Sierpinski triangle: Difference between revisions
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* * * * * * * * |
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* * * * * * * * * * * * * * * *</pre> |
* * * * * * * * * * * * * * * *</pre> |
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=={{header|jq}}== |
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{{works with|jq}} |
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'''Works with gojq, the Go implementation of jq''' |
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'''Preliminaries''' |
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<lang jq>def elementwise(f): |
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transpose | map(f) ; |
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# input: an array of decimal numbers |
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def bitwise_and: |
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# Input: an integer |
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# Output: a stream of 0s and 1s |
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def stream: |
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recurse(if . > 0 then ./2|floor else empty end) | . % 2 ; |
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# Input: a 0-1 array |
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def toi: |
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reduce .[] as $c ( {power:1 , ans: 0}; |
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.ans += ($c * .power) | .power *= 2 ) |
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| .ans; |
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if any(.==0) then 0 |
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else map([stream]) |
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| (map(length) | min) as $min |
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| map( .[:$min] ) | elementwise(min) | toi |
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end;</lang> |
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<lang jq> |
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def sierpinski: |
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pow(2; .) as $size |
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| range($size-1; -1; -1) as $y |
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| reduce range(0; $size - $y) as $x ( (" " * $y); |
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. + (if ([$x,$y]|bitwise_and) == 0 then "* " else " " end)); |
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4 | sierpinski</lang> |
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{{out}} |
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As elsewhere. |
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=={{header|Julia}}== |
=={{header|Julia}}== |
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Revision as of 08:34, 5 April 2022
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Produce an ASCII representation of a Sierpinski triangle of order N.
- Example
The Sierpinski triangle of order 4 should look like this:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
- Related tasks
- Sierpinski triangle/Graphical for graphics images of this pattern.
- Sierpinski carpet
11l
<lang 11l>F sierpinski(n)
V d = [String(‘*’)]
L(i) 0 .< n
V sp = ‘ ’ * (2 ^ i)
d = d.map(x -> @sp‘’x‘’@sp) [+] d.map(x -> x‘ ’x)
R d
print(sierpinski(4).join("\n"))</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
8080 Assembly
<lang 8080asm>argmt: equ 5Dh ; Command line argument puts: equ 9 ; CP/M syscall to print a string putch: equ 2 ; CP/M syscall to print a character org 100h mvi b,4 ; Default order is 4 mvi e,' ' ; Keep space in E since we're saving it anyway lda argmt ; Argument given? cmp e ; If not, use default jz start sui '0' ; Make sure given N makes sense cpi 3 ; <3? jc start cpi 8 ; >=8? jnc start mov b,a start: mvi a,1 ; Find size (2 ** order) shift: rlc dcr b jnz shift mov b,a ; B = size mov c,a ; C = current line line: mov d,c ; D = column indent: mov a,e ; Indent line call chout dcr d jnz indent column: mov a,c ; line + col <= size? add d dcr a cmp b jnc cdone mov a,c ; (line - 1) & col == 0? dcr a ana d mov a,e ; space if not, star if so jnz print mvi a,'*' print: call chout mov a,e call chout inr d jmp column cdone: push b ; done, print newline push d lxi d,nl mvi c,puts call 5 pop d pop b dcr c ; next line jnz line ret chout: push b ; save BC and DE push d mov e,a ; print character mvi c,putch call 5 pop d ; restore BC and DE pop b ret nl: db 13,10,'$'</lang>
- Output:
For order 4 (default if no given):
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
8086 Assembly
<lang asm>putch: equ 2 ; MS-DOS syscall to print character puts: equ 9 ; MS-DOS syscall to print string argmt: equ 5Dh ; MS-DOS still has FCB in same place as CP/M cpu 8086 org 100h section .text mov cx,4 ; Default order is 4 mov al,[argmt] sub al,'3' ; Argument is there and makes sense? (3 - 7) cmp al,7-3 ja start ; If not, use default add al,3 ; If so, use it mov cl,al start: mov bl,1 ; Let BL be the size (2 ** order) shl bl,cl mov bh,bl ; Let BH be the current line line: mov cl,bh ; Let CL be the column mov dl,' ' ; Indent line with spaces mov ah,putch indent: int 21h loop indent column: mov al,cl ; line + column <= size? add al,bh cmp al,bl ja .done ; then column is done mov al,bh ; (line - 1) & column == 0? dec al test al,cl jnz .print ; space if not, star if so mov dl,'*' .print: int 21h mov dl,' ' int 21h inc cx ; next column jmp column .done: mov dx,nl ; done, print newline mov ah,puts int 21h dec bh ; next line jnz line ret nl: db 13,10,'$'</lang>
- Output:
For order 4 (default if no order given):
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
ACL2
<lang Lisp>(defun pascal-row (prev)
(if (endp (rest prev))
(list 1)
(cons (+ (first prev) (second prev))
(pascal-row (rest prev)))))
(defun pascal-triangle-r (rows prev)
(if (zp rows)
nil
(let ((curr (cons 1 (pascal-row prev))))
(cons curr (pascal-triangle-r (1- rows) curr)))))
(defun pascal-triangle (rows)
(cons (list 1)
(pascal-triangle-r rows (list 1))))
(defun print-odds-row (row)
(if (endp row)
(cw "~%")
(prog2$ (cw (if (oddp (first row)) "[]" " "))
(print-odds-row (rest row)))))
(defun print-spaces (n)
(if (zp n)
nil
(prog2$ (cw " ")
(print-spaces (1- n)))))
(defun print-odds (triangle height)
(if (endp triangle)
nil
(progn$ (print-spaces height)
(print-odds-row (first triangle))
(print-odds (rest triangle) (1- height)))))
(defun print-sierpenski (levels)
(let ((height (1- (expt 2 levels))))
(print-odds (pascal-triangle height)
height)))</lang>
Action!
<lang Action!>PROC Main()
BYTE x,y,size=[16]
Graphics(0) PutE() PutE()
y=size-1
DO
FOR x=1 TO y+2
DO Put(' ) OD
FOR x=0 TO size-y-1
DO
IF (x&y)=0 THEN
Print("* ")
ELSE
Print(" ")
FI
OD
PutE()
IF y=0 THEN
EXIT
FI
y==-1
OD</lang>
- Output:
Screenshot from Atari 8-bit computer
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Ada
This Ada example creates a string of the binary value for each line, converting the '0' values to spaces. <lang ada>with Ada.Text_Io; use Ada.Text_Io; with Ada.Strings.Fixed; with Interfaces; use Interfaces;
procedure Sieteri_Triangles is
subtype Practical_Order is Unsigned_32 range 0..4;
function Pow(X : Unsigned_32; N : Unsigned_32) return Unsigned_32 is
begin
if N = 0 then
return 1;
else
return X * Pow(X, N - 1);
end if;
end Pow;
procedure Print(Item : Unsigned_32) is
use Ada.Strings.Fixed;
package Ord_Io is new Ada.Text_Io.Modular_Io(Unsigned_32);
use Ord_Io;
Temp : String(1..36) := (others => ' ');
First : Positive;
Last : Positive;
begin
Put(To => Temp, Item => Item, Base => 2);
First := Index(Temp, "#") + 1;
Last := Index(Temp(First..Temp'Last), "#") - 1;
for I in reverse First..Last loop
if Temp(I) = '0' then
Put(' ');
else
Put(Temp(I));
end if;
end loop;
New_Line;
end Print;
procedure Sierpinski (N : Practical_Order) is
Size : Unsigned_32 := Pow(2, N);
V : Unsigned_32 := Pow(2, Size);
begin
for I in 0..Size - 1 loop
Print(V);
V := Shift_Left(V, 1) xor Shift_Right(V,1);
end loop;
end Sierpinski;
begin
for N in Practical_Order loop
Sierpinski(N);
end loop;
end Sieteri_Triangles;</lang>
alternative using modular arithmetic: <lang Ada>with Ada.Command_Line; with Ada.Text_IO;
procedure Main is
subtype Order is Natural range 1 .. 32; type Mod_Int is mod 2 ** Order'Last;
procedure Sierpinski (N : Order) is
begin
for Line in Mod_Int range 0 .. 2 ** N - 1 loop
for Col in Mod_Int range 0 .. 2 ** N - 1 loop
if (Line and Col) = 0 then
Ada.Text_IO.Put ('X');
else
Ada.Text_IO.Put (' ');
end if;
end loop;
Ada.Text_IO.New_Line;
end loop;
end Sierpinski;
N : Order := 4;
begin
if Ada.Command_Line.Argument_Count = 1 then
N := Order'Value (Ada.Command_Line.Argument (1));
end if;
Sierpinski (N);
end Main;</lang>
- Output:
XXXXXXXXXXXXXXXX X X X X X X X X XX XX XX XX X X X X XXXX XXXX X X X X XX XX X X XXXXXXXX X X X X XX XX X X XXXX X X XX X
ALGOL 68
<lang algol68>PROC sierpinski = (INT n)[]STRING: (
FLEX[0]STRING d := "*";
FOR i TO n DO
[UPB d * 2]STRING next;
STRING sp := " " * (2 ** (i-1));
FOR x TO UPB d DO
STRING dx = d[x];
next[x] := sp+dx+sp;
next[UPB d+x] := dx+" "+dx
OD;
d := next
OD;
d
);
printf(($gl$,sierpinski(4)))</lang>
ALGOL W
<lang algolw>begin
integer SIZE;
SIZE := 16;
for y := SIZE - 1 step - 1 until 0 do begin
integer x;
for i := 0 until y - 1 do writeon( " " );
x := 0;
while x + y < SIZE do begin
writeon( if number( bitstring( x ) and bitstring( y ) ) not = 0 then " " else "* " );
x := x + 1
end while_x_plus_y_lt_SIZE ;
write();
end for_y
end.</lang>
AppleScript
Centering any previous triangle block over two adjacent duplicates: <lang AppleScript>------------------- SIERPINKSI TRIANGLE ------------------
-- sierpinski :: Int -> [String] on sierpinski(n)
if n > 0 then
set previous to sierpinski(n - 1)
set padding to replicate(2 ^ (n - 1), space)
script alignedCentre
on |λ|(s)
concat(padding & s & padding)
end |λ|
end script
script adjacentDuplicates
on |λ|(s)
unwords(replicate(2, s))
end |λ|
end script
-- Previous triangle block centered,
-- and placed on 2 adjacent duplicates.
map(alignedCentre, previous) & map(adjacentDuplicates, previous)
else
{"*"}
end if
end sierpinski
TEST -------------------------
on run
unlines(sierpinski(4))
end run
GENERIC FUNCTIONS -------------------
-- concat :: a -> [a] | [String] -> String on concat(xs)
if length of xs > 0 and class of (item 1 of xs) is string then
set acc to ""
else
set acc to {}
end if
repeat with i from 1 to length of xs
set acc to acc & item i of xs
end repeat
acc
end concat
-- 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
-- replicate :: Int -> a -> [a] on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}
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
-- unlines, unwords :: [String] -> String on unlines(xs)
intercalate(linefeed, xs)
end unlines
on unwords(xs)
intercalate(space, xs)
end unwords</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Or generating each line as an XOR / Rule 90 / Pascal triangle rewrite of the previous line.
