# Sierpinski triangle

Sierpinski triangle
You are encouraged to solve this task according to the task description, using any language you may know.

Produce an ASCII representation of a Sierpinski triangle of order   N.

Example

The Sierpinski triangle of order   4   should look like this:

```                       *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## 11l

Translation of: Python
```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"))```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## 8080 Assembly

```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?
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,'\$'```
Output:

For order 4 (default if no given):

```                *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## 8086 Assembly

```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?
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,'\$'
```
Output:

For order 4 (default if no order given):

```                *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## ACL2

```(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)))
```

## 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```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

This Ada example creates a string of the binary value for each line, converting the '0' values to spaces.

```with Ada.Text_Io; use Ada.Text_Io;
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 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;
```

alternative using modular arithmetic:

```with Ada.Command_Line;

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
else
end if;
end loop;
end loop;
end Sierpinski;

N : Order := 4;
begin
end if;
Sierpinski (N);
end Main;
```
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

Translation of: python
Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386
```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)))```

## ALGOL W

Translation of: C
```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.```

## AppleScript

Translation of: JavaScript

Centering any previous triangle block over two adjacent duplicates:

```------------------- 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)
end |λ|
end script

on |λ|(s)
unwords(replicate(2, s))
end |λ|
end script

-- Previous triangle block centered,
-- and placed on 2 adjacent duplicates.
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
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

Or generating each line as an XOR / Rule 90 / Pascal triangle rewrite of the previous line.

Translation of: JavaScript
```----------- 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)

-- 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, {{"*"}}, 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
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## Arturo

```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
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## ATS

```(* ****** ****** *)
//
// How to compile:
//
// patscc -DATS_MEMALLOC_LIBC -o sierpinski sierpinski.dats
//
(* ****** ****** *)
//
#include
//
(* ****** ****** *)

#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] *)```

## AutoHotkey

ahk discussion

```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
}
```

## APL

```A←67⍴0⋄A[34]←1⋄' #'[1+32 67⍴{~⊃⍵:⍵,∇(1⌽⍵)≠¯1⌽⍵⋄⍬}A]
```

## 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)
}
```

## 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.

```#!/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' '  *'
```

## Bash

Translation of: BASH (feat. sed & tr)
Works with: Bash version 3.2.57
Works with: Bash version 5.2.9
```#!/bin/bash

### BASH (pure-bash)
### https://rosettacode.org/wiki/Bourne_Again_SHell
### Ported from bash+sed+tr version
### Tested with bash versions 3.2.57 and 5.2.9
### 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 Bash Parameter Expansion
###     \${parameter/pattern/string}
### syntax used for pure-bash global-pattern-substitution.
### (Search "man bash" output for "Parameter Expansion" for additional details
###  on the
###     \${parameter/pattern/string}
###  and
###     \${parameter:-word}
###  syntax)

# Basic principle:
#
#
#  x ->  dxd       d -> dd      s -> s
#        xsx            dd           s
#
# In the end all 'd' and 's' are removed.
function rec(){
if [ \$1 == 0 ]
then
echo "x"
else
rec \$[ \$1 - 1 ] | while read line ; do
A="\$line" ; A="\${A//d/dd}" ; A="\${A//x/dxd}" ; echo "\$A"
A="\$line" ; A="\${A//d/dd}" ; A="\${A//x/xsx}" ; echo "\$A"
done
fi
}

### If the script has no arguments, then the default is n=4
### Else n is the first argument to the script
export n="\${1:-4}"

B="\$(rec "\$n")" ; B="\${B//d/ }" ; B="\${B//s/ }" ; B="\${B//x/*}"
echo "\$B"
```

## BASIC

Works with: QBasic
Works with: FreeBASIC
```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
```

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

```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```

### BBC BASIC

```      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
```

### 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)
```

### 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```

## BCPL

Translation of: C
```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')
\$)
\$)```
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.

```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<
```

## Burlesque

```{JPp{
-.'sgve!
J{JL[2./+.' j.*PppP.+PPj.+}m[
j{J" "j.+.+}m[
.+
}{vv{"*"}}PPie} 's sv
4 'sgve!unsh```

## BQN

```Sierp ← {" •" ⊏˜ (⌽↕2⋆𝕩)⌽˘∾˘∾⟜0¨∧´∘∨⌜˜⥊↕2⥊˜𝕩}
```
Output:
```   Sierp 3
┌─
╵"       •
• •
•   •
• • • •
•       •
• •     • •
•   •   •   •
• • • • • • • • "
┘
```

## 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;
}
```

### Automaton

This solution uses a cellular automaton (rule 90) with a proper initial status.

