Skull Head fractal

[marmakoide]

Hi,

 I was fumbling around, trying to understand how the Mandelbox works, and I came-up with this


It does not have as much as interesting details as the Mandelbox (some areas are just boring variations on Cantor dust), but it still interesting enough to explore


I made a small gallery here : http://imgur.com/a/T6z1i

Pseudo-code to generate the fractal is here

Code:

MAX_ITER_COUNT = 15 
SCALE_FACTOR = 2.5
SHIFT_FACTOR = .5

bool
get_sample(vec2 c) {
    float S = 1. / 6.;

    vec2 U = (c / length(c));
    mat2 M = SCALE_FACTOR * mat2(vec2(U.x, U.y), vec2(-U.y, U.x));
    vec2 T = SHIFT_FACTOR * c;

    vec2 z = c;
    for(int iter_count = 0; iter_count < MAX_ITER_COUNT; ++iter_count) {
        // Inner hole
        if (length(z) < S)
            return true;

        // Fold to a 1/3 square
        z = clamp(z, -S, S) * 2. - z;

        // Scale-up to unit square
        z = M * z + T;
    }

    return false;
}

The [-3,3] square contains the whole fractal. To render the pictures I show here, I used 4x4 supersampling. The fractal itself is a variation on this

[cKleinhuis]

nice, indeed the mandelbox contains a lot of other fractal types, cantor dust obviously, sierpinsky triangles can be found, and a various other clearly identifiable sets

the location for these is in the corners of the box