<lang AppleScript>----------- SIERPINSKI TRIANGLE BY XOR / RULE 90 ---------
-- sierpinskiTriangle :: Int -> String on sierpinskiTriangle(intOrder)
-- A Sierpinski triangle of order N -- is a Pascal triangle (of N^2 rows) -- mod 2 -- pascalModTwo :: Int -> String script pascalModTwo on |λ|(intRows) -- addRow Int -> Int script addRow -- nextRow :: [Int] -> [Int] on nextRow(row) -- The composition of AsciiBinary . mod two . add -- is reduced here to a rule from -- two parent characters above, -- to the child character below. -- Rule 90 also reduces to this XOR relationship -- between left and right neighbours. -- rule :: Character -> Character -> Character script rule on |λ|(a, b) if a = b then space else "*" end if end |λ| end script zipWith(rule, {" "} & row, row & {" "}) end nextRow on |λ|(xs) xs & {nextRow(item -1 of xs)} end |λ| end script foldr(addRow, Template:"*", enumFromTo(1, intRows - 1)) end |λ| end script -- The centring foldr (fold right) below starts from the end of the list, -- (the base of the triangle) which has zero indent. -- Each preceding row has one more indent space than the row below it. script centred on |λ|(sofar, row) set strIndent to indent of sofar {triangle:strIndent & intercalate(space, row) & linefeed & ¬ triangle of sofar, indent:strIndent & space} end |λ| end script triangle of foldr(centred, {triangle:"", indent:""}, ¬ pascalModTwo's |λ|(intOrder ^ 2))
end sierpinskiTriangle
TEST -------------------------
on run
set strTriangle to sierpinskiTriangle(4) set the clipboard to strTriangle strTriangle
end run
GENERIC FUNCTIONS -------------------
-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)
if m > n then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- foldr :: (a -> b -> a) -> a -> [b] -> a on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldr
-- 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
-- min :: Ord a => a -> a -> a on min(x, y)
if y < x then
y
else
x
end if
end min
-- 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
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] on zipWith(f, xs, ys)
set lng to min(length of xs, length of ys)
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 zipWith</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Arturo
<lang rebol>sierpinski: function [order][
s: shl 1 order
loop (s-1)..0 'y [
do.times: y -> prints " "
loop 0..dec s-y 'x [
if? zero? and x y -> prints "* "
else -> prints " "
]
print ""
]
]
sierpinski 4</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
ATS
<lang ATS> (* ****** ****** *) // // How to compile: // // patscc -DATS_MEMALLOC_LIBC -o sierpinski sierpinski.dats // (* ****** ****** *) //
- include
"share/atspre_staload.hats" // (* ****** ****** *)
- define SIZE 16
implement main0 () = { // var x: int // val () = for (x := SIZE-1; x >= 0; x := x-1) {
var i: int
val () =
for (i := 0; i < x; i := i+1)
{
val () = print_char(' ')
}
var y: int
val () =
for (y := 0; y + x < SIZE; y := y+1)
{
val y = g0int2uint_int_uint(y)
val x = g0int2uint_int_uint(x)
val () = print_string(if (x land y) != 0 then " " else "* ")
}
val ((*flushed*)) = print_newline()
} // } (* end of [main0] *) </lang>
AutoHotkey
ahk discussion <lang autohotkey>Loop 6
MsgBox % Triangle(A_Index)
Triangle(n,x=0,y=1) { ; Triangle(n) -> string of dots and spaces of Sierpinski triangle
Static t, l ; put chars in a static string
If (x < 1) { ; when called with one parameter
l := 2*x := 1<<(n-1) ; - compute location, string size
VarSetCapacity(t,l*x,32) ; - allocate memory filled with spaces
Loop %x%
NumPut(13,t,A_Index*l-1,"char") ; - new lines in the end of rows
}
If (n = 1) ; at the bottom of recursion
Return t, NumPut(46,t,x-1+(y-1)*l,"char") ; - write "." (better at proportional fonts)
u := 1<<(n-2)
Triangle(n-1,x,y) ; draw smaller triangle here
Triangle(n-1,x-u,y+u) ; smaller triangle down-left
Triangle(n-1,x+u,y+u) ; smaller triangle down right
Return t
}</lang>
APL
<lang APL>A←67⍴0⋄A[34]←1⋄' #'[1+32 67⍴{~⊃⍵:⍵,∇(1⌽⍵)≠¯1⌽⍵⋄⍬}A]</lang>
AWK
<lang AWK># WST.AWK - Waclaw Sierpinski's triangle contributed by Dan Nielsen
- syntax: GAWK -f WST.AWK [-v X=anychar] iterations
- example: GAWK -f WST.AWK -v X=* 2
BEGIN {
n = ARGV[1] + 0 # iterations
if (n !~ /^[0-9]+$/) { exit(1) }
if (n == 0) { width = 3 }
row = split("X,X X,X X,X X X X",A,",") # seed the array
for (i=1; i<=n; i++) { # build triangle
width = length(A[row])
for (j=1; j<=row; j++) {
str = A[j]
A[j+row] = sprintf("%-*s %-*s",width,str,width,str)
}
row *= 2
}
for (j=1; j<=row; j++) { # print triangle
if (X != "") { gsub(/X/,substr(X,1,1),A[j]) }
sub(/ +$/,"",A[j])
printf("%*s%s\n",width-j+1,"",A[j])
}
exit(0)
}</lang>
BASH (feat. sed & tr)
This version completely avoids any number-theoretic workarounds. Instead, it repeatedly replaces characters by "blocks of characters". The strategy is in no way bash-specific, it would work with any other language just as well, but is particularly well suited for tools like sed and tr. <lang bash>
- !/bin/bash
- Basic principle:
- x -> dxd d -> dd s -> s
- xsx dd s
- In the end all 'd' and 's' are removed.
- 0x7F800000
function rec(){
if [ $1 == 0 ]
then
echo "x"
else
rec $[ $1 - 1 ] | while read line ; do
echo "$line" | sed "s/d/dd/g" | sed "s/x/dxd/g"
echo "$line" | sed "s/d/dd/g" | sed "s/x/xsx/g"
done
fi
}
rec $1 | tr 'dsx' ' *' </lang>
BASIC
<lang qbasic>DECLARE SUB triangle (x AS INTEGER, y AS INTEGER, length AS INTEGER, n AS INTEGER)
CLS triangle 1, 1, 16, 5
SUB triangle (x AS INTEGER, y AS INTEGER, length AS INTEGER, n AS INTEGER)
IF n = 0 THEN
LOCATE y, x: PRINT "*";
ELSE
triangle x, y + length, length / 2, n - 1
triangle x + length, y, length / 2, n - 1
triangle x + length * 2, y + length, length / 2, n - 1
END IF
END SUB</lang>
Note: The total height of the triangle is 2 * parameter length. It should be power of two so that the pattern matches evenly with the character cells. Value 16 will thus create pattern of 32 lines.
BASIC256
<lang BASIC256> clg call triangle (1, 1, 60) end
subroutine triangle (x, y, l) if l = 0 then color blue text (x, y, "*") else call triangle (x, y + l, int(l/2)) call triangle (x + l, y, int(l/2)) call triangle (x + l * 2, y + l, int(l/2)) end if end subroutine </lang>
BBC BASIC
<lang bbcbasic> MODE 8
OFF
order% = 5
PROCsierpinski(0, 0, 2^(order%-1))
REPEAT UNTIL GET
END
DEF PROCsierpinski(x%, y%, l%)
IF l% = 0 THEN
PRINT TAB(x%,y%) "*";
ELSE
PROCsierpinski(x%, y%+l%, l% DIV 2)
PROCsierpinski(x%+l%, y%, l% DIV 2)
PROCsierpinski(x%+l%+l%, y%+l%, l% DIV 2)
ENDIF
ENDPROC</lang>
FreeBASIC
<lang freebasic>sub sier(x as uinteger, y as uinteger, l as uinteger)
if l=0 then
locate y, x: print "*"
else
sier(x,y+l,l\2)
sier(x+l,y,l\2)
sier(x+2*l,y+l,l\2)
end if
end sub
cls sier(1,1,2^3)</lang>
IS-BASIC
<lang IS-BASIC>100 PROGRAM "Triangle.bas" 110 TEXT 40 120 CALL TRIANGLE(1,1,8) 130 DEF TRIANGLE(X,Y,L) 140 IF L=0 THEN 150 PRINT AT Y,X:"*" 160 ELSE 170 CALL TRIANGLE(X,Y+L,INT(L/2)) 180 CALL TRIANGLE(X+L,Y,INT(L/2)) 190 CALL TRIANGLE(X+2*L,Y+L,INT(L/2)) 200 END IF 210 END DEF</lang>
BCPL
<lang BCPL>get "libhdr"
manifest $( SIZE = 1 << 4 $)
let start() be $( for y = SIZE-1 to 0 by -1 do
$( for i=1 to y do wrch(' ')
for x=0 to SIZE-y-1 do
writes((x & y) ~= 0 -> " ", "** ")
wrch('*N')
$)
$)</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Befunge
This is a version of the cellular automaton (rule 90) construction. The order, N, is specified by the first number on the stack. It uses a single line of the playfield for the cell buffer, so the upper limit for N should be 5 on a standard Befunge-93 implementation. Interpreters with poor memory handling may not work with anything over 3, though, and a Befunge-98 interpreter should theoretically be unlimited.
<lang befunge>41+2>\#*1#2-#<:#\_$:1+v v:$_:#`0#\\#00#:p#->#1< >2/1\0p:2/\::>1-:>#v_1v >8#4*#*+#+,#5^#5g0:< 1 vg11<\*g11!:g 0-1:::<p< >!*+!!\0g11p\ 0p1-:#^_v @$$_\#!:#::#-^#1\$,+55<</lang>
Burlesque
<lang burlesque>{JPp{
-.'sgve!
J{JL[2./+.' j.*PppP.+PPj.+}m[
j{J" "j.+.+}m[
.+
}{vv{"*"}}PPie} 's sv 4 'sgve!unsh</lang>
BQN
<lang bqn>Sierp ← {" •" ⊏˜ (⌽↕2⋆𝕩)⌽˘∾˘∾⟜0¨∧´∘∨⌜˜⥊↕2⥊˜𝕩}</lang>
- Output:
Sierp 3
┌─
╵" •
• •
• •
• • • •
• •
• • • •
• • • •
• • • • • • • • "
┘
C
<lang C>#include <stdio.h>
- define SIZE (1 << 4)
int main() { int x, y, i; for (y = SIZE - 1; y >= 0; y--, putchar('\n')) { for (i = 0; i < y; i++) putchar(' '); for (x = 0; x + y < SIZE; x++) printf((x & y) ? " " : "* "); } return 0; }</lang>
Automaton
This solution uses a cellular automaton (rule 90) with a proper initial status. <lang c>#include <stdio.h>
- include <stdlib.h>
- include <stdbool.h>
- include <string.h>
- ifndef _POSIX_C_SOURCE
char *strdup(const char *s) {
int l = strlen(s); char *r = malloc(l+1); memcpy(r, s, l+1); return r;
}
- endif
- define truth(X) ((X)=='*'?true:false)
void rule_90(char *evstr) {
int i; int l = strlen(evstr); bool s[3]; char *cp = strdup(evstr);
for(i=0;i < l; i++) {
s[1] = truth(cp[i]);
s[0] = (i-1) < 0 ? false : truth(cp[i-1]);
s[2] = (i+1) < l ? truth(cp[i+1]) : false;
if ( (s[0] && !s[2]) || (!s[0] && s[2]) ) {
evstr[i] = '*';
} else {
evstr[i] = ' ';
}
}
free(cp);
}</lang>
<lang c>void sierpinski_triangle(int n) {
int i; int l = 1<<(n+1); char *b = malloc(l+1);
memset(b, ' ', l); b[l] = 0; b[l>>1] = '*';
printf("%s\n", b);
for(i=0; i < l/2-1;i++) {
rule_90(b);
printf("%s\n", b);
}
free(b);
}</lang>
<lang c>int main() {
sierpinski_triangle(4); return EXIT_SUCCESS;
}</lang>
C#
<lang csharp>using System; using System.Collections;
namespace RosettaCode {
class SierpinskiTriangle {
int len;
BitArray b;
public SierpinskiTriangle(int n) {
if (n < 1) {
throw new ArgumentOutOfRangeException("Order must be greater than zero");
}
len = 1 << (n+1);
b = new BitArray(len+1, false);
b[len>>1] = true;
}
public void Display() {
for (int j = 0; j < len / 2; j++) {
for (int i = 0; i < b.Count; i++) {
Console.Write("{0}", b[i] ? "*" : " ");
}
Console.WriteLine();
NextGen();
}
}
private void NextGen() {
BitArray next = new BitArray(b.Count, false);
for (int i = 0; i < b.Count; i++) {
if (b[i]) {
next[i - 1] = next[i - 1] ^ true;
next[i + 1] = next[i + 1] ^ true;
}
}
b = next;
}
}
}</lang>
<lang csharp>namespace RosettaCode {
class Program {
static void Main(string[] args) {
SierpinskiTriangle t = new SierpinskiTriangle(4);
t.Display();
}
}
}</lang>
<lang csharp>using static System.Console; class Sierpinsky {
static void Main(string[] args)
{
int order;
if(!int.TryParse(args.Length > 0 ? args[0] : "", out order)) order = 4;
int size = (1 << order);
for (int y = size - 1; y >= 0; y--, WriteLine())
{
for (int i = 0; i < y; i++) Write(' ');
for (int x = 0; x + y < size; x++)
Write((x & y) != 0 ? " " : "* ");
}
}
}</lang>
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
class Program {
public static List<String> Sierpinski(int n)
{
var lines = new List<string> { "*" };
string space = " ";
for (int i = 0; i < n; i++)
{
lines = lines.Select(x => space + x + space)
.Concat(lines.Select(x => x + " " + x)).ToList();
space += space;
}
return lines; }
static void Main(string[] args)
{
foreach (string s in Sierpinski(4))
Console.WriteLine(s);
}
}</lang>
Or, with fold / reduce (a.k.a. aggregate):
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
class Program {
static List<string> Sierpinski(int n)
{
return Enumerable.Range(0, n).Aggregate( new List<string>(){"*"}, (p, i) => { string SPACE = " ".PadRight((int)Math.Pow(2, i));
var temp = new List<string>(from x in p select SPACE + x + SPACE); temp.AddRange(from x in p select x + " " + x);
return temp; } );
}
static void Main ()
{
foreach(string s in Sierpinski(4)) { Console.WriteLine(s); }
}
}</lang>
C++
A STL-centric recursive solution that uses the new lambda functions in C++11. <lang cpp>#include <iostream>
- include <string>
- include <list>
- include <algorithm>
- include <iterator>
using namespace std;
template<typename OutIt> void sierpinski(int n, OutIt result) {
if( n == 0 )
{
*result++ = "*";
}
else
{
list<string> prev;
sierpinski(n-1, back_inserter(prev));
string sp(1 << (n-1), ' ');
result = transform(prev.begin(), prev.end(),
result,
[sp](const string& x) { return sp + x + sp; });
transform(prev.begin(), prev.end(),
result,
[sp](const string& x) { return x + " " + x; });
}
}
int main() {
sierpinski(4, ostream_iterator<string>(cout, "\n")); return 0;
}</lang>
Clojure
With a touch of Clojure's sequence handling. <lang clojure>(ns example
(:require [clojure.contrib.math :as math]))
- Length of integer in binary
- (copied from a private multimethod in clojure.contrib.math)
(defmulti #^{:private true} integer-length class)
(defmethod integer-length java.lang.Integer [n]
(count (Integer/toBinaryString n)))
(defmethod integer-length java.lang.Long [n]
(count (Long/toBinaryString n)))
(defmethod integer-length java.math.BigInteger [n]
(count (.toString n 2)))
(defn sierpinski-triangle [order]
(loop [size (math/expt 2 order)
v (math/expt 2 (- size 1))]
(when (pos? size)
(println
(apply str (map #(if (bit-test v %) "*" " ")
(range (integer-length v)))))
(recur
(dec size)
(bit-xor (bit-shift-left v 1) (bit-shift-right v 1))))))
(sierpinski-triangle 4)</lang>
CLU
<lang clu>sierpinski = proc (size: int) returns (string)
ss: stream := stream$create_output()
for i: int in int$from_to(0, size*4-1) do
c: int := 1
for j: int in int$from_to(1, size*4-1-i) do
stream$putc(ss, ' ')
end
for k: int in int$from_to(0, i) do
if c//2=0 then
stream$puts(ss, " ")
else
stream$puts(ss, " *")
end
c := c*(i-k)/(k+1)
end
stream$putc(ss, '\n')
end
return(stream$get_contents(ss))
end sierpinski
start_up = proc ()
stream$puts(
stream$primary_output(),
sierpinski(4)
)
end start_up</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
COBOL
and retains a more Fortran-like coding style than is really idiomatic in COBOL.
