively, representing different phases of the weaving shuttle as <*> and <>:
carpet :: Int -> String
carpet = unlines . (iterate weave ["██"] !!)
weave :: [String] -> [String]
weave =
let thread = zipWith (<>)
in ( (>>=)
. ( (:)
<*> ( ((:) . fmap (fmap (const ' ')))
<*> return
)
)
)
<*> ((.) <$> flip thread <*> thread)
main :: IO ()
main = mapM_ (putStrLn . carpet) [0 .. 2]
- Output:
██ ██████ ██ ██ ██████ ██████████████████ ██ ████ ████ ██ ██████████████████ ██████ ██████ ██ ██ ██ ██ ██████ ██████ ██████████████████ ██ ████ ████ ██ ██████████████████
GUI variant
Via high-level vector graphics (diagrams -> cairo -> gtk), very slow.
{-# LANGUAGE DoRec #-}
import Control.Monad.Trans (lift)
import Data.Colour (Colour)
import Diagrams.Prelude hiding (after)
import Diagrams.Backend.Cairo (Cairo)
import Diagrams.Backend.Cairo.Gtk (defaultRender)
import Graphics.Rendering.Diagrams.Points ()
import Graphics.UI.Gtk
import Graphics.UI.Gtk.Gdk.GC (gcNew)
main :: IO ()
main = do
_ <- initGUI
window <- windowNew
_ <- window `onDestroy` mainQuit
window `windowSetResizable` False
area <- drawingAreaNew
_ <- area `on` sizeRequest $ return (Requisition 500 500)
_ <- window `containerAdd` area
widgetShowAll window
rec con <- area `on` exposeEvent $ do
lift $ signalDisconnect con
lift $ area `defaultRender` carpet 5
switchToPixBuf area
mainGUI
-- just workaround for slow redrawing
switchToPixBuf :: DrawingArea -> EventM EExpose Bool
switchToPixBuf area =
eventArea >>= \ea -> lift $ do
dw <- widgetGetDrawWindow area
(w,h) <- drawableGetSize dw
Just pb <- pixbufGetFromDrawable dw ea
gc <- gcNew dw
_ <- area `on` exposeEvent $ lift $
False <$ drawPixbuf dw gc pb 0 0 0 0 w h RgbDitherNone 0 0
return False
carpet :: Int -> Diagram Cairo R2
carpet = (iterate next (cell white) !!)
-- of course, one can use hcat / vcat - combinators
next :: Diagram Cairo R2 -> Diagram Cairo R2
next block =
scale (1/3) . centerXY $
(block ||| block ||| block)
===
(block ||| centr ||| block)
===
(block ||| block ||| block)
where
centr = cell black
cell :: Colour Float -> Diagram Cairo R2
cell color = square 1 # lineWidth 0 # fillColor color
Icon and Unicon
The IsFilled procedure is a translation of Java and Python.
- Output:
Carpet order= 2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Io
Based on Python translation of Ruby.
sierpinskiCarpet := method(n,
carpet := list("@")
n repeat(
next := list()
carpet foreach(s, next append(s .. s .. s))
carpet foreach(s, next append(s .. (s asMutable replaceSeq("@"," ")) .. s))
carpet foreach(s, next append(s .. s .. s))
carpet = next
)
carpet join("\n")
)
sierpinskiCarpet(3) println
- Output:
@@@@@@@@@@@@@@@@@@@@@@@@@@@ @ @@ @@ @@ @@ @@ @@ @@ @@ @ @@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@ @@@@@@ @@@@@@ @@@ @ @ @ @@ @ @ @@ @ @ @ @@@ @@@@@@ @@@@@@ @@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@ @ @@ @@ @@ @@ @@ @@ @@ @@ @ @@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@ @@@@@@@@@ @ @@ @@ @ @ @@ @@ @ @@@@@@@@@ @@@@@@@@@ @@@ @@@ @@@ @@@ @ @ @ @ @ @ @ @ @@@ @@@ @@@ @@@ @@@@@@@@@ @@@@@@@@@ @ @@ @@ @ @ @@ @@ @ @@@@@@@@@ @@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@ @ @@ @@ @@ @@ @@ @@ @@ @@ @ @@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@ @@@@@@ @@@@@@ @@@ @ @ @ @@ @ @ @@ @ @ @ @@@ @@@@@@ @@@@@@ @@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@ @ @@ @@ @@ @@ @@ @@ @@ @@ @ @@@@@@@@@@@@@@@@@@@@@@@@@@@
J
Like the sierpinski triangle, the carpet is straightforward to produce in J. One approach is based on repeatedly putting a function's argument in a box, forming 9 copies of it into a 3 by 3 array, and then replacing the contents of the middle box with blanks:
N=:3
(a:(<1;1)}3 3$<)^:N' '
But N=:3 is big, so let's use N=:2
N=:2
(a:(<1;1)}3 3$<)^:N' '
┌─────────────┬─────────────┬─────────────┐
│┌───┬───┬───┐│┌───┬───┬───┐│┌───┬───┬───┐│
││ │ │ │││ │ │ │││ │ │ ││
│├───┼───┼───┤│├───┼───┼───┤│├───┼───┼───┤│
││ │ │ │││ │ │ │││ │ │ ││
│├───┼───┼───┤│├───┼───┼───┤│├───┼───┼───┤│
││ │ │ │││ │ │ │││ │ │ ││
│└───┴───┴───┘│└───┴───┴───┘│└───┴───┴───┘│
├─────────────┼─────────────┼─────────────┤
│┌───┬───┬───┐│ │┌───┬───┬───┐│
││ │ │ ││ ││ │ │ ││
│├───┼───┼───┤│ │├───┼───┼───┤│
││ │ │ ││ ││ │ │ ││
│├───┼───┼───┤│ │├───┼───┼───┤│
││ │ │ ││ ││ │ │ ││
│└───┴───┴───┘│ │└───┴───┴───┘│
├─────────────┼─────────────┼─────────────┤
│┌───┬───┬───┐│┌───┬───┬───┐│┌───┬───┬───┐│
││ │ │ │││ │ │ │││ │ │ ││
│├───┼───┼───┤│├───┼───┼───┤│├───┼───┼───┤│
││ │ │ │││ │ │ │││ │ │ ││
│├───┼───┼───┤│├───┼───┼───┤│├───┼───┼───┤│
││ │ │ │││ │ │ │││ │ │ ││
│└───┴───┴───┘│└───┴───┴───┘│└───┴───┴───┘│
└─────────────┴─────────────┴─────────────┘
or another way of getting the same image starts with the boolean array
#:7 5 7
1 1 1
1 0 1
1 1 1
and uses that to select either a blank box or a boxed copy if the function's argument:
N=:2
((#:7 5 7){_2{.<)^:N' '
┌─────────────┬─────────────┬─────────────┐
│┌───┬───┬───┐│┌───┬───┬───┐│┌───┬───┬───┐│
││ │ │ │││ │ │ │││ │ │ ││
│├───┼───┼───┤│├───┼───┼───┤│├───┼───┼───┤│
││ │ │ │││ │ │ │││ │ │ ││
│├───┼───┼───┤│├───┼───┼───┤│├───┼───┼───┤│
││ │ │ │││ │ │ │││ │ │ ││
│└───┴───┴───┘│└───┴───┴───┘│└───┴───┴───┘│
├─────────────┼─────────────┼─────────────┤
│┌───┬───┬───┐│ │┌───┬───┬───┐│
││ │ │ ││ ││ │ │ ││
│├───┼───┼───┤│ │├───┼───┼───┤│
││ │ │ ││ ││ │ │ ││
│├───┼───┼───┤│ │├───┼───┼───┤│
││ │ │ ││ ││ │ │ ││
│└───┴───┴───┘│ │└───┴───┴───┘│
├─────────────┼─────────────┼─────────────┤
│┌───┬───┬───┐│┌───┬───┬───┐│┌───┬───┬───┐│
││ │ │ │││ │ │ │││ │ │ ││
│├───┼───┼───┤│├───┼───┼───┤│├───┼───┼───┤│
││ │ │ │││ │ │ │││ │ │ ││
│├───┼───┼───┤│├───┼───┼───┤│├───┼───┼───┤│
││ │ │ │││ │ │ │││ │ │ ││
│└───┴───┴───┘│└───┴───┴───┘│└───┴───┴───┘│
└─────────────┴─────────────┴─────────────┘
That said, using spaces and '#' characters takes a bit more work. One approach would be:
scarp=:{{' #'{~(#:7 5 7) ,/@(1 3 ,/"2@|: */)^:y ,.1}}
scarp 2
#########
# ## ## #
#########
### ###
# # # #
### ###
#########
# ## ## #
#########
scarp 3
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
######### #########
# ## ## # # ## ## #
######### #########
### ### ### ###
# # # # # # # #
### ### ### ###
######### #########
# ## ## # # ## ## #
######### #########
###########################
# ## ## ## ## ## ## ## ## #
###########################
### ###### ###### ###
# # # ## # # ## # # #
### ###### ###### ###
###########################
# ## ## ## ## ## ## ## ## #
###########################
Here, what we are doing is forming a tensor product of our #:7 5 7 boolean array with our argument and then collapsing two of the dimensions so they line up right. Our starting argument is the 1 by 1 array with the value 1. Once we have repeated this process enough times, we select spaces for our zeros and pound signs for our 1s.
