Example code from presentation: Ways of Seeing Julia Sets

I gave a presentation at yesterday’s DIT School of Mathematical Sciences lunchtime research seminar titled Ways of Seeing Julia Sets: Visualizing the forces that shape fractal Julia sets. This was the abstract:

My Prezi slides can be viewed here:
http://prezi.com/f5ymufi-bfqc/ways-of-seeing-julia-sets/

During my presentation, I demonstrated two short C programs that generated these fractal images.

This is the complete C code for the Mandelbrot example:

#include <stdio.h>
#include <complex.h>

void main()
{
    complex double z, c;
    int x, y, i;

    printf("P2\n4000 4000\n255\n");
    for (y=0 ; y<4000 ; ++y)
    {
        for (x=0 ; x<4000 ; ++x)
        {
            z = 0;
            c = (-2 + x*0.001) + (-2 + y*0.001)*I;
            i = 0;
            while (cabs(z) < 2 && ++i < 255) z = z*z + c;
            printf("%4d", i);
        }
        printf("\n");
    }
}

I compiled and ran the program as follows:

gcc mandelbrot.c -o mandelbrot -lm
./mandelbrot > mandelbrot.pgm

The C code for the Julia set example is almost identical except that it’s now z rather than c which changes from pixel to pixel (i.e. with changing x and y coordinates) and c is constant throughout the image (the value of c you choose determines which Julia set you end up with).

#include <stdio.h>
#include <complex.h>

void main()
{
    complex double z, c;
    int x, y, i;

    printf("P2\n4000 4000\n255\n");
    for (y=0 ; y<4000 ; ++y)
    {
        for (x=0 ; x<4000 ; ++x)
        {
            c = -0.625 - 0.4*I;
            z = (-2 + x*0.001) + (-2 + y*0.001)*I;
            i = 0;
            while (cabs(z) < 2 && ++i < 255) z = z*z + c;
            printf("%4d", i);
        }
        printf("\n");
    }
}

I compiled and ran the program as follows:

gcc julia.c -o julia -lm
./julia > julia.pgm