<lang cobol>identification division. program-id. sierpinski-triangle-program. data division. working-storage section. 01 sierpinski.
05 n pic 99. 05 i pic 999. 05 k pic 999. 05 m pic 999. 05 c pic 9(18). 05 i-limit pic 999. 05 q pic 9(18). 05 r pic 9.
procedure division. control-paragraph.
move 4 to n. multiply n by 4 giving i-limit. subtract 1 from i-limit. perform sierpinski-paragraph varying i from 0 by 1 until i is greater than i-limit. stop run.
sierpinski-paragraph.
subtract i from i-limit giving m. multiply m by 2 giving m. perform m times, display space with no advancing, end-perform. move 1 to c. perform inner-loop-paragraph varying k from 0 by 1 until k is greater than i. display .
inner-loop-paragraph.
divide c by 2 giving q remainder r. if r is equal to zero then display ' * ' with no advancing. if r is not equal to zero then display ' ' with no advancing. compute c = c * (i - k) / (k + 1).</lang>
Common Lisp
<lang lisp>(defun print-sierpinski (order)
(loop with size = (expt 2 order)
repeat size
for v = (expt 2 (1- size)) then (logxor (ash v -1) (ash v 1))
do (fresh-line)
(loop for i below (integer-length v)
do (princ (if (logbitp i v) "*" " ")))))</lang>
Printing each row could also be done by printing the integer in base 2 and replacing zeroes with spaces: (princ (substitute #\Space #\0 (format nil "~%~2,vR" (1- (* 2 size)) v)))
Replacing the iteration with for v = 1 then (logxor v (ash v 1)) produces a "right" triangle instead of an "equilateral" one.
Alternate approach:
<lang lisp>(defun sierpinski (n)
(if (= n 0) '("*")
(nconc (mapcar (lambda (e) (format nil "~A~A~0@*~A" (make-string (expt 2 (1- n)) :initial-element #\ ) e)) (sierpinski (1- n)))
(mapcar (lambda (e) (format nil "~A ~A" e e)) (sierpinski (1- n))))))
(mapc #'print (sierpinski 4))</lang>
Cowgol
<lang cowgol>include "cowgol.coh"; include "argv.coh";
var order: uint8 := 4; # default order
- Read order from command line if there is an argument
ArgvInit(); var argmt := ArgvNext(); if argmt != 0 as [uint8] then
var a: int32;
(a, argmt) := AToI(argmt);
if a<3 or 7<a then
print("Order must be between 3 and 7.");
print_nl();
ExitWithError();
end if;
order := a as uint8;
end if;
var one: uint8 := 1; # shift argument can't be constant... var size: uint8 := one << order;
var y: uint8 := size; while y > 0 loop
var x: uint8 := 0;
while x < y-1 loop
print_char(' ');
x := x + 1;
end loop;
x := 0;
while x + y <= size loop
if x & (y-1) != 0 then
print(" ");
else
print("* ");
end if;
x := x + 1;
end loop;
print_nl();
y := y - 1;
end loop;</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
D
Run-time Version
<lang d>void main() /*@safe*/ {
import std.stdio, std.algorithm, std.string, std.array;
enum level = 4;
auto d = ["*"];
foreach (immutable n; 0 .. level) {
immutable sp = " ".replicate(2 ^^ n);
d = d.map!(a => sp ~ a ~ sp).array ~
d.map!(a => a ~ " " ~ a).array;
}
d.join('\n').writeln;
}</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Compile-time Version
Same output. <lang d>import std.string, std.range, std.algorithm;
string sierpinski(int level) pure nothrow /*@safe*/ {
auto d = ["*"];
foreach (immutable i; 0 .. level) {
immutable sp = " ".replicate(2 ^^ i);
d = d.map!(a => sp ~ a ~ sp).array ~
d.map!(a => a ~ " " ~ a).array;
}
return d.join('\n');
}
pragma(msg, 4.sierpinski); void main() {}</lang>
Simple Version
Same output. <lang d>void showSierpinskiTriangle(in uint order) nothrow @safe @nogc {
import core.stdc.stdio: putchar;
foreach_reverse (immutable y; 0 .. 2 ^^ order) {
foreach (immutable _; 0 .. y)
' '.putchar;
foreach (immutable x; 0 .. 2 ^^ order - y) {
putchar((x & y) ? ' ' : '*');
' '.putchar;
}
'\n'.putchar;
}
}
void main() nothrow @safe @nogc {
4.showSierpinskiTriangle;
}</lang>
Alternative Version
This uses a different algorithm and shows a different output. <lang d>import core.stdc.stdio: putchar; import std.algorithm: swap;
void showSierpinskiTriangle(in uint nLevels) nothrow @safe
in {
assert(nLevels > 0);
} body {
alias Row = bool[];
static void applyRules(in Row r1, Row r2) pure nothrow @safe @nogc {
r2[0] = r1[0] || r1[1];
r2[$ - 1] = r1[$ - 2] || r1[$ - 1];
foreach (immutable i; 1 .. r2.length - 1)
r2[i] = r1[i - 1] != r1[i] || r1[i] != r1[i + 1];
}
static void showRow(in Row r) nothrow @safe @nogc {
foreach (immutable b; r)
putchar(b ? '#' : ' ');
'\n'.putchar;
}
immutable width = 2 ^^ (nLevels + 1) - 1; auto row1 = new Row(width); auto row2 = new Row(width); row1[width / 2] = true;
foreach (immutable _; 0 .. 2 ^^ nLevels) {
showRow(row1);
applyRules(row1, row2);
row1.swap(row2);
}
}
void main() @safe nothrow {
foreach (immutable i; 1 .. 6) {
i.showSierpinskiTriangle;
'\n'.putchar;
}
}</lang>
- Output:
#
###
#
###
## ##
#######
#
###
## ##
#######
## ##
#### ####
## ## ## ##
###############
#
###
## ##
#######
## ##
#### ####
## ## ## ##
###############
## ##
#### ####
## ## ## ##
######## ########
## ## ## ##
#### #### #### ####
## ## ## ## ## ## ## ##
###############################
#
###
## ##
#######
## ##
#### ####
## ## ## ##
###############
## ##
#### ####
## ## ## ##
######## ########
## ## ## ##
#### #### #### ####
## ## ## ## ## ## ## ##
###############################
## ##
#### ####
## ## ## ##
######## ########
## ## ## ##
#### #### #### ####
## ## ## ## ## ## ## ##
################ ################
## ## ## ##
#### #### #### ####
## ## ## ## ## ## ## ##
######## ######## ######## ########
## ## ## ## ## ## ## ##
#### #### #### #### #### #### #### ####
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
###############################################################
Delphi
<lang delphi>program SierpinskiTriangle;
{$APPTYPE CONSOLE}
procedure PrintSierpinski(order: Integer); var
x, y, size: Integer;
begin
size := (1 shl order) - 1;
for y := size downto 0 do
begin
Write(StringOfChar(' ', y));
for x := 0 to size - y do
begin
if (x and y) = 0 then
Write('* ')
else
Write(' ');
end;
Writeln;
end;
end;
begin
PrintSierpinski(4);
end.</lang>
Draco
<lang draco>word SIZE = 1 << 4;
proc nonrec main() void:
unsigned SIZE x, y;
for y from SIZE-1 downto 0 do
for x from 1 upto y do write(' ') od;
for x from 0 upto SIZE - y - 1 do
write(if x & y ~= 0 then " " else "* " fi)
od;
writeln()
od
corp</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
DWScript
<lang delphi>procedure PrintSierpinski(order : Integer); var
x, y, size : Integer;
begin
size := (1 shl order)-1;
for y:=size downto 0 do begin
Print(StringOfChar(' ', y));
for x:=0 to size-y do begin
if (x and y)=0 then
Print('* ')
else Print(' ');
end;
PrintLn();
end;
end;
PrintSierpinski(4); </lang>
E
<lang e>def printSierpinski(order, out) {
def size := 2**order
for y in (0..!size).descending() {
out.print(" " * y)
for x in 0..!(size-y) {
out.print((x & y).isZero().pick("* ", " "))
}
out.println()
}
}</lang>
<lang e>? printSierpinski(4, stdout)</lang>
Non-ASCII version (quality of results will depend greatly on text renderer): <lang e>def printSierpinski(order, out) {
def size := 2**order
for y in (0..!size).descending() {
out.print(" " * y)
for x in 0..!(size-y) {
out.print((x & y).isZero().pick("◢◣", " "))
}
out.println()
}
}</lang>
Elixir
<lang elixir>defmodule RC do
def sierpinski_triangle(n) do
f = fn(x) -> IO.puts "#{x}" end
Enum.each(triangle(n, ["*"], " "), f)
end
defp triangle(0, down, _), do: down
defp triangle(n, down, sp) do
newDown = (for x <- down, do: sp<>x<>sp) ++ (for x <- down, do: x<>" "<>x)
triangle(n-1, newDown, sp<>sp)
end
end
RC.sierpinski_triangle(4)</lang>
Elm
<lang elm>import String exposing (..) import Html exposing (..) import Html.Attributes as A exposing (..) import Html.Events exposing (..) import Html.App exposing (beginnerProgram) import Result exposing (..)
sierpinski : Int -> List String sierpinski n =
let down n = sierpinski (n - 1)
space n = repeat (2 ^ (n - 1)) " "
in case n of
0 -> ["*"]
_ -> List.map ((\st -> space n ++ st) << (\st -> st ++ space n)) (down n)
++ List.map (join " " << List.repeat 2) (down n)
main = beginnerProgram { model = "4", view = view, update = update }
update newStr oldStr = newStr
view : String -> Html String view levelString =
div []
([ Html.form
[]
[ label [ myStyle ] [ text "Level: "]
, input
[ placeholder "triangle level."