Java
public static boolean inCarpet(long x, long y) {
while (x!=0 && y!=0) {
if (x % 3 == 1 && y % 3 == 1)
return false;
x /= 3;
y /= 3;
}
return true;
}
public static void carpet(final int n) {
final double power = Math.pow(3,n);
for(long i = 0; i < power; i++) {
for(long j = 0; j < power; j++) {
System.out.print(inCarpet(i, j) ? "*" : " ");
}
System.out.println();
}
}
Animated version
import java.awt.*;
import java.awt.event.ActionEvent;
import javax.swing.*;
public class SierpinskiCarpet extends JPanel {
private final int dim = 513;
private final int margin = 20;
private int limit = dim;
public SierpinskiCarpet() {
setPreferredSize(new Dimension(dim + 2 * margin, dim + 2 * margin));
setBackground(Color.white);
setForeground(Color.orange);
new Timer(2000, (ActionEvent e) -> {
limit /= 3;
if (limit <= 3)
limit = dim;
repaint();
}).start();
}
void drawCarpet(Graphics2D g, int x, int y, int size) {
if (size < limit)
return;
size /= 3;
for (int i = 0; i < 9; i++) {
if (i == 4) {
g.fillRect(x + size, y + size, size, size);
} else {
drawCarpet(g, x + (i % 3) * size, y + (i / 3) * size, size);
}
}
}
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
g.translate(margin, margin);
drawCarpet(g, 0, 0, dim);
}
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Sierpinski Carpet");
f.setResizable(false);
f.add(new SierpinskiCarpet(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}
JavaScript
ES5
In-browser JavaScript (HTML output)
This version also produces a "graphic" via HTML and CSS.
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html;charset=utf-8">
<title>Sierpinski Carpet</title>
<script type='text/javascript'>
var black_char = "#";
var white_char = " ";
var SierpinskiCarpet = function(size) {
this.carpet = [black_char];
for (var i = 1; i <= size; i++) {
this.carpet = [].concat(
this.carpet.map(this.sier_top),
this.carpet.map(this.sier_middle),
this.carpet.map(this.sier_top)
);
}
}
SierpinskiCarpet.prototype.sier_top = function(x) {
var str = new String(x);
return new String(str+str+str);
}
SierpinskiCarpet.prototype.sier_middle = function (x) {
var str = new String(x);
var spacer = str.replace(new RegExp(black_char, 'g'), white_char);
return new String(str+spacer+str);
}
SierpinskiCarpet.prototype.to_string = function() {
return this.carpet.join("\n")
}
SierpinskiCarpet.prototype.to_html = function(target) {
var table = document.createElement('table');
for (var i = 0; i < this.carpet.length; i++) {
var row = document.createElement('tr');
for (var j = 0; j < this.carpet[i].length; j++) {
var cell = document.createElement('td');
cell.setAttribute('class', this.carpet[i][j] == black_char ? 'black' : 'white');
cell.appendChild(document.createTextNode('\u00a0'));
row.appendChild(cell);
}
table.appendChild(row);
}
target.appendChild(table);
}
</script>
<style type='text/css'>
table {border-collapse: collapse;}
td {width: 1em;}
.black {background-color: black;}
.white {background-color: white;}
</style>
</head>
<body>
<pre id='to_string' style='float:left; margin-right:0.25in'></pre>
<div id='to_html'></div>
<script type='text/javascript'>
var sc = new SierpinskiCarpet(3);
document.getElementById('to_string').appendChild(document.createTextNode(sc.to_string()));
sc.to_html(document.getElementById('to_html'));
</script>
</body>
</html>
- Output:
Or, in a functional idiom, generating plain text, and suitable for use in any ES5 JavaScript, whether in a browser or some other environment.
Creates an N by N array of boolean values, which are mapped to lines of characters for output.
// Orders 1, 2 and 3 of the Sierpinski Carpet
// as lines of text.
// Generic text output for use in any JavaScript environment
// Browser JavaScripts may use console.log() to return textual output
// others use print() or analogous functions.
[1, 2, 3].map(function sierpinskiCarpetOrder(n) {
// An (n * n) grid of (filled or empty) sub-rectangles
// n --> [[s]]
var carpet = function (n) {
var lstN = range(0, Math.pow(3, n) - 1);
// State of each cell in an N * N grid
return lstN.map(function (x) {
return lstN.map(function (y) {
return inCarpet(x, y);
});
});
},
// State of a given coordinate in the grid:
// Filled or not ?
// (See https://en.wikipedia.org/wiki/Sierpinski_carpet#Construction)
// n --> n --> bool
inCarpet = function (x, y) {
return (!x || !y) ? true :
!(
(x % 3 === 1) &&
(y % 3 === 1)
) && inCarpet(
x / 3 | 0,
y / 3 | 0
);
},
// Sequence of integers from m to n
// n --> n --> [n]
range = function (m, n) {
return Array.apply(null, Array(n - m + 1)).map(
function (x, i) {
return m + i;
}
);
};
// Grid of booleans mapped to lines of characters
// [[bool]] --> s
return carpet(n).map(function (line) {
return line.map(function (bool) {
return bool ? '\u2588' : ' ';
}).join('');
}).join('\n');
}).join('\n\n');
Output (orders 1, 2 and 3):
███ █ █ ███ █████████ █ ██ ██ █ █████████ ███ ███ █ █ █ █ ███ ███ █████████ █ ██ ██ █ █████████ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████ ███ ██████ ██████ ███ █ █ █ ██ █ █ ██ █ █ █ ███ ██████ ██████ ███ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████ █████████ █████████ █ ██ ██ █ █ ██ ██ █ █████████ █████████ ███ ███ ███ ███ █ █ █ █ █ █ █ █ ███ ███ ███ ███ █████████ █████████ █ ██ ██ █ █ ██ ██ █ █████████ █████████ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████ ███ ██████ ██████ ███ █ █ █ ██ █ █ ██ █ █ █ ███ ██████ ██████ ███ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████
ES6
(() => {
'use strict';
// sierpinskiCarpet :: Int -> String
let sierpinskiCarpet = n => {
// carpet :: Int -> [[String]]
let carpet = n => {
let xs = range(0, Math.pow(3, n) - 1);
return xs.map(x => xs.map(y => inCarpet(x, y)));
},
// https://en.wikipedia.org/wiki/Sierpinski_carpet#Construction
// inCarpet :: Int -> Int -> Bool
inCarpet = (x, y) =>
(!x || !y) ? true : !(
(x % 3 === 1) &&
(y % 3 === 1)
) && inCarpet(
x / 3 | 0,
y / 3 | 0
);
return carpet(n)
.map(line => line.map(bool => bool ? '\u2588' : ' ')
.join(''))
.join('\n');
};
// GENERIC
// range :: Int -> Int -> [Int]
let range = (m, n) =>
Array.from({
length: Math.floor(n - m) + 1
}, (_, i) => m + i);
// TEST
return [1, 2, 3]
.map(sierpinskiCarpet);
})();
- Output:
███ █ █ ███ █████████ █ ██ ██ █ █████████ ███ ███ █ █ █ █ ███ ███ █████████ █ ██ ██ █ █████████ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████ ███ ██████ ██████ ███ █ █ █ ██ █ █ ██ █ █ █ ███ ██████ ██████ ███ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████ █████████ █████████ █ ██ ██ █ █ ██ ██ █ █████████ █████████ ███ ███ ███ ███ █ █ █ █ █ █ █ █ ███ ███ ███ ███ █████████ █████████ █ ██ ██ █ █ ██ ██ █ █████████ █████████ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████ ███ ██████ ██████ ███ █ █ █ ██ █ █ ██ █ █ █ ███ ██████ ██████ ███ ███████████████████████████ █ ██ ██ ██ ██ ██ ██ ██ ██ █ ███████████████████████████
Or, defining the Sierpinksi carpet weave declaratively, in terms of zipWith and concatMap:
(() => {
'use strict';
// weave :: [String] -> [String]
const weave = xs => {
const f = zipWith(append);
return concatMap(
x => f(f(xs)(x))(xs)
)([
xs,
map(x => replicate(length(x))(' '))(
xs
),
xs
]);
};
// TEST -----------------------------------------------
const main = () => {
const
sierp = n => unlines(
take(1 + n, iterate(weave, ['\u2588']))[n]
),
carpet = sierp(2);
return (
// console.log(carpet),
carpet
);
};
// GENERIC ABSTRACTIONS -------------------------------
// append (++) :: [a] -> [a] -> [a]
// append (++) :: String -> String -> String
const append = xs => ys => xs.concat(ys);
// concatMap :: (a -> [b]) -> [a] -> [b]
const concatMap = f => xs =>
xs.reduce((a, x) => a.concat(f(x)), []);
// iterate :: (a -> a) -> a -> Gen [a]
function* iterate(f, x) {
let v = x;
while (true) {
yield(v);
v = f(v);
}
}
// Returns Infinity over objects without finite length
// this enables zip and zipWith to choose the shorter
// argument when one is non-finite, like cycle, repeat etc
// length :: [a] -> Int
const length = xs => xs.length || Infinity;
// map :: (a -> b) -> [a] -> [b]
const map = f => xs => xs.map(f);
// replicate :: Int -> String -> String
const replicate = n => s => s.repeat(n);
// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = (n, xs) =>
xs.constructor.constructor.name !== 'GeneratorFunction' ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = f => xs => ys => {
const
lng = Math.min(length(xs), length(ys)),
as = take(lng, xs),
bs = take(lng, ys);
return Array.from({
length: lng
}, (_, i) => f(as[i])(bs[i]));
};
// MAIN -----------------------------------------------
return main();
})();
- Output:
█████████ █ ██ ██ █ █████████ ███ ███ █ █ █ █ ███ ███ █████████ █ ██ ██ █ █████████
jq
jq does Cartesian products, so the heart of the matter is the line:
inCarpet( range(0; $power) ; range(0; $power), -1 )
This is like a "for" loop within a "for" loop in C-like languages, because range(0;n) generates a stream of n integers beginning at 0. The -1 is used to signal that a newline character is required.
