Sierpinski triangle: Difference between revisions

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{{task|Fractals}}


*
Produce an ASCII representation of a Sierpinski triangle of order N. For example, the Sierpinski triangle of order 4 should look like this:
* *
<pre>
* * *


*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
</pre>


how to print the above triangle
See also [[Sierpinski carpet]]

=={{header|Ada}}==
This Ada example creates a string of the binary value for each line, converting the '0' values to spaces.
<lang ada>with Ada.Text_Io; use Ada.Text_Io;
with Ada.Strings.Fixed;
with Interfaces; use Interfaces;

procedure Sieteri_Triangles is
subtype Practical_Order is Unsigned_32 range 0..4;
function Pow(X : Unsigned_32; N : Unsigned_32) return Unsigned_32 is
begin
if N = 0 then
return 1;
else
return X * Pow(X, N - 1);
end if;
end Pow;
procedure Print(Item : Unsigned_32) is
use Ada.Strings.Fixed;
package Ord_Io is new Ada.Text_Io.Modular_Io(Unsigned_32);
use Ord_Io;
Temp : String(1..36) := (others => ' ');
First : Positive;
Last : Positive;
begin
Put(To => Temp, Item => Item, Base => 2);
First := Index(Temp, "#") + 1;
Last := Index(Temp(First..Temp'Last), "#") - 1;
for I in reverse First..Last loop
if Temp(I) = '0' then
Put(' ');
else
Put(Temp(I));
end if;
end loop;
New_Line;
end Print;
procedure Sierpinski (N : Practical_Order) is
Size : Unsigned_32 := Pow(2, N);
V : Unsigned_32 := Pow(2, Size);
begin
for I in 0..Size - 1 loop
Print(V);
V := Shift_Left(V, 1) xor Shift_Right(V,1);
end loop;
end Sierpinski;
begin
for N in Practical_Order loop
Sierpinski(N);
end loop;
end Sieteri_Triangles;</lang>

=={{header|ALGOL 68}}==
{{trans|python}}

{{works with|ALGOL 68|Standard - no extensions to language used}}

{{works with|ALGOL 68G|Any - tested with release mk15-0.8b.fc9.i386}}

<!-- {{does not work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386 - test missing transput}} -->
<lang algol68>PROC sierpinski = (INT n)[]STRING: (
FLEX[0]STRING d := "*";
FOR i TO n DO
[UPB d * 2]STRING next;
STRING sp := " " * (2 ** (i-1));
FOR x TO UPB d DO
STRING dx = d[x];
next[x] := sp+dx+sp;
next[UPB d+x] := dx+" "+dx
OD;
d := next
OD;
d
);

printf(($gl$,sierpinski(4)))</lang>
=={{header|AutoHotkey}}==
ahk [http://www.autohotkey.com/forum/viewtopic.php?t=44657&postdays=0&postorder=asc&start=150 discussion]
<lang autohotkey>Loop 6
MsgBox % Triangle(A_Index)

Triangle(n,x=0,y=1) { ; Triangle(n) -> string of dots and spaces of Sierpinski triangle
Static t, l ; put chars in a static string
If (x < 1) { ; when called with one parameter
l := 2*x := 1<<(n-1) ; - compute location, string size
VarSetCapacity(t,l*x,32) ; - allocate memory filled with spaces
Loop %x%
NumPut(13,t,A_Index*l-1,"char") ; - new lines in the end of rows
}
If (n = 1) ; at the bottom of recursion
Return t, NumPut(46,t,x-1+(y-1)*l,"char") ; - write "." (better at proportional fonts)
u := 1<<(n-2)
Triangle(n-1,x,y) ; draw smaller triangle here
Triangle(n-1,x-u,y+u) ; smaller triangle down-left
Triangle(n-1,x+u,y+u) ; smaller triangle down right
Return t
}</lang>

=={{header|BASIC}}==
{{works with|FreeBASIC}}
{{works with|RapidQ}}
<lang freebasic>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

CLS
triangle 1,1,16,5</lang>

Note: The total height of the triangle is 2 * parameter ''length''. It should be power of two so that the pattern matches evenly with the character cells. Value 16 will thus create pattern of 32 lines.