, value levelString
, on "input" targetValue
, type' "number"
, A.min "0"
, myStyle
]
[]
]
] ++
[ pre [] (levelString
|> toInt
|> withDefault 0
|> sierpinski
|> List.map (\s -> div [] [text s]))
])
myStyle : Attribute msg myStyle =
style
[ ("height", "20px")
, ("padding", "5px 0 0 5px")
, ("font-size", "1em")
, ("text-align", "left")
]</lang>
Link to live demo: http://dc25.github.io/sierpinskiElm/
Erlang
<lang erlang>-module(sierpinski). -export([triangle/1]).
triangle(N) ->
F = fun(X) -> io:format("~s~n",[X]) end,
lists:foreach(F, triangle(N, ["*"], " ")).
triangle(0, Down, _) -> Down; triangle(N, Down, Sp) ->
NewDown = [Sp++X++Sp || X<-Down]++[X++" "++X || X <- Down], triangle(N-1, NewDown, Sp++Sp).</lang>
Euphoria
<lang euphoria>procedure triangle(integer x, integer y, integer len, integer n)
if n = 0 then
position(y,x) puts(1,'*')
else
triangle (x, y+len, floor(len/2), n-1)
triangle (x+len, y, floor(len/2), n-1)
triangle (x+len*2, y+len, floor(len/2), n-1)
end if
end procedure
clear_screen() triangle(1,1,8,4)</lang>
Excel
LAMBDA
Binding the names sierpinskiTriangle, sierpCentered and sierpDoubled to the following lambda expressions in the Name Manager of the Excel WorkBook:
(See LAMBDA: The ultimate Excel worksheet function)
<lang lisp>sierpinskiTriangle =LAMBDA(c,
LAMBDA(n,
IF(0 = n,
c,
LET(
prev, sierpinskiTriangle(c)(n - 1),
APPENDROWS(
sierpCentered(prev)
)(
sierpDoubled(prev)
)
)
)
)
)
sierpCentered
=LAMBDA(grid,
LET(
nRows, ROWS(grid),
padding, IF(
SEQUENCE(nRows, nRows, 1, 1),
" "
),
APPENDCOLS(
APPENDCOLS(padding)(grid)
)(padding)
)
)
sierpDoubled
=LAMBDA(grid,
APPENDCOLS(
APPENDCOLS(grid)(
IF(SEQUENCE(ROWS(grid), 1, 1, 1),
" "
)
)
)(grid)
)</lang>
and also assuming the following generic bindings in the Name Manager for the WorkBook:
<lang lisp>APPENDCOLS =LAMBDA(xs,
LAMBDA(ys,
LET(
nx, COLUMNS(xs),
colIndexes, SEQUENCE(1, nx + COLUMNS(ys)),
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()
)
)
)
)
gridString
=LAMBDA(grid,
LET(
ixCol, SEQUENCE(ROWS(grid), 1, 1, 1),
CHAR(10) & CONCAT(
APPENDCOLS(
IF(ixCol, " ")
)(
APPENDCOLS(grid)(
IF(ixCol, CHAR(10))
)
)
)
)
)</lang>
- Output:
As grids:
(Each formula in the B column (adjacent to an integer in the A column) defines an array which populates a whole grid (for example the range B12:P19) with a Sierpinski triangle).
| fx | =sierpinskiTriangle("▲")(A2) | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | ||
| 1 | |||||||||||||||||
| 2 | 0 | ▲ | |||||||||||||||
| 3 | |||||||||||||||||
| 4 | 1 | ▲ | |||||||||||||||
| 5 | ▲ | ▲ | |||||||||||||||
| 6 | |||||||||||||||||
| 7 | 2 | ▲ | |||||||||||||||
| 8 | ▲ | ▲ | |||||||||||||||
| 9 | ▲ | ▲ | |||||||||||||||
| 10 | ▲ | ▲ | ▲ | ▲ | |||||||||||||
| 11 | |||||||||||||||||
| 12 | 3 | ▲ | |||||||||||||||
| 13 | ▲ | ▲ | |||||||||||||||
| 14 | ▲ | ▲ | |||||||||||||||
| 15 | ▲ | ▲ | ▲ | ▲ | |||||||||||||
| 16 | ▲ | ▲ | |||||||||||||||
| 17 | ▲ | ▲ | ▲ | ▲ | |||||||||||||
| 18 | ▲ | ▲ | ▲ | ▲ | |||||||||||||
| 19 | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | ▲ | |||||||||
or as strings, using a monospaced font, and the wrap text alignment setting in Excel:
| fx | =gridString(sierpinskiTriangle("*")(A2)) | ||
|---|---|---|---|
| A | B | ||
| 1 | Iterations | Sierpinski Triangle | |
| 2 | 0 |
* | |
| 3 | 1 |
* * * | |
| 4 | 2 |
*
* *
* *
* * * *
| |
| 5 | 3 |
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
| |
| 6 | 4 |
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
| |
F#
<lang fsharp>let sierpinski n =
let rec loop down space n =
if n = 0 then
down
else
loop (List.map (fun x -> space + x + space) down @
List.map (fun x -> x + " " + x) down)
(space + space)
(n - 1)
in loop ["*"] " " n
let () =
List.iter (fun (i:string) -> System.Console.WriteLine(i)) (sierpinski 4)</lang>
Factor
<lang factor>USING: io kernel math sequences ; IN: sierpinski
- iterate-triangle ( triange spaces -- triangle' )
[ [ dup surround ] curry map ] [ drop [ dup " " glue ] map ] 2bi append ;
- (sierpinski) ( triangle spaces n -- triangle' )
dup 0 = [ 2drop "\n" join ] [
[
[ iterate-triangle ]
[ nip dup append ] 2bi
] dip 1 - (sierpinski)
] if ;
- sierpinski ( n -- )
[ { "*" } " " ] dip (sierpinski) print ;</lang>
FALSE
<lang false>[[$][$1&["*"]?$~1&[" "]?2/]#%" "]s: { stars } [$@$@|@@&~&]x: { xor } [1\[$][1-\2*\]#%]e: { 2^n } [e;!1\[$][\$s;!$2*x;!\1-]#%%]t: 4t;!</lang>
FOCAL
<lang FOCAL>01.10 A "ORDER",O;S S=2^(O+1) 01.20 F X=0,S;S L(X)=0 01.30 S L(S/2)=1 01.40 F I=1,S/2;D 2;D 3 01.90 Q
02.10 F X=1,S-1;D 2.3 02.20 T !;R 02.30 I (L(X)),2.4,2.5 02.40 T " " 02.50 T "*"
03.10 F X=0,S;S K(X)=FABS(L(X-1)-L(X+1)) 03.20 F X=0,S;S L(X)=K(X)</lang>
- Output:
ORDER:4
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Forth
<lang forth>: stars ( mask -- )
begin dup 1 and if [char] * else bl then emit 1 rshift dup while space repeat drop ;
- triangle ( order -- )
1 swap lshift ( 2^order ) 1 over 0 do cr over i - spaces dup stars dup 2* xor loop 2drop ;
5 triangle</lang>
Fortran
This method calculates a Pascal's triangle and replaces every odd number with a * and every even number with a space. The limitation of this approach is the size of the numbers in the Pascal's triangle. Tryng to print an order 8 Sierpinski's triangle will overflow a 32 bit integer and an order 16 will overflow a 64 bit integer. <lang fortran>program Sierpinski_triangle
implicit none call Triangle(4)
contains
subroutine Triangle(n)
implicit none
integer, parameter :: i64 = selected_int_kind(18)
integer, intent(in) :: n
integer :: i, k
integer(i64) :: c
do i = 0, n*4-1
c = 1
write(*, "(a)", advance="no") repeat(" ", 2 * (n*4 - 1 - i))
do k = 0, i
if(mod(c, 2) == 0) then
write(*, "(a)", advance="no") " "
else
write(*, "(a)", advance="no") " * "
end if
c = c * (i - k) / (k + 1)
end do
write(*,*)
end do
end subroutine Triangle end program Sierpinski_triangle</lang>
GAP
<lang gap># Using parity of binomial coefficients SierpinskiTriangle := function(n) local i, j, s, b; n := 2^n - 1; b := " "; while Size(b) < n do b := Concatenation(b, b); od; for i in [0 .. n] do s := ""; for j in [0 .. i] do if IsEvenInt(Binomial(i, j)) then Append(s, " "); else Append(s, "* "); fi; od; Print(b{[1 .. n - i]}, s, "\n"); od; end;
SierpinskiTriangle(4);
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
- * * * * * * * * * * * * * * * </lang>
gnuplot
Making and printing a text string, using bit-twiddling to decide whether each character should be a space or a star.
<lang gnuplot># Return a string space or star to print at x,y.
- Must have x<y. x<0 is the left side of the triangle.
- If x<-y then it's before the left edge and the return is a space.
char(x,y) = (y+x>=0 && ((y+x)%2)==0 && ((y+x)&(y-x))==0 ? "*" : " ")
- Return a string which is row y of the triangle from character
- position x through to the right hand end x==y, inclusive.
row(x,y) = (x<=y ? char(x,y).row(x+1,y) : "\n")
- Return a string of stars, spaces and newlines which is the
- Sierpinski triangle from row y to limit, inclusive.
- The first row is y=0.
triangle(y,limit) = (y <= limit ? row(-limit,y).triangle(y+1,limit) : "")
- Print rows 0 to 15, which is the order 4 triangle per the task.
print triangle(0,15)</lang>
Go
"Δ" (Greek capital letter delta) looks good for grain, as does Unicode triangle, "△". ASCII "." and "^" are pleasing. "/\\", "´`", and "◢◣"" make interesting wide triangles. <lang go>package main
import (
"fmt" "strings" "unicode/utf8"
)
var order = 4 var grain = "*"
func main() {
t := []string{grain + strings.Repeat(" ", utf8.RuneCountInString(grain))}
for ; order > 0; order-- {
sp := strings.Repeat(" ", utf8.RuneCountInString(t[0])/2)
top := make([]string, len(t))
for i, s := range t {
top[i] = sp + s + sp
t[i] += s
}
t = append(top, t...)
}
for _, r := range t {
fmt.Println(r)
}
}</lang>
Golfscript
Cambia el "3" a un número mayor para un triángulo más grande. <lang golfscript>' /\ /__\ '4/){.+\.{[2$.]*}%\{.+}%+\}3*;n*</lang>
- Output:
/\
/__\
/\ /\
/__\/__\
/\ /\
/__\ /__\
/\ /\ /\ /\
/__\/__\/__\/__\
/\ /\
/__\ /__\
/\ /\ /\ /\
/__\/__\ /__\/__\
/\ /\ /\ /\
/__\ /__\ /__\ /__\
/\ /\ /\ /\ /\ /\ /\ /\
/__\/__\/__\/__\/__\/__\/__\/__\
Groovy
Solution: <lang groovy>def stPoints; stPoints = { order, base=[0,0] ->
def right = [base[0], base[1]+2**order]
def up = [base[0]+2**(order-1), base[1]+2**(order-1)]
(order == 0) \
? [base]
: (stPoints(order-1, base) + stPoints(order-1, right) + stPoints(order-1, up))
}
def stGrid = { order ->
def h = 2**order
def w = 2**(order+1) - 1
def grid = (0..<h).collect { (0..<w).collect { ' ' } }
stPoints(order).each { grid[it[0]][it[1]] = (order%10).toString() }
grid
}</lang>
Test: <lang groovy>stGrid(0).reverse().each { println it.sum() } println() stGrid(1).reverse().each { println it.sum() } println() stGrid(2).reverse().each { println it.sum() } println() stGrid(3).reverse().each { println it.sum() } println() stGrid(4).reverse().each { println it.sum() } println() stGrid(5).reverse().each { println it.sum() } println() stGrid(6).reverse().each { println it.sum() }</lang>
- Output:
0
1
1 1
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
4
4 4
4 4
4 4 4 4
4 4
4 4 4 4
4 4 4 4
4 4 4 4 4 4 4 4
4 4
4 4 4 4
4 4 4 4
4 4 4 4 4 4 4 4
4 4 4 4
4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
5
5 5
5 5
5 5 5 5
5 5
5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5
5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5
5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
6
6 6
6 6
6 6 6 6
6 6
6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6
6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6
6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6
6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
Haskell
<lang haskell>sierpinski 0 = ["*"] sierpinski n = map ((space ++) . (++ space)) down ++
map (unwords . replicate 2) down
where down = sierpinski (n - 1)
space = replicate (2 ^ (n - 1)) ' '
main = mapM_ putStrLn $ sierpinski 4</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
We can see how the approach above (centering a preceding block over two duplicates) generates a framing rectangle at each stage, by making the right padding (plus the extra space between duplicates) more distinct and visible: <lang haskell>import Data.List (intercalate)
sierpinski :: Int -> [String] sierpinski 0 = ["▲"] sierpinski n =
[ flip
intercalate
([replicate (2 ^ (n - 1))] <*> " -"),
(<>) <*> ('+' :)
]
>>= (<$> sierpinski (n - 1))
main :: IO () main = mapM_ putStrLn $ sierpinski 4</lang>
- Output:
▲---------------
▲+▲--------------
▲-+ ▲-------------
▲+▲+▲+▲------------
▲---+ ▲-----------
▲+▲--+ ▲+▲----------
▲-+ ▲-+ ▲-+ ▲---------
▲+▲+▲+▲+▲+▲+▲+▲--------
▲-------+ ▲-------
▲+▲------+ ▲+▲------
▲-+ ▲-----+ ▲-+ ▲-----
▲+▲+▲+▲----+ ▲+▲+▲+▲----
▲---+ ▲---+ ▲---+ ▲---
▲+▲--+ ▲+▲--+ ▲+▲--+ ▲+▲--
▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-
▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲
Using bitwise and between x and y coords:
<lang haskell>import Data.Bits ((.&.))