def inCarpet(x; y):
x as $x | y as $y |
if $x == -1 or $y == -1 then "\n"
elif $x == 0 or $y == 0 then "*"
elif ($x % 3) == 1 and ($y % 3) == 1 then " "
else inCarpet($x/3 | floor; $y/3 | floor)
end;
def ipow(n):
. as $in | reduce range(0;n) as $i (1; . * $in);
def carpet(n):
(3|ipow(n)) as $power
| [ inCarpet( range(0; $power) ; range(0; $power), -1 )]
| join("") ;
carpet(3)The following command produces the required pattern, and so the output is not repeated here:
jq -n -r -c -f sierpinski.jq
Julia
function sierpinski(n::Integer, token::AbstractString="*")
x = fill(token, 1, 1)
for _ in 1:n
t = fill(" ", size(x))
x = [x x x; x t x; x x x]
end
return x
end
function printsierpinski(m::Matrix)
for r in 1:size(m, 1)
println(join(m[r, :]))
end
end
sierpinski(2, "#") |> printsierpinski
Kotlin
ASCII Art Version
// version 1.1.2
fun inCarpet(x: Int, y: Int): Boolean {
var xx = x
var yy = y
while (xx != 0 && yy != 0) {
if (xx % 3 == 1 && yy % 3 == 1) return false
xx /= 3
yy /= 3
}
return true
}
fun carpet(n: Int) {
val power = Math.pow(3.0, n.toDouble()).toInt()
for(i in 0 until power) {
for(j in 0 until power) print(if (inCarpet(i, j)) "*" else " ")
println()
}
}
fun main(args: Array<String>) = carpet(3)
- Output:
*************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * *************************** ********* ********* * ** ** * * ** ** * ********* ********* *** *** *** *** * * * * * * * * *** *** *** *** ********* ********* * ** ** * * ** ** * ********* ********* *************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * ***************************
Graphical Animated Version
// version 1.1.2
import java.awt.*
import javax.swing.*
public class SierpinskiCarpet : JPanel() {
private val dim = 513
private val margin = 20
private var limit = dim
init {
val size = dim + 2 * margin
preferredSize = Dimension(size, size)
background = Color.blue
foreground = Color.yellow
Timer(2000) {
limit /= 3
if (limit <= 3) limit = dim
repaint()
}.start()
}
private fun drawCarpet(g: Graphics2D, x: Int, y: Int, s: Int) {
var size = s
if (s < limit) return
size /= 3
for (i in 0 until 9) {
if (i == 4) {
g.fillRect(x + size, y + size, size, size)
}
else {
drawCarpet(g, x + (i % 3) * size, y + (i / 3) * size, size)
}
}
}
override fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
g.translate(margin, margin)
drawCarpet(g, 0, 0, dim)
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.title = "Sierpinski Carpet"
f.isResizable = false
f.add(SierpinskiCarpet(), BorderLayout.CENTER)
f.pack()
f.setLocationRelativeTo(null)
f.isVisible = true
}
}
Lambdatalk
{def sierpinsky
{def sierpinsky.r
{lambda {:n :w}
{if {= :n 0}
then :w
else {sierpinsky.r
{- :n 1}
{S.map {lambda {:x} :x:x:x} :w}
{S.map {lambda {:x} :x{S.replace ■ by o in :x}:x} :w}
{S.map {lambda {:x} :x:x:x} :w} }}}}
{lambda {:n}
{h2 n=:n}{S.replace o by space in
{S.replace \s by {div} in
{sierpinsky.r :n ■}}}}}
-> sierpinsky
{S.map sierpinsky 0 1 2 3}
->
S0
■
S1
■■■
■ ■
■■■
S2
■■■■■■■■■
■ ■■ ■■ ■
■■■■■■■■■
■■■ ■■■
■ ■ ■ ■
■■■ ■■■
■■■■■■■■■
■ ■■ ■■ ■
■■■■■■■■■
S3
■■■■■■■■■■■■■■■■■■■■■■■■■■■
■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■
■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■ ■■■■■■ ■■■■■■ ■■■
■ ■ ■ ■■ ■ ■ ■■ ■ ■ ■
■■■ ■■■■■■ ■■■■■■ ■■■
■■■■■■■■■■■■■■■■■■■■■■■■■■■
■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■
■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■ ■■■■■■■■■
■ ■■ ■■ ■ ■ ■■ ■■ ■
■■■■■■■■■ ■■■■■■■■■
■■■ ■■■ ■■■ ■■■
■ ■ ■ ■ ■ ■ ■ ■
■■■ ■■■ ■■■ ■■■
■■■■■■■■■ ■■■■■■■■■
■ ■■ ■■ ■ ■ ■■ ■■ ■
■■■■■■■■■ ■■■■■■■■■
■■■■■■■■■■■■■■■■■■■■■■■■■■■
■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■
■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■ ■■■■■■ ■■■■■■ ■■■
■ ■ ■ ■■ ■ ■ ■■ ■ ■ ■
■■■ ■■■■■■ ■■■■■■ ■■■
■■■■■■■■■■■■■■■■■■■■■■■■■■■
■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■
■■■■■■■■■■■■■■■■■■■■■■■■■■■
Lua
An excellent opportunity to show off tail calls, so, recursively..
local function carpet(n, f)
print("n = " .. n)
local function S(x, y)
if x==0 or y==0 then return true
elseif x%3==1 and y%3==1 then return false end
return S(x//3, y//3)
end
for y = 0, 3^n-1 do
for x = 0, 3^n-1 do
io.write(f(S(x, y)))
end
print()
end
print()
end
for n = 0, 4 do
carpet(n, function(b) return b and "■ " or " " end)
end
- Output:
n = 0 ■ n = 1 ■ ■ ■ ■ ■ ■ ■ ■ n = 2 ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ n = 3 ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ 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■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
Mathematica /Wolfram Language
Replace a empty spot with a 3x3 empty matrix, and replace a full spot with an empty spot surrounded by 8 full spots:
full={{1,1,1},{1,0,1},{1,1,1}}
empty={{0,0,0},{0,0,0},{0,0,0}}
n=3;
Grid[Nest[ArrayFlatten[#/.{0->empty,1->full}]&,{{1}},n]//.{0->" ",1->"#"}]
MATLAB
n = 3;
c = string('#');
for k = 1 : n
c = [c + c + c, c + c.replace('#', ' ') + c, c + c + c];
end
disp(c.join(char(10)))
- Output:
########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
NetRexx
/* NetRexx */
options replace format comments java crossref symbols nobinary
numeric digits 1000
runSample(arg)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) public static
DARK_SHADE = '\u2593'
parse arg ordr filr .
if ordr = '' | ordr = '.' then ordr = 3
if filr = '' | filr = '.' then filler = DARK_SHADE
else filler = filr
drawSierpinskiCarpet(ordr, filler)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method drawSierpinskiCarpet(ordr, filler = Rexx '@') public static binary
x = long
y = long
powr = 3 ** ordr
loop x = 0 to powr - 1
loop y = 0 to powr - 1
if isSierpinskiCarpetCellFilled(x, y) then cell = filler
else cell = ' '
say cell'\-'
end y
say
end x
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method isSierpinskiCarpetCellFilled(x = long, y = long) public static binary returns boolean
isTrue = boolean (1 == 1)
isFalse = \isTrue
isFilled = isTrue
loop label edge while x \= 0 & y \= 0
if x // 3 = 1 & y // 3 = 1 then do
isFilled = isFalse
leave edge
end
x = x % 3
y = y % 3
end edge
return isFilled
- Output:
Sample shown with order "2".
▓▓▓▓▓▓▓▓▓ ▓ ▓▓ ▓▓ ▓ ▓▓▓▓▓▓▓▓▓ ▓▓▓ ▓▓▓ ▓ ▓ ▓ ▓ ▓▓▓ ▓▓▓ ▓▓▓▓▓▓▓▓▓ ▓ ▓▓ ▓▓ ▓ ▓▓▓▓▓▓▓▓▓
Nim
import math
proc inCarpet(x, y: int): bool =
var x = x
var y = y
while true:
if x == 0 or y == 0:
return true
if x mod 3 == 1 and y mod 3 == 1:
return false
x = x div 3
y = y div 3
proc carpet(n: int) =
for i in 0 ..< 3^n:
for j in 0 ..< 3^n:
stdout.write if inCarpet(i, j): "* " else: " "
echo()
carpet(3)
- Output:
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Objeck
class SierpinskiCarpet {
function : Main(args : String[]) ~ Nil {
Carpet(3);
}
function : InCarpet(x : Int, y : Int) ~ Bool {
while(x<>0 & y<>0) {
if(x % 3 = 1 & y % 3 = 1) {
return false;
};
x /= 3;
y /= 3;
};
return true;
}
function : Carpet(n : Int) ~ Nil {
power := 3.0->Power(n->As(Float));
for(i := 0; i < power; i+=1;) {
for(j := 0; j < power; j+=1;) {
c := InCarpet(i, j) ? '*' : ' ';
c->Print();
};
IO.Console->PrintLine();
};
}
}OCaml
let rec in_carpet x y =
if x = 0 || y = 0 then true
else if x mod 3 = 1 && y mod 3 = 1 then false
else in_carpet (x / 3) (y / 3)
(* I define my own operator for integer exponentiation *)
let rec (^:) a b =
if b = 0 then 1
else if b mod 2 = 0 then let x = a ^: (b / 2) in x * x
else a * (a ^: (b - 1))
let carpet n =
for i = 0 to (3 ^: n) - 1 do
for j = 0 to (3 ^: n) - 1 do
print_char (if in_carpet i j then '*' else ' ')
done;
print_newline ()
done
let nextCarpet carpet =
List.map (fun x -> x ^ x ^ x) carpet @
List.map (fun x -> x ^ String.make (String.length x) ' ' ^ x) carpet @
List.map (fun x -> x ^ x ^ x) carpet
let rec sierpinskiCarpet n =
let rec aux n carpet =
if n = 0 then carpet
else aux (n-1) (nextCarpet carpet)
in
aux n ["#"]
let () =
List.iter print_endline (sierpinskiCarpet 3)
Oforth
: carpet(n)
| dim i j k |
3 n pow ->dim
0 dim 1 - for: i [
0 dim 1 - for: j [
dim 3 / ->k
while(k) [
i k 3 * mod k / 1 == j k 3 * mod k / 1 == and ifTrue: [ break ]
k 3 / ->k
]
k ifTrue: [ " " ] else: [ "#" ] print
]
printcr
] ;Order
Since the C Preprocessor cannot print newlines, this Order program produces a string for a simple C program to print:
#include <order/interpreter.h>
#define ORDER_PP_DEF_8in_carpet ORDER_PP_FN( \
8fn(8X, 8Y, \
8if(8or(8is_0(8X), 8is_0(8Y)), \
8true, \
8let((8Q, 8quotient(8X, 3)) \
(8R, 8remainder(8X, 3)) \
(8S, 8quotient(8Y, 3)) \
(8T, 8remainder(8Y, 3)), \
8and(8not(8and(8equal(8R, 1), 8equal(8T, 1))), \
8in_carpet(8Q, 8S))))) )
#define ORDER_PP_DEF_8carpet ORDER_PP_FN( \
8fn(8N, \
8lets((8R, 8seq_iota(0, 8pow(3, 8N))) \
(8G, 8seq_map(8fn(8Y, 8seq_map(8fn(8X, 8pair(8X, 8Y)), \
8R)), \
8R)), \
8seq_map(8fn(8S, 8seq_map(8fn(8P, 8apply(8in_carpet, 8P)), \
8S)), \
8G))) )
#define ORDER_PP_DEF_8carpet_to_string ORDER_PP_FN( \
8fn(8C, \
8seq_fold( \
8fn(8R, 8S, \
8adjoin(8R, \
8seq_fold(8fn(8P, 8B, 8adjoin(8P, 8if(8B, 8("#"), 8(" ")))), \
8nil, 8S), \
8("\n"))), \
8nil, 8C)) )
#include <stdio.h>
int main(void) {
printf(ORDER_PP( 8carpet_to_string(8carpet(3)) ));
return 0;
}
(This example may take a long time to compile: change the 8carpet parameter to 2 for a much quicker compile time and a smaller graphic.)