=={{header|C}}==
This solution uses a cellular automaton (''rule 90'') with a proper initial status.

<lang c>#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <string.h>

#ifndef _POSIX_C_SOURCE
char *strdup(const char *s)
{
int l = strlen(s);
char *r = malloc(l+1);
memcpy(r, s, l+1);
return r;
}
#endif

#define truth(X) ((X)=='*'?true:false)
void rule_90(char *evstr)
{
int i;
int l = strlen(evstr);
bool s[3];
char *cp = strdup(evstr);

for(i=0;i < l; i++) {
s[1] = truth(cp[i]);
s[0] = (i-1) < 0 ? false : truth(cp[i-1]);
s[2] = (i+1) < l ? truth(cp[i+1]) : false;
if ( (s[0] && !s[2]) || (!s[0] && s[2]) ) {
evstr[i] = '*';
} else {
evstr[i] = ' ';
}
}
free(cp);
}</lang>

<lang c>void sierpinski_triangle(int n)
{
int i;
int l = 1<<(n+1);
char *b = malloc(l+1);

memset(b, ' ', l);
b[l] = 0;
b[l>>1] = '*';

printf("%s\n", b);
for(i=0; i < l/2-1;i++) {
rule_90(b);
printf("%s\n", b);
}

free(b);
}</lang>

<lang c>int main()
{
sierpinski_triangle(4);
return EXIT_SUCCESS;
}</lang>

=={{header|C sharp|C#}}==
<lang csharp>using System;
using System.Collections;

namespace RosettaCode {
class SierpinskiTriangle {
int len;
BitArray b;

public SierpinskiTriangle(int n) {
if (n < 1) {
throw new ArgumentOutOfRangeException("Order must be greater than zero");
}
len = 1 << (n+1);
b = new BitArray(len+1, false);
b[len>>1] = true;
}

public void Display() {
for (int j = 0; j < len / 2; j++) {
for (int i = 0; i < b.Count; i++) {
Console.Write("{0}", b[i] ? "*" : " ");
}
Console.WriteLine();
NextGen();
}
}

private void NextGen() {
BitArray next = new BitArray(b.Count, false);
for (int i = 0; i < b.Count; i++) {
if (b[i]) {
next[i - 1] = next[i - 1] ^ true;
next[i + 1] = next[i + 1] ^ true;
}
}
b = next;
}
}
}</lang>

<lang csharp>namespace RosettaCode {
class Program {
static void Main(string[] args) {
SierpinskiTriangle t = new SierpinskiTriangle(4);
t.Display();
}
}
}</lang>

{{trans|OCaml}}
{{works with|C sharp|C#|3.0+}}
<lang csharp>using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
public static List<String> Sierpinski(int n)
{
var lines = new List<string> { "*" };
string space = " ";

for (int i = 0; i < n; i++)
{
lines = lines.Select(x => space + x + space)
.Concat(lines.Select(x => x + " " + x)).ToList();
space += space;
}

return lines;
}

static void Main(string[] args)
{
foreach (string s in Sierpinski(4))
Console.WriteLine(s);
}
}</lang>

=={{header|Clojure}}==
'''Translation of''': Ada and Common Lisp, with a touch of Clojure's sequence handling.