sierpinski n = map row [m, m-1 .. 0] where m = 2^n - 1 row y = replicate y ' ' ++ concatMap cell [0..m - y] where cell x | y .&. x == 0 = " *" | otherwise = " "
main = mapM_ putStrLn $ sierpinski 4</lang>
<lang Haskell>import Data.List (intersperse)
-- Top down, each row after the first is an XOR / Rule90 rewrite. -- Bottom up, each line above the base is indented 1 more space. sierpinski :: Int -> String sierpinski = fst . foldr spacing ([], []) . rule90 . (2 ^)
where
rule90 = scanl next "*" . enumFromTo 1 . subtract 1
where
next =
const
. ( (zipWith xor . (' ' :))
<*> (<> " ")
)
xor l r
| l == r = ' '
| otherwise = '*'
spacing x (s, w) =
( concat
[w, intersperse ' ' x, "\n", s],
w <> " "
)
main :: IO () main = putStr $ sierpinski 4</lang>
Or simply as a right fold:
<lang haskell>sierpinski :: Int -> [String] sierpinski n =
foldr
( \i xs ->
let s = replicate (2 ^ i) ' '
in fmap ((s <>) . (<> s)) xs
<> fmap
( (<>)
<*> (' ' :)
)
xs
)
["*"]
[n - 1, n - 2 .. 0]
main :: IO () main = (putStrLn . unlines . sierpinski) 4</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Haxe
<lang haxe>class Main { static function main() { triangle(3); }
static inline var SPACE = ' '; static inline var STAR = '*';
static function triangle(o) { var n = 1 << o; var line = new Array<String>();
for (i in 0...(n*2)) line[i] = SPACE;
line[n] = '*';
for (i in 0...n) { Sys.println(line.join()); var u ='*'; var start = n - i; var end = n + i + 1; var t = SPACE; for (j in start...end) { t = (line[j-1] == line[j+1] ? SPACE : STAR); line[j-1] = u; u = t; }
line[n+i] = t; line[n+i+1] = STAR; } } }</lang>
Hoon
<lang Hoon>|= n=@ud =+ m=0 =+ o=(reap 1 '*') |^ ?: =(m n) o
$(m +(m), o (weld top bot))
++ gap (fil 3 (pow 2 m) ' ') ++ top (turn o |=(l=@t (rap 3 gap l gap ~))) ++ bot (turn o |=(l=@t (rap 3 l ' ' l ~))) --</lang>
Icon and Unicon
This is a text based adaption of a program from the IPL and Icon Graphics book. The triangle is presented with a twist. Based on an idea from "Chaos and Fractals" by Peitgen, Jurgens, and Saupe. <lang Icon># text based adaptaion of
procedure main(A)
width := 2 ^ ( 1 + (order := 0 < integer(\A[1]) | 4)) # order of arg[1] or 4
write("Triangle order= ",order)
every !(canvas := list(width)) := list(width," ") # prime the canvas
every y := 1 to width & x := 1 to width do # traverse it
if iand(x - 1, y - 1) = 0 then canvas[x,y] := "*" # fill
every x := 1 to width & y := 1 to width do
writes((y=1,"\n")|"",canvas[x,y]," ") # print
end</lang>
Adapted from graphics/sier1.icn
- Sample output for order 3:
Triangle order = 2 * * * * * * * * * * * * * * * * * * * * * * * * * * *
IDL
The only 'special' thing here is that the math is done in a byte array, filled with the numbers 32 and 42 and then output through a "string(array)" which prints the ascii representation of each individual element in the array. <lang idl>pro sierp,n
s = (t = bytarr(3+2^(n+1))+32b)
t[2^n+1] = 42b
for lines = 1,2^n do begin
print,string( (s = t) )
for i=1,n_elements(t)-2 do if s[i-1] eq s[i+1] then t[i]=32b else t[i]=42b
end
end</lang>
J
There are any number of succinct ways to produce this in J. Here's one that exploits self-similarity: <lang j> |. _31]\ ,(,.~ , ])^:4 ,: '* '</lang>
Here, (,.~ , ])^:4 ,: '* ' is the basic structure (with 4 iterations) and the rest of it is just formatting.
Here's one that leverages the relationship between Sierpinski's and Pascal's triangles: <lang j> ' *' {~ '1' = (- |."_1 [: ": 2 | !/~) i._16</lang>
Here, !/~ i._16 gives us pascal's triangle (and we want a power of 2 (or, for the formatting we are using here a negative of a power of 2) for the size of the square in which contains the triangle, and (2 + |/~) i._16 is a boolean representation where the 1s correspond to odd values in pascal's triangle, and the rest is just formatting.
(Aside: it's popular to say that booleans are not integers, but this is a false representation of George Boole's work.)
Java
Replace translations. Recursive solution. <lang java>
public class SierpinskiTriangle {
public static void main(String[] args) {
System.out.println(getSierpinskiTriangle(4));
}
private static final String getSierpinskiTriangle(int n) {
if ( n == 0 ) {
return "*";
}
String s = getSierpinskiTriangle(n-1);
String [] split = s.split("\n");
int length = split.length;
// Top triangle
StringBuilder sb = new StringBuilder();
String top = buildSpace((int)Math.pow(2, n-1));
for ( int i = 0 ; i < length ;i++ ) {
sb.append(top);
sb.append(split[i]);
sb.append("\n");
}
// Two triangles side by side
for ( int i = 0 ; i < length ;i++ ) {
sb.append(split[i]);
sb.append(buildSpace(length-i));
sb.append(split[i]);
sb.append("\n");
}
return sb.toString();
}
private static String buildSpace(int n) {
StringBuilder sb = new StringBuilder();
while ( n > 0 ) {
sb.append(" ");
n--;
}
return sb.toString();
}
} </lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
JavaFX Script
<lang javafx>function sierpinski(n : Integer) {
var down = ["*"];
var space = " ";
for (i in [1..n]) {
down = [for (x in down) "{space}{x}{space}", for (x in down) "{x} {x}"];
space = "{space}{space}";
}
for (x in down) {
println("{x}")
}
}
sierpinski(4);</lang>
JavaScript
ES5
Functional
Using a functional idiom of JavaScript, we can construct a Sierpinksi triangle as a Pascal triangle (mod 2), mapping the binary pattern to centred strings.
<lang JavaScript>(function (order) {
// Sierpinski triangle of order N constructed as
// Pascal triangle of 2^N rows mod 2
// with 1 encoded as "▲"
// and 0 encoded as " "
function sierpinski(intOrder) {
return function asciiPascalMod2(intRows) {
return range(1, intRows - 1)
.reduce(function (lstRows) {
var lstPrevRow = lstRows.slice(-1)[0];
// Each new row is a function of the previous row
return lstRows.concat([zipWith(function (left, right) {
// The composition ( asciiBinary . mod 2 . add )
// reduces to a rule from 2 parent characters
// to a single child character
// Rule 90 also reduces to the same XOR
// relationship between left and right neighbours
return left === right ? " " : "▲";
}, [' '].concat(lstPrevRow), lstPrevRow.concat(' '))]);
}, [
["▲"] // Tip of triangle
]);
}(Math.pow(2, intOrder))
// As centred lines, from bottom (0 indent) up (indent below + 1)
.reduceRight(function (sofar, lstLine) {
return {
triangle: sofar.indent + lstLine.join(" ") + "\n" +
sofar.triangle,
indent: sofar.indent + " "
};
}, {
triangle: "",
indent: ""
}).triangle;
};
var zipWith = function (f, xs, ys) {
return xs.length === ys.length ? xs
.map(function (x, i) {
return f(x, ys[i]);
}) : undefined;
},
range = function (m, n) {
return Array.apply(null, Array(n - m + 1))
.map(function (x, i) {
return m + i;
});
};
// TEST return sierpinski(order);
})(4); </lang>
Output (N=4)
▲
▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
Imperative
<lang javascript>function triangle(o) {
var n = 1 << o,
line = new Array(2 * n),
i, j, t, u;
for (i = 0; i < line.length; ++i) line[i] = ' ';
line[n] = '*';
for (i = 0; i < n; ++i) {
document.write(line.join() + "\n");
u = '*';
for (j = n - i; j < n + i + 1; ++j) {
t = (line[j - 1] == line[j + 1] ? ' ' : '*');
line[j - 1] = u;
u = t;
}
line[n + i] = t;
line[n + i + 1] = '*';
}
}
document.write("
\n");
triangle(6);
document.write("");</lang>
ES6
Directly in terms of the built-in Array methods .map, .reduce, and .from, and without much abstraction, possibly at the cost of some legibility: <lang javascript>(() => {
'use strict';
// sierpinski :: Int -> String
const sierpinski = n =>
Array.from({
length: n
})
.reduce(
(xs, _, i) => {
const s = ' '.repeat(Math.pow(2, i));
return xs.map(x => s + x + s)
.concat(
xs.map(x => x + ' ' + x)
)
},
['*']
).join('\n');
// TEST -------------------------------------------
console.log(
sierpinski(4)
);
})();</lang>
Centering any preceding triangle block over two adjacent duplicates: <lang JavaScript>(() => {
'use strict';
// LINES OF SIERPINSKI TRIANGLE AT LEVEL N -------------------------------
// sierpinski :: Int -> [String]
const sierpTriangle = n =>
// Previous triangle centered with left and right padding,
(n > 0) ? concat(ap([
map(xs => intercalate(xs, ap(
[s => concat(replicate(Math.pow(2, (n - 1)), s))], [' ', '-']
))),
// above a pair of duplicates, placed one character apart.
map(xs => intercalate('+', [xs, xs]))
], [sierpTriangle(n - 1)])) : ['▲'];
// GENERIC FUNCTIONS -----------------------------------------------------
// replicate :: Int -> a -> [a]
const replicate = (n, a) => {
let v = [a],
o = [];
if (n < 1) return o;
while (n > 1) {
if (n & 1) o = o.concat(v);
n >>= 1;
v = v.concat(v);
}
return o.concat(v);
};
// curry :: ((a, b) -> c) -> a -> b -> c const curry = f => a => b => f(a, b);
// map :: (a -> b) -> [a] -> [b] const map = curry((f, xs) => xs.map(f));
// Apply a list of functions to a list of arguments
// <*> :: [(a -> b)] -> [a] -> [b]
const ap = (fs, xs) => //
[].concat.apply([], fs.map(f => //
[].concat.apply([], xs.map(x => [f(x)]))));
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
// intercalate :: String -> [a] -> String const intercalate = (s, xs) => xs.join(s);
// concat :: a -> [a] || [String] -> String const concat = xs => { if (xs.length > 0) { const unit = typeof xs[0] === 'string' ? : []; return unit.concat.apply(unit, xs); } else return []; };
// TEST ------------------------------------------------------------------ return unlines(sierpTriangle(4));
})();</lang>
- Output:
▲---------------
▲+▲--------------
▲-+ ▲-------------
▲+▲+▲+▲------------
▲---+ ▲-----------
▲+▲--+ ▲+▲----------
▲-+ ▲-+ ▲-+ ▲---------
▲+▲+▲+▲+▲+▲+▲+▲--------
▲-------+ ▲-------
▲+▲------+ ▲+▲------
▲-+ ▲-----+ ▲-+ ▲-----
▲+▲+▲+▲----+ ▲+▲+▲+▲----
▲---+ ▲---+ ▲---+ ▲---
▲+▲--+ ▲+▲--+ ▲+▲--+ ▲+▲--
▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-
▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲
Or constructed as 2^N lines of Pascal's triangle mod 2, and mapped to centred {1:asterisk, 0:space} strings. <lang JavaScript> (order => {
// sierpinski :: Int -> [Bool]
let sierpinski = intOrder => {
// asciiPascalMod2 :: Int -> Int let asciiPascalMod2 = nRows => range(1, nRows - 1) .reduce(sofar => { let lstPrev = sofar.slice(-1)[0];
// The composition of (asciiBinary . mod 2 . add)
// is reduced here to a rule from two parent characters
// to a single child character.
// Rule 90 also reduces to the same XOR
// relationship between left and right neighbours.
return sofar
.concat([zipWith(
(left, right) => left === right ? ' ' : '*',
[' '].concat(lstPrev),
lstPrev.concat(' ')
)]);
}, [
['*'] // Tip of triangle
]);
// Reduce/folding from the last item (base of list)
// which has zero left indent.
// Each preceding row has one more indent space than the row beneath it
return asciiPascalMod2(Math.pow(2, intOrder))
.reduceRight((a, x) => {
return {
triangle: a.indent + x.join(' ') + '\n' + a.triangle,
indent: a.indent + ' '
}
}, {
triangle: ,
indent:
}).triangle
};
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
let zipWith = (f, xs, ys) =>
xs.length === ys.length ? (
xs.map((x, i) => f(x, ys[i]))
) : undefined,
// range(intFrom, intTo, optional intStep)
// Int -> Int -> Maybe Int -> [Int]
range = (m, n, step) => {
let d = (step || 1) * (n >= m ? 1 : -1);
return Array.from({
length: Math.floor((n - m) / d) + 1
}, (_, i) => m + (i * d));
};
return sierpinski(order);
})(4);</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
jq
Works with gojq, the Go implementation of jq
Preliminaries <lang jq>def elementwise(f):
transpose | map(f) ;
- input: an array of decimal numbers
def bitwise_and:
# Input: an integer # Output: a stream of 0s and 1s def stream: recurse(if . > 0 then ./2|floor else empty end) | . % 2 ;
# Input: a 0-1 array
def toi:
reduce .[] as $c ( {power:1 , ans: 0};
.ans += ($c * .power) | .power *= 2 )
| .ans;
if any(.==0) then 0 else map([stream]) | (map(length) | min) as $min | map( .[:$min] ) | elementwise(min) | toi end;</lang>
<lang jq> def sierpinski:
pow(2; .) as $size
| range($size-1; -1; -1) as $y
| reduce range(0; $size - $y) as $x ( (" " * $y);
. + (if ([$x,$y]|bitwise_and) == 0 then "* " else " " end));
4 | sierpinski</lang>
- Output:
As elsewhere.