The 8carpet function creates a 2-dimensional array of boolean values (i.e. an internal representation of the Sierpinski carpet), and the 8carpet_to_string function then converts this to a C string.
Since the # and space characters are rather difficult for the C Preprocessor to handle (as a result Order can only print them, not concatenate them), this program takes advantage of the fact that two string literals side-by-side in C must be interpreted as a single string. An alternative method might be to pass the carpet to a print function, that prints the carpet string and returns nil, and then use a regular C macro to stringify the entire result of the Order program.
Oz
declare
%% A carpet is a list of lines.
fun {NextCarpet Carpet}
{Flatten
[{Map Carpet XXX}
{Map Carpet X_X}
{Map Carpet XXX}
]}
end
fun {XXX X} X#X#X end
fun {X_X X} X#{Spaces {VirtualString.length X}}#X end
fun {Spaces N} if N == 0 then nil else & |{Spaces N-1} end end
fun lazy {Iterate F X}
X|{Iterate F {F X}}
end
SierpinskiCarpets = {Iterate NextCarpet ["#"]}
in
%% print all lines of the Sierpinski carpet of order 3
{ForAll {Nth SierpinskiCarpets 4} System.showInfo}PARI/GP
Plotting helper functions
Note: wrtmat() can be found here on RC Brownian tree page.
\\ Improved simple plotting using matrix mat (color and scaling added).
\\ Matrix should be filled with 0/1. 7/6/16 aev
iPlotmat(mat,clr)={
my(xz=#mat[1,],yz=#mat[,1],vx=List(),vy=vx,xmin,xmax,ymin,ymax,c=0.625);
for(i=1,yz, for(j=1,xz, if(mat[i,j]==0, next, listput(vx,i); listput(vy,j))));
xmin=listmin(vx); xmax=listmax(vx); ymin=listmin(vy); ymax=listmax(vy);
plotinit(0); plotcolor(0,clr);
plotscale(0, xmin,xmax,ymin,ymax);
plotpoints(0, Vec(vx)*c,Vec(vy));
plotdraw([0,xmin,ymin]);
print(" *** matrix: ",xz,"x",yz,", ",#vy," DOTS");
}
\\ iPlotV2(): Improved plotting from a file written by the wrtmat(). (color added)
\\ Saving possibly huge generation time if re-plotting needed.
iPlotV2(fn, clr)={
my(F,nf,vx=List(),vy=vx,Vr,xmin,xmax,ymin,ymax,c=0.625);
F=readstr(fn); nf=#F;
print(" *** Plotting from: ", fn, " - ", nf, " DOTS");
for(i=1,nf, Vr=stok(F[i]," "); listput(vx,eval(Vr[1])); listput(vy,eval(Vr[2])));
xmin=listmin(vx); xmax=listmax(vx); ymin=listmin(vy); ymax=listmax(vy);
plotinit(0); plotcolor(0,clr);
plotscale(0, xmin,xmax,ymin,ymax);
plotpoints(0, Vec(vx)*c,Vec(vy));
plotdraw([0,xmin,ymin]);
}
\\ Are x,y inside Sierpinski carpet? (1-yes, 0-no) 6/10/16 aev
inSC(x,y)={
while(1, if(!x||!y,return(1));
if(x%3==1&&y%3==1, return(0));
x\=3; y\=3;);\\wend
}Sierpinski carpet fractal.
\\ Sierpinski carpet fractal (n - order, clr - color, dfn - data file name)
\\ 6/10/16, upgraded 11/29/16 aev
pSierpinskiC(n, clr=5, dfn="")={
my(n3=3^n-1,M,pf=n>=5);
if(pf, M=matrix(n3+1,n3+1));
for(i=0,n3, for(j=0,n3,
if(inSC(i,j),
if(pf, M[i+1,j+1]=1, print1("* ")), if(!pf, print1(" ")));
); if(!pf, print(""));
);\\fend i
if(!pf, return(0));
if(dfn=="", c, wrtmat(M, dfn));
}
{\\ Test:
pSierpinskiC(3);
pSierpinskiC(5,14); \\ SierpC5.png, color - navy
}
{pSierpinskiC(5,,"c:\\pariData\\SC5.dat");
iPlotV2("c:\\pariData\\SC5.dat",10);} \\ SierpC5a.png, color - dark-green- Output:
> pSierpinskiC(3);
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * *
* * * * * * * *
* * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * *
> pSierpinskiC(5,14); \\ SierpC5.png, color navy
*** matrix: 243x243, 32768 DOTS
> {pSierpinskiC(5,,"c:\\pariData\\SC5.dat");
iPlotV2("c:\\pariData\\SC5.dat",10);} \\ SierpC5a.png, color - dark-green
*** matrix(243x243) 32768 DOTS put in c:\pariData\SC5.dat
*** Plotting from: c:\pariData\SC5.dat - 32768 DOTS
Pascal
program SierpinskiCarpet;
uses
Math;
function In_carpet(a, b: longint): boolean;
var
x, y: longint;
begin
x := a;
y := b;
while true do
begin
if (x = 0) or (y = 0) then
begin
In_carpet := true;
break;
end
else if ((x mod 3) = 1) and ((y mod 3) = 1) then
begin
In_carpet := false;
break;
end;
x := x div 3;
y := y div 3;
end;
end;
procedure Carpet(n: integer);
var
i, j, limit: longint;
begin
{$IFDEF FPC}
limit := 3 * * n - 1;
{$ELSE}
limit := Trunc(IntPower(3, n) - 1);
{$ENDIF}
for i := 0 to limit do
begin
for j := 0 to limit do
if In_carpet(i, j) then
write('*')
else
write(' ');
writeln;
end;
end;
begin
Carpet(3);
{$IFNDEF UNIX} readln; {$ENDIF}
end.
- Output:
:> ./SierpinskiCarpet *************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * *************************** ********* ********* * ** ** * * ** ** * ********* ********* *** *** *** *** * * * * * * * * *** *** *** *** ********* ********* * ** ** * * ** ** * ********* ********* *************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * ***************************
Perl
my @c = '##';
@c = (map($_ x 3, @c), map($_.(' ' x length).$_, @c), map($_ x 3, @c))
for 1 .. 3;
print join("\n", @c), "\n";
Phix
constant order = 4 function InCarpet(atom x, atom y) while x!=0 and y!=0 do if floor(mod(x,3))=1 and floor(mod(y,3))=1 then return ' ' end if x /= 3 y /= 3 end while return '#' end function for i=0 to power(3,order)-1 do for j=0 to power(3,order)-1 do puts(1,InCarpet(i,j)) end for puts(1,'\n') end for
- Output:
################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ### ### ### ###### ### ### ###### ### ### ### # # # # # # # ## # # # # # # ## # # # # # # # ### ### ### ###### ### ### ###### ### ### ### ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ### ###### ###### ### ### ###### ###### ### # # # ## # # ## # # # # # # ## # # ## # # # ### ###### ###### ### ### ###### ###### ### ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ######### ######### ######### ######### # ## ## # # ## ## # # ## ## # # ## ## # ######### ######### ######### ######### ### ### ### ### ### ### ### ### # # # # # # # # # # # # # # # # ### ### ### ### ### ### ### ### ######### ######### ######### ######### # ## ## # # ## ## # # ## ## # # ## ## # ######### ######### ######### ######### ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ### ###### ###### ### ### ###### ###### ### # # # ## # # ## # # # # # # ## # # ## # # # ### ###### ###### ### ### ###### ###### ### ########################### ########################### # ## ## ## ## ## ## ## ## # # ## ## ## ## ## ## ## ## # ########################### ########################### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ### ### ### ###### ### ### ###### ### ### ### # # # # # # # ## # # # # # # ## # # # # # # # ### ### ### ###### ### ### ###### ### ### ### ######### ################## ################## ######### # ## ## # # ## ## ## ## ## # # ## ## ## ## ## # # ## ## # ######### ################## ################## ######### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # ################################################################################# ### ###### ###### ###### ###### ###### ###### ###### ###### ### # # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # ## # # # ### ###### ###### ###### ###### ###### ###### ###### ###### ### ################################################################################# # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # #################################################################################
PHP
<?php
function isSierpinskiCarpetPixelFilled($x, $y) {
while (($x > 0) or ($y > 0)) {
if (($x % 3 == 1) and ($y % 3 == 1)) {
return false;
}
$x /= 3;
$y /= 3;
}
return true;
}
function sierpinskiCarpet($order) {
$size = pow(3, $order);
for ($y = 0 ; $y < $size ; $y++) {
for ($x = 0 ; $x < $size ; $x++) {
echo isSierpinskiCarpetPixelFilled($x, $y) ? '#' : ' ';
}
echo PHP_EOL;
}
}
for ($order = 0 ; $order <= 3 ; $order++) {
echo 'N=', $order, PHP_EOL;
sierpinskiCarpet($order);
echo PHP_EOL;
}
- Output:
N=0 # N=1 ### # # ### N=2 ######### # ## ## # ######### ### ### # # # # ### ### ######### # ## ## # ######### N=3 ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
Picat
in_carpet(X, Y) =>
while (X != 0, Y != 0)
if (X mod 3 == 1, Y mod 3 == 1) then
false
end,
X := X div 3,
Y := Y div 3
end.