```#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);
}
```
```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);
}
```
```int main()
{
sierpinski_triangle(4);
return EXIT_SUCCESS;
}
```

## C#

```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;
}
}
}
```
```namespace RosettaCode {
class Program {
static void Main(string[] args) {
SierpinskiTriangle t = new SierpinskiTriangle(4);
t.Display();
}
}
}
```
Translation of: C
Works with: C# version 6.0+
```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 ? "  " : "* ");
}
}
}
```
Translation of: OCaml
Works with: C# version 3.0+
```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);
}
}
```

Or, with fold / reduce (a.k.a. aggregate):

```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); }
}
}
```

## C++

Works with: C++11

A STL-centric recursive solution that uses the new lambda functions in C++11.

```#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;
}
```

## Clojure

Translation of: Common Lisp

With a touch of Clojure's sequence handling.

```(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)
```

## CLU

Translation of: Fortran
```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```
Output:
```                *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## COBOL

Translation of: Fortran

and retains a more Fortran-like coding style than is really idiomatic in 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,
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).
```

## Comal

```0010 DIM part\$(FALSE:TRUE) OF 2
0020 part\$(FALSE):="  ";part\$(TRUE):="* "
0030 INPUT "Order? ":order#
0040 size#:=2^order#
0050 FOR y#:=size#-1 TO 0 STEP -1 DO
0060   PRINT " "*y#,
0070   FOR x#:=0 TO size#-y#-1 DO PRINT part\$(x# BITAND y#=0),
0080   PRINT
0090 ENDFOR y#
0100 END
```
Output:
```Order? 4
*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## Common 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) "*" " ")))))
```

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:

```(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))
```

## 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;```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## D

### Run-time Version

```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;
}
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

### Compile-time Version

Same output.

```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() {}
```

### Simple Version

Translation of: C

Same output.

```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;
}
```

### Alternative Version

This uses a different algorithm and shows a different output.

```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;
}
}
```
Output:
``` #
###

#
###
## ##
#######

#
###
## ##
#######
##     ##
####   ####
##  ## ##  ##
###############

#
###
## ##
#######
##     ##
####   ####
##  ## ##  ##
###############
##             ##
####           ####
##  ##         ##  ##
########       ########
##      ##     ##      ##
####    ####   ####    ####
##  ##  ##  ## ##  ##  ##  ##
###############################

#
###
## ##
#######
##     ##
####   ####
##  ## ##  ##
###############
##             ##
####           ####
##  ##         ##  ##
########       ########
##      ##     ##      ##
####    ####   ####    ####
##  ##  ##  ## ##  ##  ##  ##
###############################
##                             ##
####                           ####
##  ##                         ##  ##
########                       ########
##      ##                     ##      ##
####    ####                   ####    ####
##  ##  ##  ##                 ##  ##  ##  ##
################               ################
##              ##             ##              ##
####            ####           ####            ####
##  ##          ##  ##         ##  ##          ##  ##
########        ########       ########        ########
##      ##      ##      ##     ##      ##      ##      ##
####    ####    ####    ####   ####    ####    ####    ####
##  ##  ##  ##  ##  ##  ##  ## ##  ##  ##  ##  ##  ##  ##  ##
###############################################################```

## Delphi

Translation of: DWScript
```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.
```

## Draco

Translation of: C
```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```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## DWScript

Translation of: E
```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);
```

## 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()
}
}```
`? printSierpinski(4, stdout)`

Non-ASCII version (quality of results will depend greatly on text renderer):

```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()
}
}```

## EasyLang

Translation of: Nim
```size = bitshift 1 4 - 1
for y = size downto 0
for i = 0 to y - 1
write " "
.
for x = 0 to size - y
if bitand x y <> 0
write "  "
else
write "* "
.
.
write "\n"
.
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## Elixir

Translation of: Erlang
```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)
```

## 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")
]
```

## Erlang

Translation of: OCaml
```-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).
```

## Euphoria

Translation of: BASIC
```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)```

## Excel

### LAMBDA

Binding the names sierpinskiTriangle, sierpCentered and sierpDoubled to the following lambda expressions in the Name Manager of the Excel WorkBook:

```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),
SEQUENCE(nRows, nRows, 1, 1),
" "
),

APPENDCOLS(
)
)

sierpDoubled
=LAMBDA(grid,
APPENDCOLS(
APPENDCOLS(grid)(
IF(SEQUENCE(ROWS(grid), 1, 1, 1),
" "
)
)
)(grid)
)
```

and also assuming the following generic bindings in the Name Manager for the WorkBook:

```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))
)
)
)
)
)
```
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).

 =sierpinskiTriangle("▲")(A2) fx 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:

 =gridString(sierpinskiTriangle("*")(A2)) fx A B 1 Iterations Sierpinski Triangle 2 0 ``` * ``` 3 1 ``` * * * ``` 4 2 ``` * * * * * * * * * ``` 5 3 ``` * * * * * * * * * * * * * * * * * * * * * * * * * * * ``` 6 4 ``` * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ```

## F#

```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)
```

## Factor

Translation of: OCaml
```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 ;
```

A more idiomatic version taking advantage of the with, each-integer, and ? combinator as well as leveraging the looping combinator each-integer.

