These are some nice little programs to create PBM pictures of classic fractals.
You will need pbmtool.* (see below) for compiling the following
programs.
Yes, some code is stolen from pbmholstein.c by
John Walker and bitarray.c from a rather old version of the
snippets package. In the meanwhile I found the newer
http://www.snippets.org .
<![CDATA[
/* Create a sierpinski gasket using recursion */
#include <stdio.h>
#include "pbmtool.h"
#define WURZ3 1.7320508
void sierpinski(int x,int y, /*Position of lower left corner*/ int generation)
{
if(generation==0)
setpixel(x,y);
else{
int i,power=1;
sierpinski(x,y,generation-1);
for(i=0;i<(generation-2);i++)power*=2;
sierpinski(x+2*power,y,generation-1);
sierpinski(x+power,(int) (y+WURZ3*power),generation-1); /*y mit 1/2Wurzel3*/
}
}
main(int argc,char ** argv)
{
int x,y,maxgen,size;
maxgen=atoi(argv[1]);
size=1;for(x=0;x<maxgen;x++)size*=2;
for(x=0;x<size;x++)
for(y=0;y<size;y++)
clearpixel(x,y);
sierpinski(0,0,maxgen);
WritePbm(size,size*0.5*WURZ3+1);
}
]]>
There are other ways of creating the sierpinski gasket. The following two
are similar to those in the book "Fractals Everywhere" by Michael Barnsley.
<![CDATA[
/* create a part of the v. Koch snow flake using recursion */
#include <stdio.h>
#include <math.h>
#include <values.h>
#include "pbmtool.h"
#define WURZ2 1.4142136
#define WURZ3 1.7320508
double m_sin(int alfa)
{ return sin(M_PI*(double)alfa/180.0);}
double m_cos(int alfa)
{ return cos(M_PI*(double)alfa/180.0);}
void koch(int x,int y, /*Position of lower left corner*/
int alfa, int generation)
{
if(generation==0)
setpixel(x,y);
else{
int i,len=1;
if(alfa>=360)alfa-=360;
if(alfa<0)alfa+=360;
for(i=1;i<generation;i++)len*=3; /* Length of one branch */
koch(x,y,alfa,generation-1);
koch(x+len*m_cos(alfa),y+len*m_sin(alfa),alfa+60,generation-1);
koch(x+len*(m_cos(alfa)+m_cos(alfa+60)),y+len*(m_sin(alfa+60)+m_sin(alfa)),alfa-60,generation-1);
koch(x+2*len*m_cos(alfa),y+2*len*m_sin(alfa),alfa,generation-1);
}
}
main(int argc,char ** argv)
{
int x,y,maxgen,size;
maxgen=atoi(argv[1]);
size=1;for(x=0;x<maxgen;x++)size*=3;
for(x=0;x<size;x++)
for(y=0;y<size;y++)
clearpixel(x,y);
koch(0,0,0,maxgen);
WritePbm(size,0.17*WURZ3*size); /* 0.17 == 1/6 remember _/\_ */
}
]]>
Generalized Koch curves
<![CDATA[
/* a little mandelbrot program */
#include<stdio.h>
#define MAXITER 10000
int tepoint(double r,double i)
{
int zeahl;
double re=0, oldre=0, im=0, oldim=0, betr;
for(zeahl=1;zeahl<MAXITER;zeahl++){
re= oldre*oldre - oldim*oldim +r;
im= 2*oldre*oldim+i;
betr=re*re+im*im;
if(betr>5) return (1); /* outside */
oldre=re; oldim=im;
}
return(0); /* inside */
}
main()
{
FILE* outfile;
int count;
double i,j;
outfile=fopen("mandel.pbm","w");
fprintf(outfile,"P1 1201 800 \n");
for(i=-1;i<1;i+=0.0025)
for(j=-2;j<1;j+=0.0025){
count++;
fprintf(outfile," %d",tepoint(j,i));
if(count%20==0)fprintf(outfile,"\n"),fflush(outfile);
}
close(outfile);
}
]]>
Some more:
Jürgen Dollinger