in_carpet(_, _) =>
true.
main(Args) =>
N = to_int(Args[1]),
Power1 = 3 ** N - 1,
foreach (I in 0..Power1)
foreach (J in 0..Power1)
printf("%w", cond(in_carpet(I, J), "*", " "))
end,
nl
end.- Output:
*************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * *************************** ********* ********* * ** ** * * ** ** * ********* ********* *** *** *** *** * * * * * * * * *** *** *** *** ********* ********* * ** ** * * ** ** * ********* ********* *************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * ***************************
PicoLisp
(de carpet (N)
(let Carpet '("#")
(do N
(setq Carpet
(conc
(mapcar '((S) (pack S S S)) Carpet)
(mapcar
'((S) (pack S (replace (chop S) "#" " ") S))
Carpet )
(mapcar '((S) (pack S S S)) Carpet) ) ) ) ) )
(mapc prinl (carpet 3))PL/I
/* Sierpinski carpet */
Sierpinski_carpet: procedure options (main); /* 28 January 2013 */
call carpet(3);
In_carpet: procedure (a, b) returns (bit(1));
declare (a, b) fixed binary nonassignable;
declare (x, y) fixed binary;
declare (true value ('1'b), false value ('0'b)) bit (1);
x = a ; y = b;
do forever;
if x = 0 | y = 0 then
return (true);
else if mod(x, 3) = 1 & mod(y, 3) = 1 then
return (false);
x = x / 3;
y = y / 3;
end;
end in_carpet;
Carpet: procedure (n);
declare n fixed binary nonassignable;
declare (i, j) fixed binary;
do i = 0 to 3**n - 1;
do j = 0 to 3**n - 1;
if In_carpet(i, j) then
put edit ('#') (a);
else
put edit (' ') (a);
end;
put skip;
end;
end Carpet;
end Sierpinski_carpet;The above is a translation of the Fortran version. Output for n=3:
########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
PostScript
%!PS-Adobe-3.0
%%BoundingBox 0 0 300 300
/r { moveto 0 -1 1 0 0 1 3 { rlineto } repeat closepath fill } def
/serp { gsave
3 1 roll translate
1 3 div dup scale
1 1 r
dup 1 sub dup 0 eq not {
0 0 0 1 0 2 1 0 1 2 2 0 2 1 2 2 17 -1 roll 8 { serp } repeat
} if pop
grestore
} def
300 300 scale 0 0 r 1 setgray
0 0 5 serp
pop showpage
%%EOF
PowerShell
Text based solution
function Draw-SierpinskiCarpet ( [int]$N )
{
$Carpet = @( '#' ) * [math]::Pow( 3, $N )
ForEach ( $i in 1..$N )
{
$S = [math]::Pow( 3, $i - 1 )
ForEach ( $Row in 0..($S-1) )
{
$Carpet[$Row+$S+$S] = $Carpet[$Row] * 3
$Carpet[$Row+$S] = $Carpet[$Row] + ( " " * $Carpet[$Row].Length ) + $Carpet[$Row]
$Carpet[$Row] = $Carpet[$Row] * 3
}
}
$Carpet
}
Draw-SierpinskiCarpet 3
- Output:
########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
Graphics based solution
Function Draw-SierpinskiCarpet ( [int]$N )
{
# Define form
$Form = [System.Windows.Forms.Form]@{ Size = '300, 300' }
$Form.Controls.Add(( $PictureBox = [System.Windows.Forms.PictureBox]@{ Size = $Form.ClientSize; Anchor = 'Top, Bottom, Left, Right' } ))
# Main code to draw Sierpinski carpet
$Draw = {
# Create graphics objects to use
$PictureBox.Image = ( $Canvas = New-Object System.Drawing.Bitmap ( $PictureBox.Size.Width, $PictureBox.Size.Height ) )
$Graphics = [System.Drawing.Graphics]::FromImage( $Canvas )
# Draw single pixel
$Graphics.FillRectangle( [System.Drawing.Brushes]::Black, 0, 0, 1, 1 )
# If N was not specified, use an N that will fill the form
If ( -not $N ) { $N = [math]::Ceiling( [math]::Log( [math]::Max( $PictureBox.Size.Height, $PictureBox.Size.Width ) ) / [math]::Log( 3 ) ) }
# Define the shape of the fractal
$P = @( @( 0, 0 ), @( 0, 1 ), @( 0, 2 ) )
$P += @( @( 1, 0 ), @( 1, 2 ) )
$P += @( @( 2, 0 ), @( 2, 1 ), @( 2, 2 ) )
# For each iteration
ForEach ( $i in 0..$N )
{
# Copy the result of the previous iteration
$Copy = New-Object System.Drawing.TextureBrush ( $Canvas )
# Calulate the size of the copy
$S = [math]::Pow( 3, $i )
# For each position in the next layer of the fractal
ForEach ( $i in 1..7 )
{
# Adjust the copy for the new location
$Copy.TranslateTransform( - $P[$i-1][0] * $S + $P[$i][0] * $S, - $P[$i-1][1] * $S + $P[$i][1] * $S )
# Paste the copy of the previous iteration into the new location
$Graphics.FillRectangle( $Copy, $P[$i][0] * $S, $P[$i][1] * $S, $S, $S )
}
}
}
# Add the main drawing code to the appropriate events to be drawn when the form is first shown and redrawn when the form size is changed
$Form.Add_Shown( $Draw )
$Form.Add_Resize( $Draw )
# Launch the form
$Null = $Form.ShowDialog()
}
Draw-SierpinskiCarpet 4
- Output:
Processing
float delta;
void setup() {
size(729, 729);
fill(0);
background(255);
noStroke();
rect(width/3, height/3, width/3, width/3);
rectangles(width/3, height/3, width/3);
}
void rectangles(int x, int y, int s) {
if (s < 1) return;
int xc = x-s;
int yc = y-s;
for (int row = 0; row < 3; row++) {
for (int col = 0; col < 3; col++) {
if (!(row == 1 && col == 1)) {
int xx = xc+row*s;
int yy = yc+col*s;
delta = s/3;
rect(xx+delta, yy+delta, delta, delta);
rectangles(xx+s/3, yy+s/3, s/3);
}
}
}
}
The sketch can be run online :
here.
Processing Python mode
def setup():
size(729, 729)
fill(0)
background(255)
noStroke()
rect(width / 3, height / 3, width / 3, width / 3)
rectangles(width / 3, height / 3, width / 3)
def rectangles(x, y, s):
if s < 1: return
xc, yc = x - s, y - s
for row in range(3):
for col in range(3):
if not (row == 1 and col == 1):
xx, yy = xc + row * s, yc + col * s
delta = s / 3
rect(xx + delta, yy + delta, delta, delta)
rectangles(xx + s / 3, yy + s / 3, s / 3)
Prolog
This program produces an image file in SVG format.
main:-
write_sierpinski_carpet('sierpinski_carpet.svg', 486, 4).
write_sierpinski_carpet(File, Size, Order):-
open(File, write, Stream),
format(Stream,
"<svg xmlns='http://www.w3.org/2000/svg' width='~d' height='~d'>\n",
[Size, Size]),
write(Stream, "<rect width='100%' height='100%' fill='white'/>\n"),
Side is Size/3.0,
sierpinski_carpet(Stream, 0, 0, Side, Order),
write(Stream, "</svg>\n"),
close(Stream).
sierpinski_carpet(Stream, X, Y, Side, 0):-
!,
X0 is X + Side,
Y0 is Y + Side,
write_square(Stream, X0, Y0, Side).
sierpinski_carpet(Stream, X, Y, Side, Order):-
Order1 is Order - 1,
Side1 is Side / 3.0,
X0 is X + Side,
Y0 is Y + Side,
X1 is X0 + Side,
Y1 is Y0 + Side,
write_square(Stream, X0, Y0, Side),
sierpinski_carpet(Stream, X, Y, Side1, Order1),
sierpinski_carpet(Stream, X0, Y, Side1, Order1),
sierpinski_carpet(Stream, X1, Y, Side1, Order1),
sierpinski_carpet(Stream, X, Y0, Side1, Order1),
sierpinski_carpet(Stream, X1, Y0, Side1, Order1),
sierpinski_carpet(Stream, X, Y1, Side1, Order1),
sierpinski_carpet(Stream, X0, Y1, Side1, Order1),
sierpinski_carpet(Stream, X1, Y1, Side1, Order1).
write_square(Stream, X, Y, Side):-
format(Stream,
"<rect fill='black' x='~g' y='~g' width='~g' height='~g'/>\n",
[X, Y, Side, Side]).
- Output:
Media:Sierpinski_carpet_prolog.svg
Python
This inserts a space after every character; but this makes the spacing look better anyway.
def in_carpet(x, y):
while True:
if x == 0 or y == 0:
return True
elif x % 3 == 1 and y % 3 == 1:
return False
x /= 3
y /= 3
def carpet(n):
for i in xrange(3 ** n):
for j in xrange(3 ** n):
if in_carpet(i, j):
print '*',
else:
print ' ',
print
This version is elegant:
def sierpinski_carpet(n):
carpet = ["#"]
for i in xrange(n):
carpet = [x + x + x for x in carpet] + \
[x + x.replace("#"," ") + x for x in carpet] + \
[x + x + x for x in carpet]
return "\n".join(carpet)
print sierpinski_carpet(3)
We can also define a Sierpinski carpet weave declaratively, in terms of generic abstractions like zipWith and bind:
'''Iterations of the Sierpinski carpet'''
from itertools import chain, islice
from inspect import signature
from operator import add
# sierpinskiCarpet :: Int -> [String]
def sierpinskiCarpet(n):
'''A string representing the nth
iteration of a Sierpinski carpet.