<lang clojure>(ns example
(:require [clojure.contrib.math :as math]))

; Length of integer in binary
; (copied from a private multimethod in clojure.contrib.math)
(defmulti #^{:private true} integer-length class)

(defmethod integer-length java.lang.Integer [n]
(count (Integer/toBinaryString n)))
(defmethod integer-length java.lang.Long [n]
(count (Long/toBinaryString n)))
(defmethod integer-length java.math.BigInteger [n]
(count (.toString n 2)))

(defn sierpinski-triangle [order]
(loop [size (math/expt 2 order)
v (math/expt 2 (- size 1))]
(when (pos? size)
(println
(apply str (map #(if (bit-test v %) "*" " ")
(range (integer-length v)))))
(recur
(dec size)
(bit-xor (bit-shift-left v 1) (bit-shift-right v 1))))))

(sierpinski-triangle 4)
</lang>

=={{header|Common Lisp}}==

<lang lisp>(defun print-sierpinski (order)
(loop with size = (expt 2 order)
repeat size
for v = (expt 2 (1- size)) then (logxor (ash v -1) (ash v 1))
do (fresh-line)
(loop for i below (integer-length v)
do (princ (if (logbitp i v) "*" " ")))))</lang>

Printing each row could also be done by printing the integer in base 2 and replacing zeroes with spaces: <tt>(princ (substitute #\Space #\0 (format nil "~%~2,vR" (1- (* 2 size)) v)))</tt>

Replacing the iteration with <tt>for v = 1 then (logxor v (ash v 1))</tt> produces a "right" triangle instead of an "equilateral" one.

=={{header|D}}==
Adapted from Java version (this version is slower than the Python one).
<lang d>import std.stdio, std.string;

string[] sierpinski(int n) {
string[] parts = ["*"];
string space = " ";
for (int i; i < n; i++) {
string[] parts2;
foreach (x; parts)
parts2 ~= space ~ x ~ space;
foreach (x; parts)
parts2 ~= x ~ " " ~ x;
parts = parts2;
space ~= space;
}
return parts;
}

void main() {
writefln(sierpinski(4).join("\n"));
}</lang>

That sierpinski() function can run at compile time too, so with a compile-time join it can compute the whole result at compile-time:

<lang d>string[] sierpinski(int n) {
string[] parts = ["*"];
string space = " ";
for (int i; i < n; i++) {
string[] parts2;
foreach (x; parts)
parts2 ~= space ~ x ~ space;
foreach (x; parts)
parts2 ~= x ~ " " ~ x;
parts = parts2;
space ~= space;
}
return parts;
}

string joinCT(string[] parts, char sep) {
string result;
if (parts.length) {
foreach (part; parts[0 .. $-1]) {
result ~= part;
result ~= sep;
}
result ~= parts[$-1];
}
return result;
}

pragma(msg, sierpinski(4).joinCT('\n'));

void main() {}</lang>

=={{header|E}}==

<lang e>def printSierpinski(order, out) {
def size := 2**order
for y in (0..!size).descending() {
out.print(" " * y)
for x in 0..!(size-y) {
out.print((x & y).isZero().pick("* ", " "))
}
out.println()
}
}</lang>

<lang e>? printSierpinski(4, stdout)</lang>

Non-ASCII version (quality of results will depend greatly on text renderer):
<lang e>def printSierpinski(order, out) {
def size := 2**order
for y in (0..!size).descending() {
out.print("　" * y)
for x in 0..!(size-y) {
out.print((x & y).isZero().pick("◢◣", "　　"))
}
out.println()
}
}</lang>

=={{header|Erlang}}==
{{trans|OCaml}}
<lang erlang>
-module(sierpinski).
-export([triangle/1]).

triangle(N) ->
F = fun(X) -> io:format("~s~n",[X]) end,
lists:foreach(F, triangle(N, ["*"], " ")).

triangle(0, Down, _) -> Down;
triangle(N, Down, Sp) ->
NewDown = [Sp++X++Sp || X<-Down]++[X++" "++X || X <- Down],
triangle(N-1, NewDown, Sp++Sp).
</lang>