```USING: command-line io io.streams.string kernel math math.parser
namespaces sequences ;
IN: sierpinski

: plot ( i j -- )
bitand zero? "* " "  " ? write ;

: pad ( n -- )
1 - [ " " write ] times ;

: plot-row ( n -- )
dup 1 + [ tuck - plot ] with each-integer ;

: sierpinski ( n -- )
dup '[ _ over - pad plot-row nl ] each-integer ;
```

## FALSE

Runs correctly in http://www.quirkster.com/iano/js/false-js.html. Requires the pick character to be substituted with 'O' in the portable interpreter linked-to from https://strlen.com/false-language/.

```{ print spaces; in:n }
[[\$0>][" " 1-]#%]w:

{ left shift; in:x,y out:x<<y }
[[\$0>][\2*\ 1-]#%]l:

1 4 l;!       { SIZE = 1<<4 }

\$             { y = SIZE }
[\$0>]         { y > 0 }
[1-
\$w;!
1ø           { x = SIZE }
[\$0>]
[1-
1ø\$2ø\-&0=  { !((x - y) & y) }
\$ ["* "]?
~ ["  "]?
]#%
10,
]#%%```

## 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)```
Output:
```ORDER:4
*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## 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
```

## Fortran

Works with: Fortran version 90 and later

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.

```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
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
```

## 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);
*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## gnuplot

Making and printing a text string, using bit-twiddling to decide whether each character should be a space or a star.

```# 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)
```

## Go

"Δ" (Greek capital letter delta) looks good for grain, as does Unicode triangle, "△". ASCII "." and "^" are pleasing. "/\\", "´`", and "◢◣"" make interesting wide triangles.

```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)
}
}
```

## Golfscript

Cambia el "3" a un número mayor para un triángulo más grande.

`' /\ /__\ '4/){.+\.{[2\$.]*}%\{.+}%+\}3*;n*`
Output:
```               /\
/__\
/\  /\
/__\/__\
/\      /\
/__\    /__\
/\  /\  /\  /\
/__\/__\/__\/__\
/\              /\
/__\            /__\
/\  /\          /\  /\
/__\/__\        /__\/__\
/\      /\      /\      /\
/__\    /__\    /__\    /__\
/\  /\  /\  /\  /\  /\  /\  /\
/__\/__\/__\/__\/__\/__\/__\/__\
```

## Groovy

Solution:

```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
}
```

Test:

```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() }
```
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
```

```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
```
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:

```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
```
Output:
```               ▲---------------
▲+▲--------------
▲-+ ▲-------------
▲+▲+▲+▲------------
▲---+   ▲-----------
▲+▲--+  ▲+▲----------
▲-+ ▲-+ ▲-+ ▲---------
▲+▲+▲+▲+▲+▲+▲+▲--------
▲-------+       ▲-------
▲+▲------+      ▲+▲------
▲-+ ▲-----+     ▲-+ ▲-----
▲+▲+▲+▲----+    ▲+▲+▲+▲----
▲---+   ▲---+   ▲---+   ▲---
▲+▲--+  ▲+▲--+  ▲+▲--+  ▲+▲--
▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-
▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲```

Using bitwise and between x and y coords:

```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
```
Translation of: JavaScript
```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
```

Or simply as a right fold:

```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
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## 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;
}
}
}
```

## 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 ~)))
--```

## 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.

```# 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
```

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.

```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
```

## J

There are any number of succinct ways to produce this in J. Here's one that exploits self-similarity:

```   |. _31]\ ,(,.~ , ])^:4 ,: '* '
```

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:

```   ' *' {~ '1' = (- |."_1 [: ": 2 | !/~) i._16
```

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.

```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();
}

}
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## JavaFX Script

Translation of: Python
```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);```

## 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.

```(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);
```

Output (N=4)

```               ▲
▲ ▲
▲   ▲
▲ ▲ ▲ ▲
▲       ▲
▲ ▲     ▲ ▲
▲   ▲   ▲   ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲               ▲
▲ ▲             ▲ ▲
▲   ▲           ▲   ▲
▲ ▲ ▲ ▲         ▲ ▲ ▲ ▲
▲       ▲       ▲       ▲
▲ ▲     ▲ ▲     ▲ ▲     ▲ ▲
▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲```

#### Imperative

```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] = '&nbsp;';
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] ? '&nbsp;' : '*');
line[j - 1] = u;
u = t;
}
line[n + i] = t;
line[n + i + 1] = '*';
}
}
document.write("<pre>\n");
triangle(6);
document.write("</pre>");
```

### 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:

```(() => {
"use strict";

// --------------- SIERPINSKI TRIANGLE ---------------

// sierpinski :: Int -> String
const sierpinski = n =>
Array.from({
length: n
})
.reduce(
(xs, _, i) => {
const s = " ".repeat(2 ** i);

return [
...xs.map(x => s + x + s),
...xs.map(x => `\${x} \${x}`)
];
},
["*"]
)
.join("\n");

// ---------------------- TEST -----------------------
return sierpinski(4);
})();
```

Centering any preceding triangle block over two adjacent duplicates:

```(() => {
"use strict";

// ----- LINES OF SIERPINSKI TRIANGLE AT LEVEL N -----

// sierpinski :: Int -> [String]
const sierpTriangle = n =>
// Previous triangle centered with
0 < n ? (
ap([
map(
xs => ap([
compose(
ks => ks.join(""),
replicate(2 ** (n - 1))
)
])([" ", "-"])
.join(xs)
),

// above a pair of duplicates,
// placed one character apart.
map(s => `\${s}+\${s}`)
])([sierpTriangle(n - 1)])
.flat()
) : ["▲"];

// ---------------------- TEST -----------------------
const main = () =>
sierpTriangle(4)
.join("\n");

// ---------------- GENERIC FUNCTIONS ----------------

// ap (<*>) :: [(a -> b)] -> [a] -> [b]
const ap = fs =>
// The sequential application of each of a list
// of functions to each of a list of values.
// apList([x => 2 * x, x => 20 + x])([1, 2, 3])
//     -> [2, 4, 6, 21, 22, 23]
xs => fs.flatMap(f => xs.map(f));

// compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
const compose = (...fs) =>
// A function defined by the right-to-left
// composition of all the functions in fs.
fs.reduce(
(f, g) => x => f(g(x)),
x => x
);

// map :: (a -> b) -> [a] -> [b]
const map = f => xs => xs.map(f);

// replicate :: Int -> a -> [a]
const replicate = n =>
// A list of n copies of x.
x => Array.from({
length: n
}, () => x);

// ---------------------- TEST -----------------------
return main();
})();
```
Output:
```               ▲---------------
▲+▲--------------
▲-+ ▲-------------
▲+▲+▲+▲------------
▲---+   ▲-----------
▲+▲--+  ▲+▲----------
▲-+ ▲-+ ▲-+ ▲---------
▲+▲+▲+▲+▲+▲+▲+▲--------
▲-------+       ▲-------
▲+▲------+      ▲+▲------
▲-+ ▲-----+     ▲-+ ▲-----
▲+▲+▲+▲----+    ▲+▲+▲+▲----
▲---+   ▲---+   ▲---+   ▲---
▲+▲--+  ▲+▲--+  ▲+▲--+  ▲+▲--
▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-
▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲```

Or constructed as 2^N lines of Pascal's triangle mod 2, and mapped to centred {1:asterisk, 0:space} strings.

```(() => {
"use strict";

// --------------- SIERPINSKI TRIANGLE ---------------

// sierpinski :: Int -> [Bool]
const sierpinski = intOrder =>
// 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.
pascalMod2Chars(2 ** intOrder)
.reduceRight((a, x) => ([
`\${a[1]}\${x.join(" ")}\n\${a[0]}`,
`\${a[1]} `
]), ["", ""])[0];

// pascalMod2Chars :: Int -> [[Char]]
const pascalMod2Chars = nRows =>
enumFromTo(1)(nRows - 1)
.reduce(sofar => {
const rows = sofar.slice(-1)[0];

// Rule 90 also reduces to the same XOR
// relationship between left and right neighbours.
return ([
...sofar,
zipWith(
l => r => l === r ? (
" "
) : "*"
)([" ", ...rows])([...rows, " "])
]);
}, [
["*"]
]);

// ---------------------- TEST -----------------------
// main :: IO ()
const main = () =>
sierpinski(4);

// --------------------- GENERIC ---------------------

// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = f =>
// A list constructed by zipping with a
// custom function, rather than with the
// default tuple constructor.
xs => ys => xs.map(
(x, i) => f(x)(ys[i])
).slice(
0, Math.min(xs.length, ys.length)
);

// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m =>
n => Array.from({
length: 1 + n - m
}, (_, i) => m + i);

// MAIN ---
return main();
})();
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

Preliminaries

```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;```
```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```
Output:

As elsewhere.

## Julia

Works with: Julia version 0.6
```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
```

## Kotlin

Translation of: C
```// 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()
}
}
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## Lambdatalk

### 1) define

```{def sierp
{def sierp.r
{lambda {:order :length :angle}
{if {= :order 0}
then M:length                            // move :length
else {sierp.r {- :order 1}               // recurse
{/ :length 2}
{- :angle}}
T:angle                             // turn :angle
{sierp.r {- :order 1}               // recurse
{/ :length 2}
{+ :angle}}
T:angle                             // turn :angle
{sierp.r {- :order 1}               // recurse
{/ :length 2}
{- :angle}}
}}}
{lambda {:order :length}
{if {= {% :order 2} 0}                     // if :order is even
then {sierp.r :order :length 60}          // recurse with 60°
else T60                                  // else turn 60°
{sierp.r :order :length -60}         // recurse with -60°
}}}
-> sierp
```

### 2) draw

Four curves drawn in 50ms on a PowerBookPro. using the turtle primitive.

```{svg {@ width="580" height="580" style="box-shadow:0 0 8px #000;"}
{polyline  {@ points="{turtle 50 5 0 {sierp 1 570}}"
stroke="#ccc" fill="transparent" stroke-width="7"}}
{polyline  {@ points="{turtle 50 5 0 {sierp 3 570}}"
stroke="#8ff" fill="transparent" stroke-width="5"}}
{polyline  {@ points="{turtle 50 5 0 {sierp 5 570}}"
stroke="#f88" fill="transparent" stroke-width="3"}}
{polyline  {@ points="{turtle 50 5 0 {sierp 7 570}}"
stroke="#000" fill="transparent" stroke-width="1"}}
```

## Liberty BASIC

```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```

## 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 []
]```

## Lua

Ported from the list-comprehension Python version.