'''
f = zipWith(add)
g = flip(f)
# weave :: [String] -> [String]
def weave(xs):
return bind([
xs,
[' ' * len(s) for s in xs],
xs
])(compose(g(xs))(f(xs)))
return index(
iterate(weave)(['▓▓'])
)(n)
# TEST ----------------------------------------------------
def main():
'''Test iteration of the Sierpinski carpet'''
levels = enumFromTo(0)(3)
t = ' ' * (
len(' -> ') +
max(map(compose(len)(str), levels))
)
print(
fTable(__doc__ + ':')(lambda x: '\n' + str(x))(
lambda xs: xs[0] + '\n' + (
unlines(map(lambda x: t + x, xs[1:])))
)
(sierpinskiCarpet)(levels)
)
# GENERIC -------------------------------------------------
# bind (>>=) :: [a] -> (a -> [b]) -> [b]
def bind(xs):
'''List monad injection operator.
Two computations sequentially composed,
with any value produced by the first
passed as an argument to the second.'''
return lambda f: list(chain.from_iterable(
map(f, xs)
))
# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
'''Right to left function composition.'''
return lambda f: lambda x: g(f(x))
# enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
'''Integer enumeration from m to n.'''
return lambda n: list(range(m, 1 + n))
# flip :: (a -> b -> c) -> b -> a -> c
def flip(f):
'''The (curried or uncurried) function f with its
arguments reversed.'''
if 1 < len(signature(f).parameters):
return lambda a, b: f(b, a)
else:
return lambda a: lambda b: f(b)(a)
# index (!!) :: [a] -> Int -> a
def index(xs):
'''Item at given (zero-based) index.'''
return lambda n: None if 0 > n else (
xs[n] if (
hasattr(xs, "__getitem__")
) else next(islice(xs, n, None))
)
# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated
applications of f to x.
'''
def go(x):
v = x
while True:
yield v
v = f(v)
return lambda x: go(x)
# unlines :: [String] -> String
def unlines(xs):
'''A single string derived by the intercalation
of a list of strings with the newline character.'''
return '\n'.join(xs)
# zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
def zipWith(f):
'''A list constructed by zipping with a
custom function, rather than with the
default tuple constructor.'''
return lambda xs: lambda ys: (
map(f, xs, ys)
)
# OUTPUT FORMATTING ---------------------------------------
# fTable :: String -> (a -> String) ->
# (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
'''Heading -> x display function -> fx display function ->
f -> xs -> tabular string.
'''
def go(xShow, fxShow, f, xs):
ys = [xShow(x) for x in xs]
w = max(map(len, ys))
return s + '\n' + '\n'.join(map(
lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
xs, ys
))
return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
xShow, fxShow, f, xs
)
# MAIN ---
if __name__ == '__main__':
main()- Output:
Iterations of the Sierpinski carpet:
0 -> ▓▓
1 -> ▓▓▓▓▓▓
▓▓ ▓▓
▓▓▓▓▓▓
2 -> ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
▓▓ ▓▓▓▓ ▓▓▓▓ ▓▓
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
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▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
3 -> ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
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Quackery
[ over 3 mod 1 = ] is 1? ( n1 n2 --> n1 n2 f )
[ 3 / swap ] is 3/ ( n1 n2 --> n2/3 n1 )
[ true unrot
[ 2dup or while
1? 1? and iff
[ rot not unrot ] done
3/ 3/ again ]
2drop ] is incarpet ( n --> )
[ 1 swap times [ 3 * ]
dup times
[ i^ over times
[ i^ over incarpet iff
[ say "[]" ]
else
[ say " " ] ]
drop cr ]
drop ] is carpet ( n --> )
4 carpet- Output:
Shown at half size.
[][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][] [] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][] [][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][] [] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [] [][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][] [] [][] [][] [][] [][] [][] [][] [][] 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[][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][] [][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][] [] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [] [][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][] [] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][] [][][][][][][][][] [][][][][][][][][][][][][][][][][][] [][][][][][][][][][][][][][][][][][] [][][][][][][][][] [] [][] [][] [] [] [][] [][] [][] [][] [][] [] [] [][] [][] [][] [][] [][] [] [] [][] [][] [] [][][][][][][][][] [][][][][][][][][][][][][][][][][][] [][][][][][][][][][][][][][][][][][] [][][][][][][][][] [][][] [][][] [][][] [][][][][][] [][][] [][][] [][][][][][] [][][] [][][] [][][] [] [] [] [] [] [] [] [][] [] [] [] [] [] [] [][] [] [] [] [] [] [] [] [][][] [][][] [][][] [][][][][][] [][][] [][][] [][][][][][] [][][] [][][] [][][] [][][][][][][][][] [][][][][][][][][][][][][][][][][][] [][][][][][][][][][][][][][][][][][] [][][][][][][][][] [] [][] [][] [] [] [][] [][] [][] [][] [][] [] [] [][] [][] [][] [][] [][] [] [] [][] [][] [] [][][][][][][][][] [][][][][][][][][][][][][][][][][][] [][][][][][][][][][][][][][][][][][] [][][][][][][][][] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][] [] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][] [][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][] [] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [][] [] [] [] [][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][][][][] [][][] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][] [] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [][] [] [][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][]
R
Version #1.
Note: Find plotmat() here on RC R Helper Functions page.
## Are x,y inside Sierpinski carpet (and where)? (1-yes, 0-no)
inSC <- function(x, y) {
while(TRUE) {
if(!x||!y) {return(1)}
if(x%%3==1&&y%%3==1) {return(0)}
x=x%/%3; y=y%/%3;
} return(0);
}
## Plotting Sierpinski carpet fractal. aev 4/1/17
## ord - order, fn - file name, ttl - plot title, clr - color
pSierpinskiC <- function(ord, fn="", ttl="", clr="navy") {
m=640; abbr="SCR"; dftt="Sierpinski carpet fractal";
n=3^ord-1; M <- matrix(c(0), ncol=n, nrow=n, byrow=TRUE);
cat(" *** START", abbr, date(), "\n");
if(fn=="") {pf=paste0(abbr,"o", ord)} else {pf=paste0(fn, ".png")};
if(ttl!="") {dftt=ttl}; ttl=paste0(dftt,", order ", ord);
cat(" *** Plot file:", pf,".png", "title:", ttl, "\n");
for(i in 0:n) {
for(j in 0:n) {if(inSC(i,j)) {M[i,j]=1}
}}
plotmat(M, pf, clr, ttl);
cat(" *** END", abbr, date(), "\n");
}
## Executing:
pSierpinskiC(5);- Output:
> pSierpinskiC(5); *** START SCR Sun Apr 02 12:39:21 2017 *** Plot file: SCRo5 .png title: Sierpinski carpet fractal, order 5 *** Matrix( 242 x 242 ) 32283 DOTS *** END SCR Sun Apr 02 12:39:28 2017
Version #2.
Note: Find plotmat() here on RC R Helper Functions page.
## Plotting Sierpinski carpet fractal v.2. aev 4/2/17
## ord - order, fn - file name, ttl - plot title, clr - color
pSierpinskiC2 <- function(ord, fn="", ttl="", clr="brown") {
m=640; abbr="SCR2"; dftt="Sierpinski carpet fractal v.2";
cat(" *** START", abbr, date(), "\n");
if(fn=="") {pf=paste0(abbr,"o", ord)} else {pf=paste0(fn, ".png")};
if(ttl!="") {dftt=ttl}; ttl=paste0(dftt,", order ", ord);
cat(" *** Plot file:", pf,".png", "title:", ttl, "\n");
S = matrix(1,1,1);
for (i in 1:ord) {
Q = cbind(S,S,S); R = cbind(S,0*S,S); S = rbind(Q,R,Q);
}
plotmat(S, pf, clr, ttl);
cat(" *** END", abbr, date(), "\n");
}
## Executing:
pSierpinskiC2(5);- Output:
> pSierpinskiC2(5); *** START SCR2 Sun Apr 02 14:44:17 2017 *** Plot file: SCR2o5 .png title: Sierpinski carpet fractal v.2, order 5 *** Matrix( 243 x 243 ) 32768 DOTS *** END SCR2 Sun Apr 02 14:44:24 2017
Racket
#lang racket
(define (carpet n)
(if (zero? n)
'("#")
(let* ([prev (carpet (sub1 n))]
[spaces (regexp-replace* #rx"#" (car prev) " ")])
(append (map (λ(x) (~a x x x)) prev)
(map (λ(x) (~a x spaces x)) prev)
(map (λ(x) (~a x x x)) prev)))))
(for-each displayln (carpet 3))Raku
(formerly Perl 6)
sub carpet
{
(['#'], -> @c {
[
|@c.map({$_ x 3}),
|@c.map({ $_ ~ $_.trans('#'=>' ') ~ $_}),
|@c.map({$_ x 3})
]
} ... *).map: { .join("\n") };
}
say carpet[3];