=={{header|F Sharp|F#}}==
<lang fsharp>let sierpinski n =
let rec loop down space n =
if n = 0 then
down
else
loop (List.map (fun x -> space + x + space) down @
List.map (fun x -> x + " " + x) down)
(space + space)
(n - 1)
in loop ["*"] " " n
let () =
List.iter (fun (i:string) -> System.Console.WriteLine(i)) (sierpinski 4)</lang>

=={{header|FALSE}}==
<lang false>[[$][$1&["*"]?$~1&[" "]?2/]#%"
"]s: { stars }
[$@$@|@@&~&]x: { xor }
[1\[$][1-\2*\]#%]e: { 2^n }
[e;!1\[$][\$s;!$2*x;!\1-]#%%]t:
4t;!</lang>

=={{header|Factor}}==
{{trans|OCaml}}
<lang factor>USING: io kernel math sequences ;
IN: sierpinski

: iterate-triangle ( triange spaces -- triangle' )
[ [ dup surround ] curry map ]
[ drop [ dup " " glue ] map ] 2bi append ;

: (sierpinski) ( triangle spaces n -- triangle' )
dup 0 = [ 2drop "\n" join ] [
[
[ iterate-triangle ]
[ nip dup append ] 2bi
] dip 1 - (sierpinski)
] if ;

: sierpinski ( n -- )
[ { "*" } " " ] dip (sierpinski) print ;</lang>

=={{header|Forth}}==
<lang forth>: stars ( mask -- )
begin
dup 1 and if [char] * else bl then emit
1 rshift dup
while space repeat drop ;

: triangle ( order -- )
1 swap lshift ( 2^order )
1 over 0 do
cr over i - spaces dup stars
dup 2* xor
loop 2drop ;
5 triangle</lang>

=={{header|Haskell}}==

<lang haskell>sierpinski 0 = ["*"]
sierpinski (n+1) = map ((space ++) . (++ space)) down
++ map (unwords . replicate 2) down
where down = sierpinski n
space = replicate (2^n) ' '

printSierpinski = mapM_ putStrLn . sierpinski</lang>

=={{header|HaXe}}==
{{trans|JavaScript}}

<lang HaXe>class Main
{
static function main()
{
triangle(3);
}
static inline function println(str) {
Lib.println(str);
}
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) {
println(line.join(''));
var u ='*';
var start = n - i;
var end = n + i + 1;
var t = SPACE;
for (j in start...end) {
t = (line[j-1] == line[j+1] ? SPACE : STAR);
line[j-1] = u;
u = t;
}
line[n+i] = t;
line[n+i+1] = STAR;
}
}
}</lang>
=={{header|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 "<tt>string(array)</tt>" which prints the ascii representation of each individual element in the array.

<lang idl>pro sierp,n
s = (t = bytarr(3+2^(n+1))+32b)
t[2^n+1] = 42b
for lines = 1,2^n do begin
print,string( (s = t) )
for i=1,n_elements(t)-2 do if s[i-1] eq s[i+1] then t[i]=32b else t[i]=42b
end
end</lang>

=={{header|J}}==

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

<lang j> |._31]\,(,.~,])^:4,:'* '</lang>

Here's one that leverages the relationship between Sierpinski's and Pascal's triangles:

<lang j> ' *'{~'1'=(-|."_1[:":2|!/~)i.-16</lang>

=={{header|Java}}==
{{trans|JavaScript}}

<lang java>public static void triangle(int n){
n= 1 << n;
StringBuilder line= new StringBuilder(); //use a "mutable String"
char t= 0;
char u= 0; // avoid warnings
for(int i= 0;i <= 2 * n;++i)
line.append(" "); //start empty
line.setCharAt(n, '*'); //with the top point of the triangle
for(int i= 0;i < n;++i){
System.out.println(line);
u= '*';
for(int j= n - i;j < n + i + 1;++j){
t= (line.charAt(j - 1) == line.charAt(j + 1) ? ' ' : '*');
line.setCharAt(j - 1, u);
u= t;
}
line.setCharAt(n + i, t);
line.setCharAt(n + i + 1, '*');
}
}</lang>

