Coloring mandelbrot set

Question

I have came up to something like this:

float MinRe = -2.0f; // real
float MaxRe = 1.0f;
float MinIm = -1.0f; // imaginary
float MaxIm = MinIm + (MaxRe - MinRe) * WindowData.Height / WindowData.Width;

float Re_factor = (MaxRe - MinRe) / (WindowData.Width - 1);
float Im_factor = (MaxIm - MinIm) / (WindowData.Height - 1);

int MaxIterations = 50;
int iter=0;

for (int y = 0; y < WindowData.Height; ++y)
{
    double c_im = MaxIm - y * Im_factor; // complex imaginary
    for (int x = 0; x < WindowData.Width; ++x)
    {
        double c_re = MinRe + x * Re_factor; // complex real

        // calculate mandelbrot set
        double Z_re = c_re, Z_im = c_im; // Set Z = c
        bool isInside = true;

        for (iter=0; iter < MaxIterations; ++iter)
        {
            double Z_re2 = Z_re * Z_re, Z_im2 = Z_im * Z_im;
            if (Z_re2 + Z_im2 > 4)
            {
                isInside = false;
                break;
            }
            Z_im = 2 * Z_re * Z_im + c_im;
            Z_re = Z_re2 - Z_im2 + c_re;
        }

        if(isInside) 
        {
            GL.Color3(0, 0, 0);
            GL.Vertex2(x, y);
        }
    }
}

I have tried in few ways, but most of the times ended with single color around set, or whole screen with the same color.

How to set up colors properly?

Answer 1

When I tried this, I just set the outside colour to RGB (value, value, 1) where value is (in your parlance) the fourth root of (iter / MaxIterations). That comes out as a quite nice fade from white to blue. Not so bright as duffymo's, though, but with less of a 'stripy' effect.

Answer 2

Here's how I did it: check out the Source Forge repository for source code.

http://craicpropagation.blogspot.com/2011/03/mandelbrot-set.html

Answer 3

try to display result of your computation. Check what input is required by your coloring function

See also

http://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Mandelbrot_set

HTH

Adam

Answer 4

I found empirically that if you use something like that: color(R,G,B) where R,G,B takes values from 0 to 255.

Then this function gives a really good looking result. f(x,f,p) = 255*(cos(sqrt(x)*f + p))^2 where x denotes the current iteration, f the frequency and p the phase.

And then apply the function for each color argument with a phase difference of 120:

color(f(iter,1,0),f(iter,1,120),f(iter,1,240)