# Same as above, structured as an array bound to a sequence, with a separate sub for clarity.
sub weave ( @c ) {
[
|@c.map({ $_ x 3 }),
|@c.map({ $_ ~ .trans( '#' => ' ' ) ~ $_ }),
|@c.map({ $_ x 3 })
]
}
my @carpet = ( ['#'], &weave ... * ).map: { .join: "\n" };
say @carpet[3];
# Output of both versions matches task example.Relation
Used _ instead of spaces beause wikitext compacts subsequents spaces
function incarpet(x,y)
set a = x
set b = y
while floor(a)>0 and floor(b)>0
if floor(a mod 3) = 1 and floor(b mod 3) = 1
set a = -1
set b = -1
else
set a = a / 3
set b = b / 3
end if
end while
if a < 0
set result = "_"
else
set result = "#"
end if
end function
program carpet(n)
set d = pow(3,n)
set y = 0
while y < d
set x = 0
set result = " "
while x < d
set result = result . incarpet(x,y)
set x = x + 1
end while
echo result
set y = y + 1
end while
end program
run carpet(3)########################### #_##_##_##_##_##_##_##_##_# ########################### ###___######___######___### #_#___#_##_#___#_##_#___#_# ###___######___######___### ########################### #_##_##_##_##_##_##_##_##_# ########################### #########_________######### #_##_##_#_________#_##_##_# #########_________######### ###___###_________###___### #_#___#_#_________#_#___#_# ###___###_________###___### #########_________######### #_##_##_#_________#_##_##_# #########_________######### ########################### #_##_##_##_##_##_##_##_##_# ########################### ###___######___######___### #_#___#_##_#___#_##_#___#_# ###___######___######___### ########################### #_##_##_##_##_##_##_##_##_# ###########################
REXX
/*REXX program draws any order Sierpinski carpet (order 20 would be ≈ 3.4Gx3.4G carpet).*/
parse arg N char . /*get the order of the carpet. */
if N=='' | N=="," then N= 3 /*if none specified, then assume 3. */
if char=='' then char= "*" /*use the default of an asterisk (*). */
if length(char)==2 then char= x2c(char) /*it was specified in hexadecimal char.*/
if length(char)==3 then char= d2c(char) /* " " " " decimal character*/
width= linesize() /*the width of the terminal screen. */
if N>18 then numeric digits 100 /*just in case the user went ka─razy. */
nnn= 3**N /* [↓] NNN is the cube of N. */
do j=0 for nnn; z= /*Z: will be the line to be displayed.*/
do k=0 for nnn; jj= j; kk= k; x= char
do while jj\==0 & kk\==0 /*one symbol for a not (¬) is a \ */
if jj//3==1 then if kk//3==1 then do /*in REXX: // ≡ division remainder*/
x= ' ' /*use a blank for this display line. */
leave /*LEAVE terminates this DO WHILE. */
end
jj= jj % 3; kk= kk % 3 /*in REXX: % ≡ integer division. */
end /*while*/
z= z || x /*X is either black or white. */
end /*k*/ /* [↑] " " " " blank. */
if length(z)<width then say z /*display the line if it fits on screen*/
call lineout 'Sierpinski.'N, z /*also, write the line to a (disk) file*/
end /*j*/ /*stick a fork in it, we're all done. */This REXX program makes use of linesize REXX program (or BIF) which is used to determine the screen width (or linesize) of the terminal (console).
Some REXXes don't have this BIF, so the linesize.rex REXX program is included here ──► LINESIZE.REX.
- output when using the default input:
*************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * *************************** ********* ********* * ** ** * * ** ** * ********* ********* *** *** *** *** * * * * * * * * *** *** *** *** ********* ********* * ** ** * * ** ** * ********* ********* *************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * ***************************
- output when using the following for input: 2 db
█████████ █ ██ ██ █ █████████ ███ ███ █ █ █ █ ███ ███ █████████ █ ██ ██ █ █████████
Ring
load "guilib.ring"
new qapp
{
win1 = new qwidget() {
etwindowtitle("drawing using qpainter")
setgeometry(100,100,500,500)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
new qpushbutton(win1) {
setgeometry(200,450,100,30)
settext("draw")
setclickevent("draw()")
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
new qpainter() {
begin(p1)
setpen(pen)
order = 3
side = pow(3,order)
for y = 0 to side-1
for x = 0 to side-1
if carpet(self,x,y)
drawpoint(x*16,y*16+15)
drawpoint(x*16+1,y*16+16)
drawpoint(x*16+2,y*16+17) ok
next
next
endpaint()
}
label1 { setpicture(p1) show() }
func carpet myObj,x,y
myObj{while x!=0 and y!=0
if x % 3 = 1 if y % 3 = 1 return false ok ok
x = floor(x/3)
y = floor(y/3)
end
return true}Output:
Ruby
def sierpinski_carpet(n)
carpet = ["#"]
n.times do
carpet = carpet.collect {|x| x + x + x} +
carpet.collect {|x| x + x.tr("#"," ") + x} +
carpet.collect {|x| x + x + x}
end
carpet
end
4.times{|i| puts "\nN=#{i}", sierpinski_carpet(i)}- Output:
N=0 # N=1 ### # # ### N=2 ######### # ## ## # ######### ### ### # # # # ### ### ######### # ## ## # ######### N=3 ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
Graphical Version using JRubyArt
attr_reader :limit
def setup
sketch_title 'Sierpinski Carpet'
n = 4
@limit = width / 3**n
fill 0
background 255
no_stroke
holes(0, 0, width / 3)
end
def in_carpet?(xpos, ypos)
!(xpos == 1 && ypos == 1)
end
def holes(xpos, ypos, dim)
return if dim < limit
grid(3, 3) do |row, col|
offset_x = xpos + row * dim
offset_y = ypos + col * dim
rect(offset_x, offset_y, dim, dim) unless in_carpet?(row, col)
holes(offset_x, offset_y, dim / 3)
end
end
def settings
size(729, 729)
endRust
fn main() {
for i in 0..4 {
println!("\nN={}", i);
println!("{}", sierpinski_carpet(i));
}
}
fn sierpinski_carpet(n: u32) -> String {
let mut carpet = vec!["#".to_string()];
for _ in 0..n {
let mut top: Vec<_> = carpet.iter().map(|x| x.repeat(3)).collect();
let middle: Vec<_> = carpet
.iter()
.map(|x| x.to_string() + &x.replace("#", " ") + x)
.collect();
let bottom = top.clone();
top.extend(middle);
top.extend(bottom);
carpet = top;
}
carpet.join("\n")
}Scala
def nextCarpet(carpet: List[String]): List[String] = (
carpet.map(x => x + x + x) :::
carpet.map(x => x + x.replace('#', ' ') + x) :::
carpet.map(x => x + x + x))
def sierpinskiCarpets(n: Int) = (Iterator.iterate(List("#"))(nextCarpet) drop n next) foreach printlnScheme
(define (carpet n)
(define (in-carpet? x y)
(cond ((or (zero? x) (zero? y))
#t)
((and (= 1 (remainder x 3)) (= 1 (remainder y 3)))
#f)
(else
(in-carpet? (quotient x 3) (quotient y 3)))))
(do ((i 0 (+ i 1))) ((not (< i (expt 3 n))))
(do ((j 0 (+ j 1))) ((not (< j (expt 3 n))))
(display (if (in-carpet? i j)
#\*
#\space)))
(newline)))Seed7
$ include "seed7_05.s7i";
const func boolean: inCarpet (in var integer: x, in var integer: y) is func
result
var boolean: result is TRUE;
begin
while result and x <> 0 and y <> 0 do
if x rem 3 = 1 and y rem 3 = 1 then
result := FALSE;
else
x := x div 3;
y := y div 3;
end if;
end while;
end func;
const proc: carpet (in integer: n) is func
local
var integer: i is 0;
var integer: j is 0;
begin
for i range 0 to pred(3 ** n) do
for j range 0 to pred(3 ** n) do
if inCarpet(i, j) then
write("#");
else
write(" ");
end if;
end for;
writeln;
end for;
end func;
const proc: main is func
begin
carpet(3);
end func;Sidef
var c = ['##']
3.times {
c = (c.map{|x| x * 3 } +
c.map{|x| x + ' '*x.len + x } +
c.map{|x| x * 3 })
}
say c.join("\n")Swift
import Foundation
func sierpinski_carpet(n:Int) -> String {
func middle(str:String) -> String {
let spacer = str.stringByReplacingOccurrencesOfString("#", withString:" ", options:nil, range:nil)
return str + spacer + str
}
var carpet = ["#"]
for i in 1...n {
let a = carpet.map{$0 + $0 + $0}
let b = carpet.map(middle)
carpet = a + b + a
}
return "\n".join(carpet)
}
println(sierpinski_carpet(3))Tcl
package require Tcl 8.5
proc map {lambda list} {
foreach elem $list {
lappend result [apply $lambda $elem]
}
return $result
}
proc sierpinski_carpet n {
set carpet [list "#"]
for {set i 1} {$i <= $n} {incr i} {
set carpet [concat \
[map {x {subst {$x$x$x}}} $carpet] \
[map {x {subst {$x[string map {"#" " "} $x]$x}}} $carpet] \
[map {x {subst {$x$x$x}}} $carpet] \
]
}
return [join $carpet \n]
}
puts [sierpinski_carpet 3]UNIX Shell
Bash + paste(1)
Doesn't pretend to be efficient.
Note that this code inserts a space between characters; some versions of paste(1) (notably the one that ships with OS X) won't allow an empty delimiter. If yours does, you can replace the -d ' ' in the function body with -d ' ' for more compact output.
#!/bin/bash
sierpinski_carpet() {
local -i n="${1:-3}"
local carpet="${2:-#}"
while (( n-- )); do
local center="${carpet//#/ }"
carpet="$(paste -d ' ' <(echo "$carpet"$'\n'"$carpet"$'\n'"$carpet") <(echo "$carpet"$'\n'"$center"$'\n'"$carpet") <(echo "$carpet"$'\n'"$carpet"$'\n'"$carpet"))"
done
echo "$carpet"
}Sample run:
$ sierpinski_carpet 3 # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
Bash/Ksh/Zsh + dc(1)
Alternate version using the 'corresponding 1s in base 3' rule, with help from dc(1):
sierpinski_carpet() {
typeset -i n=${1:-3}
if (( n < 1 )); then
return 1
fi
typeset -i size x y
typeset x1 y1
(( size = 3 ** n ))
for (( y=0; y<size; ++y )); do
y1=$(dc <<<"$y 3op")
for (( x=0; x<size; ++x )); do
x1=$(dc <<<"$x 3op")
if (( 2#${x1//2/0} & 2#${y1//2/0} )); then
printf ' '
else
printf '#'
fi
done
printf '\n'
done
}
sierpinski_carpet 3- Output:
########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
Ursala
The carpet function works for any natural number n and is tested on 0,1,2, and 3. The carpet is stored as a list of lists of booleans but converted to characters for display.