{{trans|Haskell}}

{{works with|Java|1.5+}}
<lang java>import java.util.*;

public class Sierpinski
{
public static List<String> sierpinski(int n)
{
List<String> down = Arrays.asList("*");
String space = " ";
for (int i = 0; i < n; i++) {
List<String> newDown = new ArrayList<String>();
for (String x : down)
newDown.add(space + x + space);
for (String x : down)
newDown.add(x + " " + x);

down = newDown;
space += space;
}
return down;
}

public static void main(String[] args)
{
for (String x : sierpinski(4))
System.out.println(x);
}
}</lang>

=={{header|JavaScript}}==
<lang javascript>function triangle(o) {
var n = 1<<o, line = new Array(2*n), i,j,t,u;
for (i=0; i<line.length; ++i) line[i] = '&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>");</lang>

=={{header|Logo}}==
This will draw a graphical Sierpinski gasket using turtle graphics.
<lang logo>to sierpinski :n :length
if :n = 0 [stop]
repeat 3 [sierpinski :n-1 :length/2 fd :length rt 120]
end
seth 30 sierpinski 5 200</lang>

=={{header|Mathematica}}==
Cellular automaton (rule 90) based solution:
<lang mathematica>n=4;Grid[CellularAutomaton[90,{{1},0},2^n-1]/.{0->" ",1->"*"},ItemSize->All]</lang>

=={{header|OCaml}}==
<lang ocaml>let sierpinski n =
let rec loop down space n =
if n = 0 then
down
else
loop (List.map (fun x -> space ^ x ^ space) down @
List.map (fun x -> x ^ " " ^ x) down)
(space ^ space)
(n - 1)
in loop ["*"] " " n

let () =
List.iter print_endline (sierpinski 4)</lang>

=={{header|Oz}}==
<lang oz>declare
fun {NextTriangle Triangle}
Sp = {Spaces {Length Triangle}}
in
{Flatten
[{Map Triangle fun {$ X} Sp#X#Sp end}
{Map Triangle fun {$ X} X#" "#X end}
]}
end

fun {Spaces N} if N == 0 then nil else & |{Spaces N-1} end end
fun lazy {Iterate F X}
X|{Iterate F {F X}}
end

SierpinskiTriangles = {Iterate NextTriangle ["*"]}
in
{ForAll {Nth SierpinskiTriangles 5} System.showInfo}</lang>

=={{header|Pascal}}==
{{trans|C}}

{{works with|Free Pascal}}
<lang pascal>program Sierpinski;

function ipow(b, n : Integer) : Integer;
var
i : Integer;
begin
ipow := 1;
for i := 1 to n do
ipow := ipow * b
end;

function truth(a : Char) : Boolean;
begin
if a = '*' then
truth := true
else
truth := false
end;</lang>

<lang pascal>function rule_90(ev : String) : String;
var
l, i : Integer;
cp : String;
s : Array[0..1] of Boolean;
begin
l := length(ev);
cp := copy(ev, 1, l);
for i := 1 to l do begin
if (i-1) < 1 then
s[0] := false
else
s[0] := truth(ev[i-1]);
if (i+1) > l then
s[1] := false
else
s[1] := truth(ev[i+1]);
if ( (s[0] and not s[1]) or (s[1] and not s[0]) ) then
cp[i] := '*'
else
cp[i] := ' ';
end;
rule_90 := cp
end;

procedure triangle(n : Integer);
var
i, l : Integer;
b : String;
begin
l := ipow(2, n+1);
b := ' ';
for i := 1 to l do
b := concat(b, ' ');
b[round(l/2)] := '*';
writeln(b);
for i := 1 to (round(l/2)-1) do begin
b := rule_90(b);
writeln(b)
end
end;</lang>