```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))
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## 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:```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## Mathematica /Wolfram Language

Cellular automaton (rule 90) based solution:

```n=4;Grid[CellularAutomaton[90,{{1},0},2^n-1]/.{0->" ",1->"*"},ItemSize->All]
```

Using built-in function:

```SierpinskiMesh[3]
```

## MATLAB

STRING was introduced in version R2016b.

```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)))
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

### Cellular Automaton Version

```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)
```

### Mixed Version

```spy(mod(abs(pascal(32,1)),2)==1)
```

## NetRexx

Translation of: Java
```/* 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
```
Output:
```                ▲
▲ ▲
▲   ▲
▲ ▲ ▲ ▲
▲       ▲
▲ ▲     ▲ ▲
▲   ▲   ▲   ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲               ▲
▲ ▲             ▲ ▲
▲   ▲           ▲   ▲
▲ ▲ ▲ ▲         ▲ ▲ ▲ ▲
▲       ▲       ▲       ▲
▲ ▲     ▲ ▲     ▲ ▲     ▲ ▲
▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
```

## Nim

Translation of: C
```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"
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
"               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * * ```

## Oberon-07

Translation of: C
Works with: OBNC

A version of this program for Oberon System can be found here: https://github.com/hansklav/Fractals-in-Oberon-07/blob/main/Sierpinski-Sieve/SierStarV5.Mod
Note that LSL means "Logical Shift Left". The SET type is a bitset, the SET operator ∗ performs set intersection (equivalent to bitwise AND), and # is ≠ .

```MODULE SierpinskiTriangle;
IMPORT S := SYSTEM, Out;

CONST
N = 4;
size = LSL(1, N);  (* size = 2^N *)

VAR x, y, i: INTEGER;

BEGIN
FOR y := size - 1 TO 0 BY -1 DO
FOR i := 0 TO y - 1 DO Out.Char(" ") END;
x := 0;
WHILE x + y < size DO
(* use SET intersection (bitwise AND) *)
IF ORD(S.VAL(SET, x) * S.VAL(SET, y)) # 0 THEN
Out.String("  ")
ELSE
Out.String("* ")
END;
INC(x)
END;
Out.Ln
END
END SierpinskiTriangle.
```
Output:
```\$ obnc SierpinskiTriangle.obn
\$ ./SierpinskiTriangle
*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
\$ _
```

## 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)
```

## Oforth

This solution uses a cellular automaton (rule 90 for triangle).

automat(rule, n) runs cellular automaton for rule "rule" for n generations.

```: 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 ;```
Output:
```>4 sierpinskiTriangle
*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
ok
>
```

## 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}```

## PARI/GP

Translation of: C
```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)```
Output:
```               *
**
* *
****
*   *
**  **
* * * *
********
*       *
**      **
* *     * *
****    ****
*   *   *   *
**  **  **  **
* * * * * * * *
****************```

## Pascal

Translation of: C
Works with: Free 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;
```
```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;
```
```begin
triangle(4)
end.
```

## Perl

### version 1

```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;
```

### one-liner

```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;}'
```

## Phix

Translation of: C
```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

```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```

## PHP

Translation of: JavaScript
```<?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);
```
Output:
```                #
# #
#   #
# # # #
#       #
# #     # #
#   #   #   #
# # # # # # # #
#               #
# #             # #
#   #           #   #
# # # #         # # # #
#       #       #       #
# #     # #     # #     # #
#   #   #   #   #   #   #   #
# # # # # # # # # # # # # # # #
```

## Picat

Translation of: E
```go =>
foreach(N in 1..4)
sierpinski(N),
nl
end,
nl.

sierpinski(N)  =>
Size = 2**N,
foreach(Y in Size-1..-1..0)
printf("%s", [' ' : _I in 1..Y]),
foreach(X in 0..Size-Y-1)
printf("%s ", cond(X /\ Y == 0, "*", " "))
end,
nl
end.```
Output:
``` *
* *

*
* *
*   *
* * * *

*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *

*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * * ```

## PicoLisp

Translation of: Python
```(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))```

## 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;```

## PL/M

```100H:

DECLARE ORDER LITERALLY '4';

/* CP/M BDOS CALL */
BDOS: PROCEDURE (FN, ARG);
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```
Output:
```                *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## Pop11