#import std
#import nat
carpet = ~&a^?\<<&>>! (-*<7,5,7>; *=DS ~&K7+ ~&B**DS*=rlDS)^|R/~& predecessor
#show+
test = mat0 ~&?(`#!,` !)*** carpet* <0,1,2,3>- Output:
# ### # # ### ######### # ## ## # ######### ### ### # # # # ### ### ######### # ## ## # ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
V (Vlang)
import math
fn main() {
carpet(3)
}
fn carpet(n int) {
power := int(math.pow(3.0, n))
for i in 0..power {
for j in 0..power {
if in_carpet(i, j) == true {print("*")} else{print(" ")}
}
println('')
}
}
fn in_carpet(x int, y int) bool {
mut xx := x
mut yy := y
for xx != 0 && yy != 0 {
if xx % 3 == 1 && yy % 3 == 1 {return false}
xx /= 3
yy /= 3
}
return true
}- Output:
*************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * *************************** ********* ********* * ** ** * * ** ** * ********* ********* *** *** *** *** * * * * * * * * *** *** *** *** ********* ********* * ** ** * * ** ** * ********* ********* *************************** * ** ** ** ** ** ** ** ** * *************************** *** ****** ****** *** * * * ** * * ** * * * *** ****** ****** *** *************************** * ** ** ** ** ** ** ** ** * ***************************
Wren
var inCarpet = Fn.new { |x, y|
while (true) {
if (x == 0 || y == 0) return true
if (x%3 == 1 && y%3 == 1) return false
x = (x/3).floor
y = (y/3).floor
}
}
var carpet = Fn.new { |n|
var power = 3.pow(n)
for (i in 0...power) {
for (j in 0...power) {
System.write(inCarpet.call(i, j) ? "#" : " ")
}
System.print()
}
}
carpet.call(3)- Output:
########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
X86 Assembly
Uses magic number division to avoid repeatedly using the div instruction in a loop.
;x86-64 assembly code for Microsoft Windows
;Tested in windows 7 Enterprise Service Pack 1 64 bit
;With the AMD FX(tm)-6300 processor
;Assembled with NASM version 2.11.06
;Linked to C library with gcc version 4.9.2 (x86_64-win32-seh-rev1, Built by MinGW-W64 project)
;Assembled and linked with the following commands:
;nasm -f win64 <filename>.asm -o <filename>.obj
;gcc <filename>.obj -o <filename>
;Takes magnitude of Sierpinski Carpet as command line argument.
extern atoi,puts,putchar,exit
section .data
errmsg_noarg: db "Magnitude of Sierpinski Carpet was not specified.",0
errmsg_argnumber: db "There should be no more than one argument.",0
section .bss
section .text
global main
main:
;check for argument
cmp rcx,1
jle err_noarg
;ensure that only one argument was entered
cmp rcx,2
jg err_argnumber
;column in rsi
;row in rdi
;x in r8
;y in r9
;width in r13
;magic number in r14
mov r14,2863311531
;get magnitude in rbx from first arg
mov rcx,[rdx + 8]
call atoi
mov rbx,rax
cmp rbx,0
jz magnitude_zero
;determine dimensions of square
mov rax,1
find_width:
lea rax,[rax * 3]
dec rbx
jg find_width
sub rax,1
mov r13,rax
mov rdi,rax
next_row:
mov rsi,r13
fill_row:
;x in r8, y in r9
mov r8,rsi
mov r9,rdi
is_filled:
;if(x%3==1 && y%3==1)
;x%3 in rbx
mov rax,r8
mov rbx,r8
mul r14
shr rax,33
mov r8,rax
lea rax,[rax * 3]
sub rbx,rax
;y%3 in rcx
mov rax,r9
mov rcx,r9
mul r14
shr rax,33
mov r9,rax
lea rax,[rax * 3]
sub rcx,rax
;x%3==1 && y%3==1
xor rbx,1
xor rcx,1
or rbx,rcx
mov rcx,' '
cmp rbx,0
jz dont_fill
;x>0 || y>0
mov rax,r8
or rax,r9
cmp rax,0
jg is_filled
mov rcx,'#'
dont_fill:
call putchar
dec rsi
jge fill_row
;put newline at the end of each row
mov rcx,0xa
call putchar
dec rdi
jge next_row
xor rcx,rcx
call exit
magnitude_zero:
mov rcx,'#'
call putchar
mov rcx,0xa
call putchar
xor rcx,rcx
call exit
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;error message
err_noarg:
mov rcx,errmsg_noarg
call puts
mov rcx,1
call exit
err_argnumber:
mov rcx,errmsg_argnumber
call puts
mov rcx,1
call exit- Sample:
F:\>asciisierpinski.exe Magnitude of Sierpinski Carpet was not specified. F:\>asciisierpinski.exe 1 1 1 There should be no more than one arguement. F:\>asciisierpinski.exe 0 # F:\>asciisierpinski.exe 1 ### # # ### F:\>asciisierpinski.exe 2 ######### # ## ## # ######### ### ### # # # # ### ### ######### # ## ## # ######### F:\>asciisierpinski.exe 3 ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ### ### ### ### # # # # # # # # ### ### ### ### ######### ######### # ## ## # # ## ## # ######### ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ###########################
XPL0
include c:\cxpl\codes; \intrinsic 'code' declarations
proc DrawPat(X0, Y0, S); \Draw 3x3 pattern with hole in middle
int X0, Y0, S; \coordinate of upper-left corner, size
int X, Y;
[for Y:= 0 to 2 do
for X:= 0 to 2 do
if X#1 or Y#1 then \don't draw middle pattern
[if S>1 then \recurse
DrawPat(X*S+X0, Y*S+Y0, S/3)
else Point(X+X0, Y+Y0, 4\red\);
];
];
[SetVid($13); \set 320x200 graphic video mode
DrawPat(0, 0, 3*3*3); \draw Sierpinski carpet
if ChIn(1) then []; \wait for keystroke
SetVid($3); \restore normal text mode
]Z80 Assembly
8-bit BCT (Binary-Coded Ternary) values are used so maximum N is 4, sjasmplus syntax, CP/M executable:
; Sierpinski carpet in Z80 assembly (for CP/M OS - you can use `tnylpo` or `z88dk-ticks` on PC)
OPT --syntax=abf : OUTPUT "sierpinc.com" ; asm syntax for z00m's variant of sjasmplus
ORG $100
; start for n=0, total size is 1x1 (just '#'), show five carpets for n=0,1,2,3,4
ld h,%00000001 ; 3**0 = 1 in BCT form (0t0001)
carpets_loop: ; n == 4 is maximum for 8bit BCT math (3**4 = 81 = 0x100 as BCT value)
call show_carpet
ld a,h ; do ++n -> H = 3**n in BCT form, ie. `H <<= 2;` in binary way
add a,a
jp z,0 ; return to CP/M if the biggest carpet for n=4 (H==0) was already displayed
add a,a
ld h,a ; zero for n=4, which will correctly wrap to 0t2222 in base3_dec_a
jr carpets_loop
show_carpet:
ld l,h ; L = 3**n (row counter and Y coordinate)
.rows:
ld a,l
call base3_dec_a
ld l,a ; --L for this row
ld b,h ; B = 3**n (char counter and X coordinate)
.chars:
ld a,b
call base3_dec_a
ld b,a ; --B
and l ; check if X and Y coordinate have digit "1" at same position(s) in ternary
and %01010101 ; non-zero if both coordinates have digit "1" at same position(s)
ld e,'#'
jr z,.fill_char
ld e,' '
.fill_char:
call print_char
inc b
djnz .chars ; loop chars until B==0 was displayed
call print_crlf
ld a,l
or a
jr nz,.rows ; loop rows until L==0 was displayed
; fallthrough into print_crlf for extra empty line after each carpet is finished
print_crlf:
ld e,10
call print_char
ld e,13
print_char:
push bc
push hl
ld c,2
call 5
pop hl
pop bc
ret
; in: A = BCT value (Binary-coded Ternary = pair of bits for ternary digit 0,1,2 (3 not allowed))
; out: A-1 in BCT encoding, modifies C and F (ZF signals zero result, 0t0000-1 = 0t2222 (0xAA))
base3_dec_a:
dec a ; --A (%00 digits may become %11 when involved in decrement)
ld c,a
rra
and c
and %01010101 ; %11 bit-pairs to %01, anything else to %00
xor c ; fix %11 -> %10 in result to have only 0,1,2 digits
ret
/* ;;; bonus routine ;;;
; in: A = BCT value (Binary-coded Ternary = pair of bits for ternary digit 0,1,2 (3 not allowed))
; out: A+1 in BCT encoding, modifies C and F (ZF signals zero result, ie. 0t2222+1 = 0t0000)
base3_inc_a:
add a,%01'01'01'10 ; +1 to every digit (0,1,2 -> 1,2,3), and +1 overall to increment
ld c,a
rra
or c
and %01'01'01'01 ; 00,01,10,11 -> 00,01,01,01
neg
add a,c ; revert digits 3,2,1 back to 2,1,0 (0 -> 0)
ret
*/- Output:
# ### # # ### ######### # ## ## # ######### ### ### # # # # ### ### ######### # ## ## # ######### ########################### # ## ## ## ## ## ## ## ## # ########################### ### ###### ###### ### # # # ## # # ## # # # ### ###### ###### ### ########################### # ## ## ## ## ## ## ## ## # ########################### ######### ######### # ## ## # # ## ## # ######### ######### ...
zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
fcn drawPat(x0,y0,s,img){ // Draw 3x3 pattern with hole in middle
foreach y,x in (3,3){
if(x.isEven or y.isEven){ // don't draw middle pattern
if(s>1) self.fcn(x*s + x0, y*s + y0, s/3, img); // recurse
else img[x + x0, y + y0]=0xff0000; // red
}
}
}img:=PPM(800,800);
drawPat(0,0,(3).pow(5),img);
img.write(File("foo.ppm","wb"));Categories:
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