<lang pascal>begin
triangle(4)
end.</lang>

=={{header|Perl}}==
<lang perl>sub sierpinski {
my ($n) = @_;
my @down = '*';
my $space = ' ';
foreach (1..$n) {
@down = (map("$space$_$space", @down), map("$_ $_", @down));
$space = "$space$space";
}
return @down;
}

print "$_\n" foreach sierpinski 4;</lang>

=={{header|PL/I}}==
<lang PL/I>
sierpinski: procedure options (main); /* 2010-03-30 */
declare t (79,79) char (1);
declare (i, j, k) fixed binary;
declare (y, xs, ys, xll, xrr, ixrr, limit) fixed binary;

t = ' ';
xs = 40; ys = 1;
/* Make initial triangle */
call make_triangle (xs, ys);
y = ys + 4;
xll = xs-4; xrr = xs+4;
do k = 1 to 3;
limit = 0;
do forever;
ixrr = xrr;
do i = xll to xll+limit by 8;
if t(y-1, i) = ' ' then
do;
call make_triangle (i, y);
if t(y+3,i-5) = '*' then
t(y+3,i-4), t(y+3,ixrr+4) = '*';
call make_triangle (ixrr, y);
end;
ixrr = ixrr - 8;
end;
xll = xll - 4; xrr = xrr + 4;
y = y + 4;
limit = limit + 8;
if xll+limit > xs-1 then leave;
end;
t(y-1,xs) = '*';
end;

/* Finished generation; now print the Sierpinski triangle. */
put edit (t) (skip, (hbound(t,2)) a);

make_triangle: procedure (x, y);
declare (x, y) fixed binary;
declare i fixed binary;

do i = 0 to 3;
t(y+i, x-i), t(y+i, x+i) = '*';
end;
do i = x-2 to x+2; /* The base of the triangle. */
t(y+3, i) = '*';
end;
end make_triangle;

end sierpinski;
</lang>

=={{header|PicoLisp}}==
{{trans|Python}}
<lang PicoLisp>(de sierpinski (N)
(let (D '("*") S " ")
(do N
(setq
D (conc
(mapcar '((X) (pack S X S)) D)
(mapcar '((X) (pack X " " X)) D) )
S (pack S S) ) )
D ) )

(mapc prinl (sierpinski 4))</lang>

=={{header|Pop11}}==

Solution using line buffer in an integer array oline, 0 represents ' '
(space), 1 represents '*' (star).
<lang pop11>define triangle(n);
lvars k = 2**n, j, l, oline, nline;
initv(2*k+3) -> oline;
initv(2*k+3) -> nline;
for l from 1 to 2*k+3 do 0 -> oline(l) ; endfor;
1 -> oline(k+2);
0 -> nline(1);
0 -> nline(2*k+3);
for j from 1 to k do
for l from 1 to 2*k+3 do
printf(if oline(l) = 0 then ' ' else '*' endif);
endfor;
printf('\n');
for l from 2 to 2*k+2 do
(oline(l-1) + oline(l+1)) rem 2 -> nline(l);
endfor;
(oline, nline) -> (nline, oline);
endfor;
enddefine;

triangle(4);</lang>

Alternative solution, keeping all triangle as list of strings
<lang pop11>define triangle2(n);
lvars acc = ['*'], spaces = ' ', j;
for j from 1 to n do
maplist(acc, procedure(x); spaces >< x >< spaces ; endprocedure)
<> maplist(acc, procedure(x); x >< ' ' >< x ; endprocedure) -> acc;
spaces >< spaces -> spaces;
endfor;
applist(acc, procedure(x); printf(x, '%p\n'); endprocedure);
enddefine;

triangle2(4);</lang>

=={{header|PowerShell}}==
{{Trans|JavaScript}}
<lang powershell>function triangle($o) {
$n = [Math]::Pow(2, $o)
$line = ,' '*(2*$n+1)
$line[$n] = '█'
$OFS = ''
for ($i = 0; $i -lt $n; $i++) {
Write-Host $line
$u = '█'
for ($j = $n - $i; $j -lt $n + $i + 1; $j++) {
if ($line[$j-1] -eq $line[$j+1]) {
$t = ' '
} else {
$t = '█'
}
$line[$j-1] = $u
$u = $t
}
$line[$n+$i] = $t
$line[$n+$i+1] = '█'
}
}</lang>