Julia
<lang julia>function sierpinski(n, token::AbstractString="*") x = fill(token, 1, 1) for _ in 1:n h, w = size(x) s = fill(" ", h,(w + 1) ÷ 2) t = fill(" ", h,1) x = [[s x s] ; [x t x]] end return x end
function printsierpinski(m::Matrix)
for r in 1:size(m, 1)
println(join(m[r, :]))
end
end
sierpinski(4) |> printsierpinski</lang>
Kotlin
<lang scala>// version 1.1.2
const val ORDER = 4 const val SIZE = 1 shl ORDER
fun main(args: Array<String>) {
for (y in SIZE - 1 downTo 0) {
for (i in 0 until y) print(" ")
for (x in 0 until SIZE - y) print(if ((x and y) != 0) " " else "* ")
println()
}
}</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Liberty BASIC
<lang lb>nOrder=4 call triangle 1, 1, nOrder end
SUB triangle x, y, n
IF n = 0 THEN
LOCATE x,y: PRINT "*";
ELSE
n=n-1
length=2^n
call triangle x, y+length, n
call triangle x+length, y, n
call triangle x+length*2, y+length, n
END IF
END SUB</lang>
Logo
<lang logo>; Print rows of the triangle from 0 to :limit inclusive.
- limit=15 gives the order 4 form per the task.
- The range of
- y is arbitrary, any rows of the triangle can be printed.
make "limit 15 for [y 0 :limit] [
for [x -:limit :y] [
type ifelse (and :y+:x >= 0 ; blank left of triangle
(remainder :y+:x 2) = 0 ; only "even" squares
(bitand :y+:x :y-:x) = 0 ; Sierpinski bit test
) ["*] ["| |] ; star or space
]
print []
]</lang>
Lua
Ported from the list-comprehension Python version.
<lang lua>function sierpinski(depth)
lines = {}
lines[1] = '*'
for i = 2, depth+1 do
sp = string.rep(' ', 2^(i-2))
tmp = {}
for idx, line in ipairs(lines) do
tmp[idx] = sp .. line .. sp
tmp[idx+#lines] = line .. ' ' .. line
end
lines = tmp
end
return table.concat(lines, '\n')
end
print(sierpinski(4))</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Maple
<lang maple>S := proc(n)
local i, j, values, position;
values := [ seq(" ",i=1..2^n-1), "*" ];
printf("%s\n",cat(op(values)));
for i from 2 to 2^n do
position := [ ListTools:-SearchAll( "*", values ) ];
values := Array([ seq(0, i=1..2^n+i-1) ]);
for j to numelems(position) do
values[position[j]-1] := values[position[j]-1] + 1;
values[position[j]+1] := values[position[j]+1] + 1;
end do;
values := subs( { 2 = " ", 0 = " ", 1 = "*"}, values );
printf("%s\n",cat(op(convert(values, list))));
end do:
end proc:</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Mathematica/Wolfram Language
Cellular automaton (rule 90) based solution: <lang mathematica>n=4;Grid[CellularAutomaton[90,{{1},0},2^n-1]/.{0->" ",1->"*"},ItemSize->All]</lang> Using built-in function: <lang mathematica>SierpinskiMesh[3]</lang>
MATLAB
STRING was introduced in version R2016b. <lang MATLAB>n = 4; d = string('*'); for k = 0 : n - 1
sp = repelem(' ', 2 ^ k);
d = [sp + d + sp, d + ' ' + d];
end disp(d.join(char(10))) </lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Cellular Automaton Version
<lang MATLAB>n = 2 ^ 4 - 1; tr = + ~(-n : n); for k = 1:n
tr(k + 1, :) = bitget(90, 1 + filter2([4 2 1], tr(k, :)));
end char(10 * tr + 32)</lang>
Mixed Version
<lang matlab>spy(mod(abs(pascal(32,1)),2)==1)</lang>
NetRexx
<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols nobinary
numeric digits 1000 runSample(arg) return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method runSample(arg) public static
BLACK_UPPOINTING_TRIANGLE = '\u25b2' parse arg ordr filr . if ordr = | ordr = '.' then ordr = 4 if filr = | filr = '.' then filler = BLACK_UPPOINTING_TRIANGLE else filler = filr drawSierpinskiTriangle(ordr, filler) return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method drawSierpinskiTriangle(ordr, filler = Rexx '^') public static
n = 1 * (2 ** ordr)
line = ' '.copies(2 * n)
line = line.overlay(filler, n + 1) -- set the top point of the triangle
loop row = 1 to n -- NetRexx arrays, lists etc. index from 1
say line.strip('t')
u = filler
loop col = 2 + n - row to n + row
cl = line.substr(col - 1, 1)
cr = line.substr(col + 1, 1)
if cl == cr then t = ' '
else t = filler
line = line.overlay(u, col - 1)
u = t
end col
j2 = n + row - 1
j3 = n + row
line = line.overlay(t, j2 + 1)
line = line.overlay(filler, j3 + 1)
end row
return
</lang>
- Output:
▲
▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
Nim
<lang nim>const size = 1 shl 4 - 1
for y in countdown(size, 0):
for i in 0 .. <y:
stdout.write " "
for x in 0 .. size-y:
if (x and y) != 0:
stdout.write " "
else:
stdout.write "* "
stdout.write "\n"</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
OCaml
<lang ocaml>let sierpinski n =
let rec loop down space n =
if n = 0 then
down
else
loop (List.map (fun x -> space ^ x ^ space) down @
List.map (fun x -> x ^ " " ^ x) down)
(space ^ space)
(n - 1)
in loop ["*"] " " n
let () =
List.iter print_endline (sierpinski 4)</lang>
Oforth
This solution uses a cellular automaton (rule 90 for triangle).
automat(rule, n) runs cellular automaton for rule "rule" for n generations.
<lang Oforth>: nextGen(l, r) | i |
StringBuffer new
l size loop: i [
l at(i 1 -) '*' == 4 *
l at(i) '*' == 2 * +
l at(i 1 +) '*' == +
2 swap pow r bitAnd ifTrue: [ '*' ] else: [ ' ' ] over addChar
] ;
- automat(rule, n)
StringBuffer new " " <<n(n) "*" over + + #[ dup println rule nextGen ] times(n) drop ;
- sierpinskiTriangle(n)
90 4 n * automat ;</lang>
- Output:
>4 sierpinskiTriangle
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
ok
>
Oz
<lang oz>declare
fun {NextTriangle Triangle}
Sp = {Spaces {Length Triangle}}
in
{Flatten
[{Map Triangle fun {$ X} Sp#X#Sp end}
{Map Triangle fun {$ X} X#" "#X end}
]}
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
SierpinskiTriangles = {Iterate NextTriangle ["*"]}
in
{ForAll {Nth SierpinskiTriangles 5} System.showInfo}</lang>
PARI/GP
<lang parigp>Sierpinski(n)={
my(s=2^n-1);
forstep(y=s,0,-1,
for(i=1,y,print1(" "));
for(x=0,s-y,
print1(if(bitand(x,y)," ","*"))
);
print()
)
}; Sierpinski(4)</lang>
- Output:
*
**
* *
****
* *
** **
* * * *
********
* *
** **
* * * *
**** ****
* * * *
** ** ** **
* * * * * * * *
****************
Pascal
<lang pascal>program Sierpinski;
function ipow(b, n : Integer) : Integer; var
i : Integer;
begin
ipow := 1;
for i := 1 to n do
ipow := ipow * b
end;
function truth(a : Char) : Boolean; begin
if a = '*' then
truth := true
else
truth := false
end;</lang>
<lang pascal>function rule_90(ev : String) : String; var
l, i : Integer; cp : String; s : Array[0..1] of Boolean;
begin
l := length(ev);
cp := copy(ev, 1, l);
for i := 1 to l do begin
if (i-1) < 1 then
s[0] := false
else
s[0] := truth(ev[i-1]);
if (i+1) > l then
s[1] := false
else
s[1] := truth(ev[i+1]);
if ( (s[0] and not s[1]) or (s[1] and not s[0]) ) then
cp[i] := '*'
else
cp[i] := ' ';
end; rule_90 := cp
end;
procedure triangle(n : Integer); var
i, l : Integer; b : String;
begin
l := ipow(2, n+1);
b := ' ';
for i := 1 to l do
b := concat(b, ' ');
b[round(l/2)] := '*';
writeln(b);
for i := 1 to (round(l/2)-1) do begin
b := rule_90(b);
writeln(b)
end
end;</lang>
<lang pascal>begin
triangle(4)
end.</lang>
Perl
version 1
<lang perl>sub sierpinski {
my ($n) = @_;
my @down = '*';
my $space = ' ';
foreach (1..$n) {
@down = (map("$space$_$space", @down), map("$_ $_", @down));
$space = "$space$space";
}
return @down;
}
print "$_\n" foreach sierpinski 4;</lang>
one-liner
<lang perl> perl -le '$l=40;$l2="!" x $l;substr+($l2^=$l2),$l/2,1,"\xFF";for(1..16){local $_=$l2;y/\0\xFF/ */;print;($lf,$rt)=map{substr $l2 x 2,$_%$l,$l;}1,-1;$l2=$lf^$rt;select undef,undef,undef,.1;}'</lang>
Phix
procedure sierpinski(integer n) integer lim = power(2,n)-1 for y=lim to 0 by -1 do puts(1,repeat(' ',y)) for x=0 to lim-y do puts(1,iff(and_bits(x,y)?" ":"* ")) end for puts(1,"\n") end for end procedure for i=1 to 5 do sierpinski(i) end for
- Output:
*
* *
*
* *
* *
* * * *
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Phixmonti
<lang Phixmonti>def sierpinski
2 swap power 1 - var lim
lim 0 -1 3 tolist for
var y
32 y 1 + repeat print
0 lim y - 2 tolist for
y bitand if 32 32 chain else "* " endif print
endfor
nl
endfor
enddef
5 for
sierpinski
endfor</lang>
PHP
<lang PHP><?php
function sierpinskiTriangle($order) {
$char = '#';
$n = 1 << $order;
$line = array();
for ($i = 0 ; $i <= 2 * $n ; $i++) {
$line[$i] = ' ';
}
$line[$n] = $char;
for ($i = 0 ; $i < $n ; $i++) {
echo implode(, $line), PHP_EOL;
$u = $char;
for ($j = $n - $i ; $j < $n + $i + 1 ; $j++) {
$t = ($line[$j - 1] == $line[$j + 1] ? ' ' : $char);
$line[$j - 1] = $u;
$u = $t;
}
$line[$n + $i] = $t;
$line[$n + $i + 1] = $char;
}
}
sierpinskiTriangle(4); </lang>
- Output:
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
PicoLisp
<lang PicoLisp>(de sierpinski (N)
(let (D '("*") S " ")
(do N
(setq
D (conc
(mapcar '((X) (pack S X S)) D)
(mapcar '((X) (pack X " " X)) D) )
S (pack S S) ) )
D ) )
(mapc prinl (sierpinski 4))</lang>
PL/I
<lang PL/I>sierpinski: procedure options (main); /* 2010-03-30 */
declare t (79,79) char (1); declare (i, j, k) fixed binary; declare (y, xs, ys, xll, xrr, ixrr, limit) fixed binary;
t = ' ';
xs = 40; ys = 1;
/* Make initial triangle */
call make_triangle (xs, ys);
y = ys + 4;
xll = xs-4; xrr = xs+4;
do k = 1 to 3;
limit = 0;
do forever;
ixrr = xrr;
do i = xll to xll+limit by 8;
if t(y-1, i) = ' ' then
do;
call make_triangle (i, y);
if t(y+3,i-5) = '*' then
t(y+3,i-4), t(y+3,ixrr+4) = '*';
call make_triangle (ixrr, y);
end;
ixrr = ixrr - 8;
end;
xll = xll - 4; xrr = xrr + 4;
y = y + 4;
limit = limit + 8;
if xll+limit > xs-1 then leave;
end;
t(y-1,xs) = '*';
end;
/* Finished generation; now print the Sierpinski triangle. */ put edit (t) (skip, (hbound(t,2)) a);
make_triangle: procedure (x, y);
declare (x, y) fixed binary; declare i fixed binary;
do i = 0 to 3;
t(y+i, x-i), t(y+i, x+i) = '*';
end;
do i = x-2 to x+2; /* The base of the triangle. */
t(y+3, i) = '*';
end;
end make_triangle;
end sierpinski;</lang>
PL/M
<lang plm>100H:
DECLARE ORDER LITERALLY '4';
/* CP/M BDOS CALL */ BDOS: PROCEDURE (FN, ARG);
DECLARE FN BYTE, ARG ADDRESS; GO TO 5;
END BDOS;
PUT$CHAR: PROCEDURE (CHAR);
DECLARE CHAR BYTE; CALL BDOS(2, CHAR);
END PUT$CHAR;
/* PRINT SIERPINSKI TRIANGLE */ DECLARE (X, Y, SIZE) BYTE; SIZE = SHL(1, ORDER);
Y = SIZE - 1; DO WHILE Y <> -1;
DO X = 0 TO Y;
CALL PUT$CHAR(' ');
END;
DO X = 0 TO SIZE-Y-1;
IF (X AND Y) = 0
THEN CALL PUT$CHAR('*');
ELSE CALL PUT$CHAR(' ');
CALL PUT$CHAR(' ');
END;
Y = Y - 1;
CALL PUT$CHAR(13);
CALL PUT$CHAR(10);
END;
CALL BDOS(0,0); EOF</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Pop11
Solution using line buffer in an integer array oline, 0 represents ' ' (space), 1 represents '*' (star). <lang pop11>define triangle(n);
lvars k = 2**n, j, l, oline, nline;
initv(2*k+3) -> oline;
initv(2*k+3) -> nline;
for l from 1 to 2*k+3 do 0 -> oline(l) ; endfor;
1 -> oline(k+2);
0 -> nline(1);
0 -> nline(2*k+3);
for j from 1 to k do
for l from 1 to 2*k+3 do
printf(if oline(l) = 0 then ' ' else '*' endif);
endfor;
printf('\n');
for l from 2 to 2*k+2 do
(oline(l-1) + oline(l+1)) rem 2 -> nline(l);
endfor;
(oline, nline) -> (nline, oline);
endfor;
enddefine;
triangle(4);</lang>
Alternative solution, keeping all triangle as list of strings <lang pop11>define triangle2(n);
lvars acc = ['*'], spaces = ' ', j;
for j from 1 to n do
maplist(acc, procedure(x); spaces >< x >< spaces ; endprocedure)
<> maplist(acc, procedure(x); x >< ' ' >< x ; endprocedure) -> acc;
spaces >< spaces -> spaces;
endfor;
applist(acc, procedure(x); printf(x, '%p\n'); endprocedure);
enddefine;
triangle2(4);</lang>
PostScript
This draws the triangles in a string-rewrite fashion, where all edges form a single polyline. 9 page document showing progession. <lang postscript>%!PS-Adobe-3.0 %%BoundingBox 0 0 300 300
/F { 1 0 rlineto } def /+ { 120 rotate } def /- {-120 rotate } def /v {.5 .5 scale } def /^ { 2 2 scale } def /!0{ dup 1 sub dup -1 eq not } def
/X { !0 { v X + F - X - F + X ^ } { F } ifelse pop } def
0 1 8 { 300 300 scale 0 1 12 div moveto
X + F + F fill showpage } for
%%EOF</lang>
PowerShell
<lang powershell>function triangle($o) {
$n = [Math]::Pow(2, $o)
$line = ,' '*(2*$n+1)
$line[$n] = '█'
$OFS =
for ($i = 0; $i -lt $n; $i++) {
Write-Host $line
$u = '█'
for ($j = $n - $i; $j -lt $n + $i + 1; $j++) {
if ($line[$j-1] -eq $line[$j+1]) {
$t = ' '
} else {
$t = '█'
}
$line[$j-1] = $u
$u = $t
}
$line[$n+$i] = $t
$line[$n+$i+1] = '█'
}
}</lang>
Processing
Characters in drawing canvas version
<lang java>void setup() {
size(410, 230); background(255); fill(0); sTriangle (10, 25, 100, 5);
}
void sTriangle(int x, int y, int l, int n) {
if( n == 0) text("*", x, y);
else {
sTriangle(x, y+l, l/2, n-1);
sTriangle(x+l, y, l/2, n-1);
sTriangle(x+l*2, y+l, l/2, n-1);
}
}</lang>
Text in console version
<lang java>void setup() {
print(getSierpinskiTriangle(3));
} String getSierpinskiTriangle(int n) {
if ( n == 0 ) {
return "*";
}
String s = getSierpinskiTriangle(n-1);
String [] split = s.split("\n");
int length = split.length;
// Top triangle
String ns = "";
String top = buildSpace((int)pow(2, n-1));
for ( int i = 0; i < length; i++ ) {
ns += top;
ns += split[i];
ns += "\n";
}
// Two triangles side by side
for ( int i = 0; i < length; i++ ) {
ns += split[i];
ns += buildSpace(length-i);
ns += split[i];
ns += "\n";
}
return ns.toString();
}
String buildSpace(int n) {
String ns = "";
while ( n > 0 ) {
ns += " ";
n--;
}
return ns;
} </lang>
Prolog
Works with SWI-Prolog; <lang Prolog>sierpinski_triangle(N) :- Len is 2 ** (N+1) - 1, length(L, Len), numlist(1, Len, LN), maplist(init(N), L, LN), atomic_list_concat(L, Line), writeln(Line), NbTours is 2**N - 1, loop(NbTours, LN, Len, L).