Solution using line buffer in an integer array oline, 0 represents ' ' (space), 1 represents '*' (star).

```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);```

Alternative solution, keeping all triangle as list of strings

```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);```

## PostScript

This draws the triangles in a string-rewrite fashion, where all edges form a single polyline. 9 page document showing progession.

```%!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
```

## PowerShell

Translation of: JavaScript
```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] = '█'
}
}
```

## Processing

### Characters in drawing canvas version

```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);
}
}
```

### Text in console version

Translation of: 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;
}
```

## Prolog

Works with SWI-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(' ',' ',' ', ' ').
```
Output:
``` ?- sierpinski_triangle(4).
*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
true ```

## 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
```

## 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))
```

Or, using fold / reduce

Works with: Python version 3.x
```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)))
```

and fold/reduce, wrapped as concatMap, can provide the list comprehensions too:

```'''Sierpinski triangle'''

from functools import reduce

# 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: (
)

print(sierpinski(4))
```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

Use Python's long integer and bit operator to make an infinite triangle:

```x = 1
while True:
print(bin(x)[2:].replace('0', ' '))
x ^= x<<1```

## Quackery

Translation of: Forth
```  [ [ 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```
Output:
```                *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## R

Based on C# but using some of R's functionality to abbreviate code where possible.

```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)```

Shortened to a function of one line.

```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")```

## 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))```

## Raku

(formerly Perl 6)

Translation of: Perl
```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;```

## 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. */```

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.)

```                                                                                                                                █
█ █
█   █
█ █ █ █
█       █
█ █     █ █
█   █   █   █
█ █ █ █ █ █ █ █
█               █
█ █             █ █
█   █           █   █
█ █ █ █         █ █ █ █
█       █       █       █
█ █     █ █     █ █     █ █
█   █   █   █   █   █   █   █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█                               █
█ █                             █ █
█   █                           █   █
█ █ █ █                         █ █ █ █
█       █                       █       █
█ █     █ █                     █ █     █ █
█   █   █   █                   █   █   █   █
█ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █
█               █               █               █
█ █             █ █             █ █             █ █
█   █           █   █           █   █           █   █
█ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █
█       █       █       █       █       █       █       █
█ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █
█   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█                                                               █
█ █                                                             █ █
█   █                                                           █   █
█ █ █ █                                                         █ █ █ █
█       █                                                       █       █
█ █     █ █                                                     █ █     █ █
█   █   █   █                                                   █   █   █   █
█ █ █ █ █ █ █ █                                                 █ █ █ █ █ █ █ █
█               █                                               █               █
█ █             █ █                                             █ █             █ █
█   █           █   █                                           █   █           █   █
█ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
█       █       █       █                                       █       █       █       █
█ █     █ █     █ █     █ █                                     █ █     █ █     █ █     █ █
█   █   █   █   █   █   █   █                                   █   █   █   █   █   █   █   █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█                               █                               █                               █
█ █                             █ █                             █ █                             █ █
█   █                           █   █                           █   █                           █   █
█ █ █ █                         █ █ █ █                         █ █ █ █                         █ █ █ █
█       █                       █       █                       █       █                       █       █
█ █     █ █                     █ █     █ █                     █ █     █ █                     █ █     █ █
█   █   █   █                   █   █   █   █                   █   █   █   █                   █   █   █   █
█ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █
█               █               █               █               █               █               █               █
█ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █
█   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █
█ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █
█       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █
█ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █
█   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█                                                                                                                               █
█ █                                                                                                                             █ █
█   █                                                                                                                           █   █
█ █ █ █                                                                                                                         █ █ █ █
█       █                                                                                                                       █       █
█ █     █ █                                                                                                                     █ █     █ █
█   █   █   █                                                                                                                   █   █   █   █
█ █ █ █ █ █ █ █                                                                                                                 █ █ █ █ █ █ █ █
█               █                                                                                                               █               █
█ █             █ █                                                                                                             █ █             █ █
█   █           █   █                                                                                                           █   █           █   █
█ █ █ █         █ █ █ █                                                                                                         █ █ █ █         █ █ █ █
█       █       █       █                                                                                                       █       █       █       █
█ █     █ █     █ █     █ █                                                                                                     █ █     █ █     █ █     █ █
█   █   █   █   █   █   █   █                                                                                                   █   █   █   █   █   █   █   █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                                                                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█                               █                                                                                               █                               █
█ █                             █ █                                                                                             █ █                             █ █
█   █                           █   █                                                                                           █   █                           █   █
█ █ █ █                         █ █ █ █                                                                                         █ █ █ █                         █ █ █ █
█       █                       █       █                                                                                       █       █                       █       █
█ █     █ █                     █ █     █ █                                                                                     █ █     █ █                     █ █     █ █
█   █   █   █                   █   █   █   █                                                                                   █   █   █   █                   █   █   █   █
█ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                                                                                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █
█               █               █               █                                                                               █               █               █               █
█ █             █ █             █ █             █ █                                                                             █ █             █ █             █ █             █ █
█   █           █   █           █   █           █   █                                                                           █   █           █   █           █   █           █   █
█ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █                                                                         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █
█       █       █       █       █       █       █       █                                                                       █       █       █       █       █       █       █       █
█ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █                                                                     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █
█   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █                                                                   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█                                                               █                                                               █                                                               █
█ █                                                             █ █                                                             █ █                                                             █ █
█   █                                                           █   █                                                           █   █                                                           █   █
█ █ █ █                                                         █ █ █ █                                                         █ █ █ █                                                         █ █ █ █
█       █                                                       █       █                                                       █       █                                                       █       █
█ █     █ █                                                     █ █     █ █                                                     █ █     █ █                                                     █ █     █ █
█   █   █   █                                                   █   █   █   █                                                   █   █   █   █                                                   █   █   █   █
█ █ █ █ █ █ █ █                                                 █ █ █ █ █ █ █ █                                                 █ █ █ █ █ █ █ █                                                 █ █ █ █ █ █ █ █
█               █                                               █               █                                               █               █                                               █               █
█ █             █ █                                             █ █             █ █                                             █ █             █ █                                             █ █             █ █
█   █           █   █                                           █   █           █   █                                           █   █           █   █                                           █   █           █   █
█ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
█       █       █       █                                       █       █       █       █                                       █       █       █       █                                       █       █       █       █
█ █     █ █     █ █     █ █                                     █ █     █ █     █ █     █ █                                     █ █     █ █     █ █     █ █                                     █ █     █ █     █ █     █ █
█   █   █   █   █   █   █   █                                   █   █   █   █   █   █   █   █                                   █   █   █   █   █   █   █   █                                   █   █   █   █   █   █   █   █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█                               █                               █                               █                               █                               █                               █                               █
█ █                             █ █                             █ █                             █ █                             █ █                             █ █                             █ █                             █ █
█   █                           █   █                           █   █                           █   █                           █   █                           █   █                           █   █                           █   █
█ █ █ █                         █ █ █ █                         █ █ █ █                         █ █ █ █                         █ █ █ █                         █ █ █ █                         █ █ █ █                         █ █ █ █
█       █                       █       █                       █       █                       █       █                       █       █                       █       █                       █       █                       █       █
█ █     █ █                     █ █     █ █                     █ █     █ █                     █ █     █ █                     █ █     █ █                     █ █     █ █                     █ █     █ █                     █ █     █ █
█   █   █   █                   █   █   █   █                   █   █   █   █                   █   █   █   █                   █   █   █   █                   █   █   █   █                   █   █   █   █                   █   █   █   █
█ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █                 █ █ █ █ █ █ █ █
█               █               █               █               █               █               █               █               █               █               █               █               █               █               █               █
█ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █             █ █
█   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █           █   █
█ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █         █ █ █ █
█       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █       █
█ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █     █ █
█   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █   █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
```

Output with an input of   64   can be viewed at:   Sierpinski triangle/REXX output 64

## 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```

Output:

```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## Ruby

From the command line:

`ruby -le'16.times{|y|print" "*(15-y),*(0..y).map{|x|~y&x>0?"  ":" *"}}'`

or,

Translation of: Python
```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)```

Using fold / reduce (aka. inject):

```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)```

## Run BASIC

```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```
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## 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;
});

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);
}```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## Scala

The Ruby command-line version (on Windows):

`scala -e "for(y<-0 to 15){println(\" \"*(15-y)++(0 to y).map(x=>if((~y&x)>0)\"  \"else\" *\")mkString)}"`

The Forth version:

```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
}
}```

```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
}```

## 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))))))```

## 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;```

## SETL

```program sierpinski;
const size = 4;

loop for i in [0..size*4-1] do
putchar(' ' * (size*4-1-i));
c := 1;
loop for j in [0..i] do
putchar(if c mod 2=0 then "  " else " *" end);
c := c*(i-j) div (j+1);
end loop;
print;
end loop;
end program;```
Output:
```                *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *```

## Sidef

```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)```

## Swift

Translation of: Java
```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] = "*"
}
}```

## Tcl

Translation of: Perl
```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]```

## TI-83 BASIC

Uses Wolfram Rule 90.

```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```

## uBasic/4tH

```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

Print
Next
End```

## 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```

This produces an infinite, left-justified triangle:

```*
**
* *
****
*   *
**  **
* * * *
********
*       *
**      **
* *     * *
****    ****
*   *   *   *
**  **  **  **
* * * * * * * *
****************
*               *
**              **
* *             * *
****            ****
*   *           *   *
**  **          **  **
* * * *         * * * *
********        ********
*       *       *       *
**      **      **      **
* *     * *     * *     * *
****    ****    ****    ****
*   *   *   *   *   *   *   *
**  **  **  **  **  **  **  **
* * * * * * * * * * * * * * * *
********************************
*                               *
**                              **
* *                             * *
........
```