=={{header|PureBasic}}==
<lang PureBasic>Procedure Triangle (X,Y, Length, N)
If N = 0
DrawText( Y,X, "*",#Blue)
Else
Triangle (X+Length, Y, Length/2, N-1)
Triangle (X, Y+Length, Length/2, N-1)
Triangle (X+Length, Y+Length*2, Length/2, N-1)
EndIf
EndProcedure

OpenWindow(0, 100, 100,700,500 ,"Sierpinski triangle", #PB_Window_SystemMenu |1)
StartDrawing(WindowOutput(0))
DrawingMode(#PB_2DDrawing_Transparent )
Triangle(10,10,120,5)
Repeat
Until WaitWindowEvent()=#PB_Event_CloseWindow
End</lang>

=={{header|Python}}==
<lang python>def sierpinski(n):
d = ["*"]
for i in xrange(n):
sp = " " * (2 ** i)
d = [sp+x+sp for x in d] + [x+" "+x for x in d]
return d

print "\n".join(sierpinski(4))</lang>

=={{header|Ruby}}==
From the command line:
<lang ruby>ruby -le'16.times{|y|print" "*(15-y),(0..y).map{|x|~y&x>0?" ":" *"}}'</lang>

or, {{trans|Python}}
<lang ruby>def sierpinski_triangle(n)
triangle = ["*"]
n.times do |i|
sp = " " * (2**i)
triangle = triangle.collect {|x| sp + x + sp} + \
triangle.collect {|x| x + " " + x}
end
triangle.join("\n")
end

puts sierpinski_triangle(4)</lang>

=={{header|Scala}}==
The Ruby command-line version (on Windows):

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

The Forth version:

<lang scala>def sierpinski(n: Int) {
def star(n: Long) = if ((n & 1L) == 1L) "*" else " "
def stars(n: Long): String = if (n == 0L) "" else star(n) + " " + stars(n >> 1)
def spaces(n: Int) = " " * n
((1 << n) - 1 to 0 by -1).foldLeft(1L) {
case (bitmap, remainingLines) =>
println(spaces(remainingLines) + stars(bitmap))
(bitmap << 1) ^ bitmap
}
}</lang>

The Haskell version:

<lang scala>def printSierpinski(n: Int) {
def sierpinski(n: Int): List[String] = {
lazy val down = sierpinski(n - 1)
lazy val space = " " * (1 << (n - 1))
n match {
case 0 => List("*")
case _ => (down map (space + _ + space)) :::
(down map (List.fill(2)(_) mkString " "))
}
}
sierpinski(n) foreach println
}</lang>

=={{header|Scheme}}==
{{trans|Haskell}}
<lang scheme>(define (sierpinski n)
(for-each
(lambda (x) (display (list->string x)) (newline))
(let loop ((acc (list (list #\*))) (spaces (list #\ )) (n n))
(if (zero? n)
acc
(loop
(append
(map (lambda (x) (append spaces x spaces)) acc)
(map (lambda (x) (append x (list #\ ) x)) acc))
(append spaces spaces)
(- n 1))))))</lang>

=={{header|Seed7}}==
<lang seed7>$ include "seed7_05.s7i";

const func array string: sierpinski (in integer: n) is func
result
var array string: parts is 1 times "*";
local
var integer: i is 0;
var string: space is " ";
var array string: parts2 is 0 times "";
var string: x is "";
begin
for i range 1 to n do
parts2 := 0 times "";
for x range parts do
parts2 &:= [] (space & x & space);
end for;
for x range parts do
parts2 &:= [] (x & " " & x);
end for;
parts := parts2;
space &:= space;
end for;
end func;
const proc: main is func
begin
writeln(join(sierpinski(4), "\n"));
end func;</lang>