init(N, Cell, Num) :- ( Num is 2 ** N + 1 -> Cell = *; Cell = ' ').
loop(0, _, _, _) :- !.
loop(N, LN, Len, L) :- maplist(compute_next_line(Len, L), LN, L1), atomic_list_concat(L1, Line), writeln(Line), N1 is N - 1, loop(N1, LN, Len, L1).
compute_next_line(Len, L, I, V) :- I1 is I - 1, I2 is I+1, ( I = 1 -> V0 = ' '; nth1(I1, L, V0)), nth1(I, L, V1), ( I = Len -> V2 = ' '; nth1(I2, L, V2)), rule_90(V0, V1, V2, V).
rule_90('*','*','*', ' '). rule_90('*','*',' ', '*'). rule_90('*',' ','*', ' '). rule_90('*',' ',' ', '*'). rule_90(' ','*','*', '*'). rule_90(' ','*',' ', ' '). rule_90(' ',' ','*', '*'). rule_90(' ',' ',' ', ' '). </lang>
- Output:
?- sierpinski_triangle(4).
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
true
PureBasic
<lang PureBasic>Procedure Triangle (X,Y, Length, N)
If N = 0
DrawText( Y,X, "*",#Blue)
Else
Triangle (X+Length, Y, Length/2, N-1)
Triangle (X, Y+Length, Length/2, N-1)
Triangle (X+Length, Y+Length*2, Length/2, N-1)
EndIf
EndProcedure
OpenWindow(0, 100, 100,700,500 ,"Sierpinski triangle", #PB_Window_SystemMenu |1)
StartDrawing(WindowOutput(0))
DrawingMode(#PB_2DDrawing_Transparent ) Triangle(10,10,120,5)
StopDrawing()
Repeat Until WaitWindowEvent()=#PB_Event_CloseWindow End</lang>
Python
<lang python>def sierpinski(n):
d = ["*"]
for i in xrange(n):
sp = " " * (2 ** i)
d = [sp+x+sp for x in d] + [x+" "+x for x in d]
return d
print "\n".join(sierpinski(4))</lang>
Or, using fold / reduce
<lang python>import functools
def sierpinski(n):
def aggregate(TRIANGLE, I):
SPACE = " " * (2 ** I)
return [SPACE+X+SPACE for X in TRIANGLE] + [X+" "+X for X in TRIANGLE]
return functools.reduce(aggregate, range(n), ["*"])
print("\n".join(sierpinski(4)))</lang>
and fold/reduce, wrapped as concatMap, can provide the list comprehensions too: <lang python>Sierpinski triangle
from functools import reduce from operator import add
- sierpinski :: Int -> String
def sierpinski(n):
Nth iteration of a Sierpinksi triangle.
def go(xs, i):
s = ' ' * (2 ** i)
return concatMap(lambda x: [s + x + s])(xs) + (
concatMap(lambda x: [x + ' ' + x])(xs)
)
return '\n'.join(reduce(go, range(n), '*'))
- concatMap :: (a -> [b]) -> [a] -> [b]
def concatMap(f):
A concatenated list or string over which a function f
has been mapped.
The list monad can be derived by using an (a -> [b])
function which wraps its output in a list (using an
empty list to represent computational failure).
return lambda xs: (
reduce(add, map(f, xs), [])
)
print(sierpinski(4))</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Use Python's long integer and bit operator to make an infinite triangle:
<lang python>x = 1
while True:
print(bin(x)[2:].replace('0', ' '))
x ^= x<<1</lang>
Quackery
<lang Quackery> [ [ dup 1 &
iff char * else space
emit
1 >> dup while
sp again ]
drop ] is stars ( mask --> )
[ bit
1 over times
[ cr over i^ - times sp
dup stars
dup 1 << ^ ]
2drop ] is triangle ( order --> )
4 triangle</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
R
Based on C# but using some of R's functionality to abbreviate code where possible. <lang r>sierpinski.triangle = function(n) { len <- 2^(n+1) b <- c(rep(FALSE,len/2),TRUE,rep(FALSE,len/2)) for (i in 1:(len/2)) { cat(paste(ifelse(b,"*"," "),collapse=""),"\n") n <- rep(FALSE,len+1) n[which(b)-1]<-TRUE n[which(b)+1]<-xor(n[which(b)+1],TRUE) b <- n } } sierpinski.triangle(5)</lang>
Shortened to a function of one line. <lang r>sierpinski.triangle = function(n) { c(paste(ifelse(b<<- c(rep(FALSE,2^(n+1)/2),TRUE,rep(FALSE,2^(n+1)/2)),"*"," "),collapse=""),replicate(2^n-1,paste(ifelse(b<<-xor(c(FALSE,b[1:2^(n+1)]),c(b[2:(2^(n+1)+1)],FALSE)),"*"," "),collapse=""))) } cat(sierpinski.triangle(5),sep="\n")</lang>
Racket
<lang Racket>
- lang racket
(define (sierpinski n)
(if (zero? n)
'("*")
(let ([spaces (make-string (expt 2 (sub1 n)) #\space)]
[prev (sierpinski (sub1 n))])
(append (map (λ(x) (~a spaces x spaces)) prev)
(map (λ(x) (~a x " " x)) prev)))))
(for-each displayln (sierpinski 5)) </lang>
Raku
(formerly Perl 6)
<lang perl6>sub sierpinski ($n) {
my @down = '*';
my $space = ' ';
for ^$n {
@down = |("$space$_$space" for @down), |("$_ $_" for @down);
$space x= 2;
}
return @down;
}
.say for sierpinski 4;</lang>
REXX
<lang rexx>/*REXX program constructs and displays a Sierpinski triangle of up to around order 10k.*/ parse arg n mark . /*get the order of Sierpinski triangle.*/ if n== | n=="," then n=4 /*Not specified? Then use the default.*/ if mark== then mark= "*" /*MARK was specified as a character. */ if length(mark)==2 then mark=x2c(mark) /* " " " in hexadecimal. */ if length(mark)==3 then mark=d2c(mark) /* " " " " decimal. */ numeric digits 12000 /*this should handle the biggy numbers.*/
/* [↓] the blood-'n-guts of the pgm. */
do j=0 for n*4; !=1; z=left(, n*4 -1-j) /*indent the line to be displayed. */
do k=0 for j+1 /*construct the line with J+1 parts. */
if !//2==0 then z=z' ' /*it's either a blank, or ··· */
else z=z mark /* ··· it's one of 'em thar characters.*/
!=! * (j-k) % (k+1) /*calculate handy-dandy thing-a-ma-jig.*/
end /*k*/ /* [↑] finished constructing a line. */
say z /*display a line of the triangle. */
end /*j*/ /* [↑] finished showing triangle. */
/*stick a fork in it, we're all done. */</lang>
output when using the default input of order: 4
(Shown at three quarter size.)
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
output when using the input of: 8 1e
(Shown at half size.)
▲
▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
output when using the input of: 32 db
(Shown at one tenth size.)
