Exploding Mandelbrot

[Chris Thomasson]

Fwiw, I have added my highly experimental Exploding escape-time fractal rescaling code to an existing shader created by the hyper-smart Inigo Quilez:

https://www.shadertoy.com/view/XtscDl

I added a little color in green wrt a simple orbit trap. Anyway, here is a link to a result of mine created in C++:

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=20582

<pseudo-code for the overall idea>
__________
int g = 0;

ct_complex jp[2] = {
    { .04, .07 },
    { -.04, -.07 }
};

for (unsigned int i = 1; i < 123; ++i)
{
    z = z * z + c;

    // escape condition
    if (z.real() * z.real() + z.imag() * z.imag() > 250)
    {
        if (g < 16)
        {
            z *= (i % 2) ? jp[1] : jp[0];
            ++g;
            continue;
        }
               
        return; // escaped, so bail!
    }
}

// did not escape...
__________

This rescaling technique just might turn out to be a fairly interesting point to play around, or experiment with if you will. The reason for my development of this algorithm has to do with a thought of mine consisting of a question: If a point escapes, what happens if we bring it back along different field lines?