=={{header|Tcl}}==
{{trans|Perl}}
<lang tcl>package require Tcl 8.5

proc map {lambda list} {
foreach elem $list {
lappend result [apply $lambda $elem]
}
return $result
}

proc sierpinski_triangle n {
set down [list *]
set space " "
for {set i 1} {$i <= $n} {incr i} {
set down [concat \
[map [subst -nocommands {x {expr {"$space[set x]$space"}}}] $down] \
[map {x {expr {"$x $x"}}} $down] \
]
append space $space
}
return [join $down \n]
}

puts [sierpinski_triangle 4]</lang>

=={{header|Ursala}}==
the straightforward recursive solution
<lang Ursala>#import nat

triangle = ~&a^?\<<&>>! ^|RNSiDlrTSPxSxNiCK9xSx4NiCSplrTSPT/~& predecessor</lang>
the cheeky cellular automaton solution
<lang Ursala>#import std
#import nat

rule = -$<0,&,0,0,&,0,0,0>@rSS zipp0*ziD iota8
evolve "n" = @iNC ~&x+ rep"n" ^C\~& @h rule*+ swin3+ :/0+ --<0>
sierpinski = iota; --<&>@NS; iota; ^H/evolve@z @NS ^T/~& :/&</lang>
an example of each (converting from booleans to characters)
<lang Ursala>#show+

examples = mat0 ~&?(`*!,` !)*** <sierpinski3,triangle4></lang>
output:
<pre style="height:30ex;overflow:scroll;">
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *

*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
</pre>

=={{header|Vedit macro language}}==
===Iterative===
{{trans|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.
<lang vedit>#3 = 16 // size (height) of the triangle
Buf_Switch(Buf_Free) // Open a new buffer for output
Ins_Char(' ', COUNT, #3*2+2) // fill first line with spaces
Ins_Newline
Line(-1) Goto_Col(#3)
Ins_Char('*', OVERWRITE) // the top of triangle
for (#10=0; #10 < #3-1; #10++) {
BOL Reg_Copy(9,1) Reg_Ins(9) // duplicate the line
#20 = '*'
for (#11 = #3-#10; #11 < #3+#10+1; #11++) {
Goto_Col(#11-1)
if (Cur_Char==Cur_Char(2)) { #21=' ' } else { #21='*' }
Ins_Char(#20, OVERWRITE)
#20 = #21
}
Ins_Char(#21, OVERWRITE)
Ins_Char('*', OVERWRITE)
}</lang>

===Recursive===
{{trans|BASIC}}

Vedit macro language does not have recursive functions, so some pushing and popping is needed to implement recursion.
<lang vedit>#1 = 1 // x
#2 = 1 // y
#3 = 16 // length (height of the triangle / 2)
#4 = 5 // depth of recursion

Buf_Switch(Buf_Free) // Open a new buffer for output
Ins_Newline(#3*2) // Create as many empty lines as needed
Call("Triangle") // Draw the triangle
BOF
Return

:Triangle:
if (#4 == 0) {
Goto_Line(#2)
EOL Ins_Char(' ', COUNT, #1-Cur_Col+1) // add spaces if needed
Goto_Col(#1)
Ins_Char('*', OVERWRITE)
} else {
Num_Push(1,4)
#2 += #3; #3 /= 2; #4--; Call("Triangle")
Num_Pop(1,4)
Num_Push(1,4)
#1 += #3; #3 /= 2; #4--; Call("Triangle")
Num_Pop(1,4)
Num_Push(1,4)
#1 += 2*#3; #2 += #3; #3 /= 2; #4--; Call("Triangle")
Num_Pop(1,4)
}
Return</lang>

Revision as of 11:12, 17 June 2010

                   *
                 *   *
               *   *   *


how to print the above triangle

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