█
█ █
█ █
█ █ █ █
█ █
█ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █
█ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █
█ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
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Output with an input of 64 can be viewed at: Sierpinski triangle/REXX output 64
Ring
<lang ring>
- Project : Sierpinski triangle
norder=4 xy = list(40) for i = 1 to 40
xy[i] = " "
next triangle(1, 1, norder) for i = 1 to 36
see xy[i] + nl
next
func triangle(x, y, n)
if n = 0
xy[y] = left(xy[y],x-1) + "*" + substr(xy[y],x+1)
else
n=n-1
length=pow(2,n)
triangle(x, y+length, n)
triangle(x+length, y, n)
triangle(x+length*2, y+length, n)
ok
</lang> Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Ruby
From the command line: <lang ruby>ruby -le'16.times{|y|print" "*(15-y),*(0..y).map{|x|~y&x>0?" ":" *"}}'</lang>
or,
<lang ruby>def sierpinski_triangle(n)
triangle = ["*"]
n.times do |i|
sp = " " * (2**i)
triangle = triangle.collect {|x| sp + x + sp} +
triangle.collect {|x| x + " " + x}
end
triangle
end
puts sierpinski_triangle(4)</lang>
Using fold / reduce (aka. inject):
<lang ruby>def sierpinski_triangle(n)
(0...n).inject(["*"]) {|triangle, i|
space = " " * (2**i)
triangle.map {|x| space + x + space} + triangle.map {|x| x + " " + x}
}
end
puts sierpinski_triangle(4)</lang>
Run BASIC
<lang runbasic>nOrder=4 dim xy$(40) for i = 1 to 40
xy$(i) = " "
next i call triangle 1, 1, nOrder for i = 1 to 36
print xy$(i)
next i end
SUB triangle x, y, n
IF n = 0 THEN
xy$(y) = left$(xy$(y),x-1) + "*" + mid$(xy$(y),x+1)
ELSE
n=n-1
length=2^n
call triangle x, y+length, n
call triangle x+length, y, n
call triangle x+length*2, y+length, n
END IF
END SUB</lang>
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Rust
<lang rust> use std::iter::repeat;
fn sierpinski(order: usize) {
let mut triangle = vec!["*".to_string()];
for i in 0..order {
let space = repeat(' ').take(2_usize.pow(i as u32)).collect::<String>();
// save original state
let mut d = triangle.clone();
// extend existing lines
d.iter_mut().for_each(|r| {
let new_row = format!("{}{}{}", space, r, space);
*r = new_row;
});
// add new lines
triangle.iter().for_each(|r| {
let new_row = format!("{}{}{}", r, " ", r);
d.push(new_row);
});
triangle = d; }
triangle.iter().for_each(|r| println!("{}", r));
} fn main() {
let order = std::env::args()
.nth(1)
.unwrap_or_else(|| "4".to_string())
.parse::<usize>()
.unwrap();
sierpinski(order);
}
</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Scala
The Ruby command-line version (on Windows): <lang scala>scala -e "for(y<-0 to 15){println(\" \"*(15-y)++(0 to y).map(x=>if((~y&x)>0)\" \"else\" *\")mkString)}"</lang>
The Forth version: <lang scala>def sierpinski(n: Int) {
def star(n: Long) = if ((n & 1L) == 1L) "*" else " "
def stars(n: Long): String = if (n == 0L) "" else star(n) + " " + stars(n >> 1)
def spaces(n: Int) = " " * n
((1 << n) - 1 to 0 by -1).foldLeft(1L) {
case (bitmap, remainingLines) =>
println(spaces(remainingLines) + stars(bitmap))
(bitmap << 1) ^ bitmap
}
}</lang>
The Haskell version: <lang scala>def printSierpinski(n: Int) {
def sierpinski(n: Int): List[String] = {
lazy val down = sierpinski(n - 1)
lazy val space = " " * (1 << (n - 1))
n match {
case 0 => List("*")
case _ => (down map (space + _ + space)) :::
(down map (List.fill(2)(_) mkString " "))
}
}
sierpinski(n) foreach println
}</lang>
Scheme
<lang scheme>(define (sierpinski n)
(for-each
(lambda (x) (display (list->string x)) (newline))
(let loop ((acc (list (list #\*))) (spaces (list #\ )) (n n))
(if (zero? n)
acc
(loop
(append
(map (lambda (x) (append spaces x spaces)) acc)
(map (lambda (x) (append x (list #\ ) x)) acc))
(append spaces spaces)
(- n 1))))))</lang>
Seed7
<lang seed7>$ include "seed7_05.s7i";
const func array string: sierpinski (in integer: n) is func
result
var array string: parts is 1 times "*";
local
var integer: i is 0;
var string: space is " ";
var array string: parts2 is 0 times "";
var string: x is "";
begin
for i range 1 to n do
parts2 := 0 times "";
for x range parts do
parts2 &:= [] (space & x & space);
end for;
for x range parts do
parts2 &:= [] (x & " " & x);
end for;
parts := parts2;
space &:= space;
end for;
end func;
const proc: main is func
begin writeln(join(sierpinski(4), "\n")); end func;</lang>
Sidef
<lang ruby>func sierpinski_triangle(n) {
var triangle = ['*']
{ |i|
var sp = (' ' * 2**i)
triangle = (triangle.map {|x| sp + x + sp} +
triangle.map {|x| x + ' ' + x})
} * n
triangle.join("\n")
} say sierpinski_triangle(4)</lang>
Swift
<lang>import Foundation
// Easy get/set of charAt extension String {
subscript(index:Int) -> String {
get {
var array = Array(self)
var charAtIndex = array[index]
return String(charAtIndex)
}
set(newValue) {
var asChar = Character(newValue)
var array = Array(self)
array[index] = asChar
self = String(array)
}
}
}
func triangle(var n:Int) {
n = 1 << n
var line = ""
var t = ""
var u = ""
for (var i = 0; i <= 2 * n; i++) {
line += " "
}
line[n] = "*"
for (var i = 0; i < n; i++) {
println(line)
u = "*"
for (var j = n - i; j < n + i + 1; j++) {
t = line[j-1] == line[j + 1] ? " " : "*"
line[j - 1] = u
u = t
}
line[n + i] = t
line[n + i + 1] = "*"
}
}</lang>
Tcl
<lang tcl>package require Tcl 8.5
proc map {lambda list} {
foreach elem $list {
lappend result [apply $lambda $elem]
}
return $result
}
proc sierpinski_triangle n {
set down [list *]
set space " "
for {set i 1} {$i <= $n} {incr i} {
set down [concat \
[map [subst -nocommands {x {expr {"$space[set x]$space"}}}] $down] \
[map {x {expr {"$x $x"}}} $down] \
]
append space $space
}
return [join $down \n]
}
puts [sierpinski_triangle 4]</lang>
TI-83 BASIC
Uses Wolfram Rule 90. <lang ti83b>PROGRAM:SIRPNSKI
- ClrHome
- Output(1,8,"^")
- {0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0}→L1
- {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}→L2
- L2→L3
- For(X,2,8,1)
- For(Y,2,17,1)
- If L1(Y-1)
- Then
- 4→N
- End
- If L1(Y)
- Then
- N+2→N
- End
- If L1(Y+1)
- Then
- N+1→N
- End
- If N=1 or N=3 or N=4 or N=6
- Then
- 1→L2(Y)
- Output(X,Y-1,"^")
- End
- 0→N
- End
- L2→L1
- L3→L2
- End
</lang>
uBasic/4tH
<lang>Input "Triangle order: ";n n = 2^n
For y = n - 1 To 0 Step -1
For i = 0 To y Print " "; Next
x = 0
For x = 0 Step 1 While ((x + y) < n)
If AND (x,y) Then
Print " ";
Else
Print "* ";
EndIf
Next
Next End</lang>
Unlambda
<lang Unlambda>```ci``s``s`ks``s`k`s``s`kc``s``s``si`kr`k. `k.*k `k``s``s``s``s`s`k`s``s`ksk`k``s``si`kk`k``s`kkk `k``s`k`s``si`kk``s`kk``s``s``s``si`kk`k`s`k`s``s`ksk`k`s`k`s`k`si``si`k`ki `k``s`k`s``si`k`ki``s`kk``s``s``s``si`kk`k`s`k`s`k`si`k`s`k`s``s`ksk``si`k`ki `k`ki``s`k`s`k`si``s`kkk</lang> This produces an infinite, left-justified triangle:
*
**
* *
****
* *
** **
* * * *
********
* *
** **
* * * *
**** ****
* * * *
** ** ** **
* * * * * * * *
****************
* *
** **
* * * *
**** ****
* * * *
** ** ** **
* * * * * * * *
******** ********
* * * *
** ** ** **
* * * * * * * *
**** **** **** ****
* * * * * * * *
** ** ** ** ** ** ** **
* * * * * * * * * * * * * * * *
********************************
* *
** **
* * * *
........
Ursala
the straightforward recursive solution <lang Ursala>#import nat
triangle = ~&a^?\<<&>>! ^|RNSiDlrTSPxSxNiCK9xSx4NiCSplrTSPT/~& predecessor</lang> the cheeky cellular automaton solution <lang Ursala>#import std
- import nat
rule = -$<0,&,0,0,&,0,0,0>@rSS zipp0*ziD iota8 evolve "n" = @iNC ~&x+ rep"n" ^C\~& @h rule*+ swin3+ :/0+ --<0> sierpinski = iota; --<&>@NS; iota; ^H/evolve@z @NS ^T/~& :/&</lang> an example of each (converting from booleans to characters) <lang Ursala>#show+
examples = mat0 ~&?(`*!,` !)*** <sierpinski3,triangle4></lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
VBA
<lang vb>Sub sierpinski(n As Integer)
Dim lim As Integer: lim = 2 ^ n - 1
For y = lim To 0 Step -1
Debug.Print String$(y, " ")
For x = 0 To lim - y
Debug.Print IIf(x And y, " ", "# ");
Next
Debug.Print
Next y
End Sub Public Sub main()
Dim i As Integer
For i = 1 To 5
sierpinski i
Next i
End Sub</lang>
- Output:
#
# #
#
# #
# #
# # # #
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
VBScript
<lang vb> Sub triangle(o) n = 2 ^ o Dim line() ReDim line(2*n) line(n) = "*" i = 0 Do While i < n WScript.StdOut.WriteLine Join(line,"") u = "*" j = n - i Do While j < (n+i+1) If line(j-1) = line(j+1) Then t = " " Else t = "*" End If line(j-1) = u u = t j = j + 1 Loop line(n+i) = t line(n+i+1) = "*" i = i + 1 Loop End Sub
triangle(4) </lang>
Vedit macro language
Iterative
The macro writes the fractal into an edit buffer where it can be viewed and saved to file if required. This allows creating images larger than screen, the size is only limited by free disk space. <lang vedit>#3 = 16 // size (height) of the triangle Buf_Switch(Buf_Free) // Open a new buffer for output Ins_Char(' ', COUNT, #3*2+2) // fill first line with spaces Ins_Newline Line(-1) Goto_Col(#3) Ins_Char('*', OVERWRITE) // the top of triangle for (#10=0; #10 < #3-1; #10++) {
BOL Reg_Copy(9,1) Reg_Ins(9) // duplicate the line
#20 = '*'
for (#11 = #3-#10; #11 < #3+#10+1; #11++) {
Goto_Col(#11-1)
if (Cur_Char==Cur_Char(2)) { #21=' ' } else { #21='*' } Ins_Char(#20, OVERWRITE) #20 = #21
}
Ins_Char(#21, OVERWRITE)
Ins_Char('*', OVERWRITE)
}</lang>
Recursive
Vedit macro language does not have recursive functions, so some pushing and popping is needed to implement recursion. <lang vedit>#1 = 1 // x
- 2 = 1 // y
- 3 = 16 // length (height of the triangle / 2)
- 4 = 5 // depth of recursion
Buf_Switch(Buf_Free) // Open a new buffer for output Ins_Newline(#3*2) // Create as many empty lines as needed Call("Triangle") // Draw the triangle BOF Return
- Triangle:
if (#4 == 0) {
Goto_Line(#2)
EOL Ins_Char(' ', COUNT, #1-Cur_Col+1) // add spaces if needed
Goto_Col(#1)
Ins_Char('*', OVERWRITE)
} else {
Num_Push(1,4)
#2 += #3; #3 /= 2; #4--; Call("Triangle")
Num_Pop(1,4)
Num_Push(1,4)
#1 += #3; #3 /= 2; #4--; Call("Triangle")
Num_Pop(1,4)
Num_Push(1,4)
#1 += 2*#3; #2 += #3; #3 /= 2; #4--; Call("Triangle")
Num_Pop(1,4)
} Return</lang>
Wren
<lang ecmascript>var size = 1 << 4 for (y in size-1..0) {
System.write(" " * y)
for (x in 0...size-y) System.write((x&y != 0) ? " " : "* ")
System.print()
}</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
X86 Assembly
Translation of XPL0. Assemble with tasm, tlink /t <lang asm> .model tiny
.code
.486
org 100h
start: xor ebx, ebx ;S1:= 0
mov edx, 8000h ;S2:= $8000
mov cx, 16 ;for I:= Size downto 1
tri10: mov ebx, edx ; S1:= S2 tri15: test edx, edx ; while S2#0
je tri20
mov al, '*' ; ChOut
test dl, 01h ; if S2&1 then '*' else ' '
jne tri18
mov al, ' '
tri18: int 29h
shr edx, 1 ; S2>>1
jmp tri15
tri20: mov al, 0Dh ;new line
int 29h
mov al, 0Ah
int 29h
shl ebx, 1 ;S2:= S2 xor S1<<1
xor edx, ebx
shr ebx, 2 ;S2:= S2 xor S1>>1
xor edx, ebx
loop tri10 ;next I
ret
end start</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
XPL0
<lang XPL0>code ChOut=8, CrLf=9; def Order=4, Size=1<<Order; int S1, S2, I; [S1:= 0; S2:= $8000; for I:= 0 to Size-1 do
[S1:= S2;
while S2 do
[ChOut(0, if S2&1 then ^* else ^ ); S2:= S2>>1];
CrLf(0);
S2:= S2 xor S1<<1;
S2:= S2 xor S1>>1;
];
]</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Yabasic
<lang Yabasic>sub rep$(n, c$)
local i, s$
for i = 1 to n
s$ = s$ + c$
next return s$
end sub
sub sierpinski(n)
local lim, y, x
lim = 2**n - 1
for y = lim to 0 step -1
print rep$(y, " ");
for x = 0 to lim-y
if and(x, y) then print " "; else print "* "; end if
next
print
next
end sub
for i = 1 to 5
sierpinski(i)
next </lang>
zkl
<lang zkl>level,d := 3,T("*"); foreach n in (level + 1){
sp:=" "*(2).pow(n);
d=d.apply('wrap(a){ String(sp,a,sp) }).extend(
d.apply(fcn(a){ String(a," ",a) }));
} d.concat("\n").println();</lang>
- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
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- Programming Tasks
- Fractals
- 11l
- 8080 Assembly
- 8086 Assembly
- ACL2
- Action!
- Ada
- ALGOL 68
- ALGOL W
- AppleScript
- Arturo
- ATS
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- APL
- AWK
- BASH (feat. sed & tr)
- BASIC
- BASIC256
- BBC BASIC
- FreeBASIC
- IS-BASIC
- BCPL
- Befunge
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- BQN
- C
- C sharp
- C++
- Clojure
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- Common Lisp
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- D
- Delphi
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- DWScript
- E
- Elixir
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- Excel
- F Sharp
- Factor
- FALSE
- FALSE examples needing attention
- Examples needing attention
- FOCAL
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- Java
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- Wren
- X86 Assembly
- XPL0
- Yabasic
- Zkl