## Ursala

the straightforward recursive solution

```#import nat

triangle = ~&a^?\<<&>>! ^|RNSiDlrTSPxSxNiCK9xSx4NiCSplrTSPT/~& predecessor```

the cheeky cellular automaton solution

```#import std
#import nat

evolve "n" = @iNC ~&x+ rep"n" ^C\~& @h rule*+ swin3+ :/0+ --<0>
sierpinski = iota; --<&>@NS; iota; ^H/evolve@z @NS ^T/~& :/&```

an example of each (converting from booleans to characters)

```#show+

examples = mat0 ~&?(`*!,` !)*** <sierpinski3,triangle4>```
Output:
```        *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *

*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## Uxntal

```( uxncli sierpinski.rom )

|100 @on-reset ( -> )

#10 STHk #01 SUB
&ver ( -- )
DUP
#00 EQUk ?{
#2018 DEO
} POP
#00
&fill
ANDk #202a ROT ?{ SWP } POP #18 DEO
#2018 DEO
POP2
#0a18 DEO
#01 SUB DUP #ff NEQ ?&ver
POP POPr

BRK```

The triangle size is given by the first instruction `#10`, representing the number of rows to print.

## VBA

Translation of: Phix
```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```
Output:
```
#

# #

#

# #

#   #

# # # #

#

# #

#   #

# # # #

#       #

# #     # #

#   #   #   #

# # # # # # # #

#

# #

#   #

# # # #

#       #

# #     # #

#   #   #   #

# # # # # # # #

#               #

# #             # #

#   #           #   #

# # # #         # # # #

#       #       #       #

# #     # #     # #     # #

#   #   #   #   #   #   #   #

# # # # # # # # # # # # # # # #

#

# #

#   #

# # # #

#       #

# #     # #

#   #   #   #

# # # # # # # #

#               #

# #             # #

#   #           #   #

# # # #         # # # #

#       #       #       #

# #     # #     # #     # #

#   #   #   #   #   #   #   #

# # # # # # # # # # # # # # # #

#                               #

# #                             # #

#   #                           #   #

# # # #                         # # # #

#       #                       #       #

# #     # #                     # #     # #

#   #   #   #                   #   #   #   #

# # # # # # # #                 # # # # # # # #

#               #               #               #

# #             # #             # #             # #

#   #           #   #           #   #           #   #

# # # #         # # # #         # # # #         # # # #

#       #       #       #       #       #       #       #

# #     # #     # #     # #     # #     # #     # #     # #

#   #   #   #   #   #   #   #   #   #   #   #   #   #   #   #

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ```

## VBScript

Translation of: PowerShell
```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)```

## Vedit macro language

### Iterative

Translation of: JavaScript

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.

```#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)
}```

### Recursive

Translation of: BASIC

Vedit macro language does not have recursive functions, so some pushing and popping is needed to implement recursion.

```#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```

## Wren

Translation of: C
```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()
}```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## X86 Assembly

Translation of XPL0. Assemble with tasm, tlink /t

```        .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```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## 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;
];
]```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```

## Yabasic

Translation of: Phix
```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```

## Zig

Translation of: C
```const std = @import("std");

pub fn main() !void {
const stdout = std.io.getStdOut().writer();
const size: u16 = 1 << 4;
var y = size;
while (y > 0) {
y -= 1;
for (0..y) |_| try stdout.writeByte(' ');
for (0..size - y) |x| try stdout.writeAll(if (x & y != 0) "  " else "* ");
try stdout.writeByte('\n');
}
}```

### Automaton

Translation of: C
Works with: Zig version 0.11.0dev
```const std = @import("std");
const Allocator = std.mem.Allocator;

pub fn main() !void {
const stdout = std.io.getStdOut().writer();

var arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);
defer arena.deinit();
const allocator = arena.allocator();

try sierpinski_triangle(allocator, stdout, 4);
}```
```inline fn truth(x: u8) bool {
return x == '*';
}```
```fn rule_90(allocator: Allocator, evstr: []u8) !void {
var cp = try allocator.dupe(u8, evstr);
defer allocator.free(cp); // free does "free" for last node in arena

for (evstr, 0..) |*evptr, i| {
var s = [2]bool{
if (i == 0) false else truth(cp[i - 1]),
if (i + 1 == evstr.len) false else truth(cp[i + 1]),
};
evptr.* = if ((s[0] and !s[1]) or (!s[0] and s[1])) '*' else ' ';
}
}```
```fn sierpinski_triangle(allocator: Allocator, writer: anytype, n: u8) !void {
const len = std.math.shl(usize, 1, n + 1);

var b = try allocator.alloc(u8, len);
defer allocator.free(b);
for (b) |*ptr| ptr.* = ' ';

b[len >> 1] = '*';

try writer.print("{s}\n", .{b});

for (0..len / 2 - 1) |_| {
try rule_90(allocator, b);
try writer.print("{s}\n", .{b});
}
}```

## zkl

Translation of: D
```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();```
Output:
```               *
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
```