Print Page - Skull Head fractal

Hi,

I was fumbling around, trying to understand how the Mandelbox works, and I came-up with this
(http://i.imgur.com/4eX8LYI.png)

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
(http://i.imgur.com/2gUqLlw.png)

I made a small gallery here : http://imgur.com/a/T6z1i (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
(http://i.imgur.com/rxbeuAv.png)

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Fractal Math, Chaos Theory & Research => General Discussion => Topic started by: marmakoide on March 21, 2016, 10:49:18 AM