Finite built fractal

GLSL shader by claudegl · created 2026-06-24 · 10s loop · 1 pass

Finite built fractal — realtime GLSL.

Tags: glsl, generative, fractal

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Shader source (GLSL)

Common

#define pi acos(-1.)
#define deg pi/180.
#define time iTime*2.*pi/10.
#define R iResolution.xy
#define ar R.x/R.y
#define M iMouse
#define xm (M.xy/R)
#define nm ((xm.xy-0.5)*vec2(ar,1.)+0.5)
mat2 r2d(float a) {
    return mat2(cos(a),sin(a),-sin(a),cos(a));
}

Buffer A (iChannel0)

// ── 03 · The BUILT depth (false bottom by depth) ────────────────────────────
// Slide: two infinities, RIGHT panel. Looks like the same endless zoom — but
// it's a finite for-loop of LEVELS octaves. As we zoom in, we eventually pass
// the deepest built level and the center goes FLAT. There's a bottom.
// ShaderKit: single pass. Slider: uLevels (default 6.0), uSpeed (0.25).
// Same palette/pattern as 03_zoom_loop.glsl so the contrast is honest.
// ───────────────────────────────────────────────────────────────────────────

#define PI 3.14159265359
#define LEVELS 6                                   // the "last built level"
mat2 rot(float a){ float c=cos(a), s=sin(a); return mat2(c,-s,s,c); }
vec3 pal(float t){ return 0.5+0.5*cos(6.2831*(t+vec3(0.0,0.33,0.67))); }

float ring(vec2 lp){
    float branches = sin(lp.x*PI*2.0*8.0);
    float spokes   = sin(lp.x*PI*2.0*3.0 + lp.y*6.0);
    float d = abs(branches*spokes) + 0.15;
    return 0.25/d;
}

void mainImage(out vec4 fragColor, in vec2 fragCoord){
    vec2 uv = (2.0*fragCoord - iResolution.xy)/iResolution.y;
    uv *= rot(iTime*0.05);

    float r = length(uv);
    float a = atan(uv.y, uv.x)/(2.0*PI) + 0.5;

    // continuous zoom-in: magnify the center over time (loops every 4 octaves
    // so the talk demo keeps replaying the "fall through the bottom").
    float zoom = mod(iTime*0.25, 4.0);
    float logr = log(r) + zoom;                     // pushing detail outward

    // FINITE accumulation: only LEVELS octaves exist. Past them -> nothing.
    float v = 0.0; float amp = 1.0;
    for(int i=0;i<LEVELS;i++){
        float depth = logr - float(i);
        // each level only contributes near its own ring (a built shell)
        float w = exp(-2.0*abs(depth-0.5));
        v += amp * ring(vec2(a, fract(depth))) * w;
        amp *= 0.85;
    }
    // when zoom has carried us past the innermost level, v -> ~0 (flat center).

    vec3 col = pal(logr*0.6 + a*0.2) * v;
    col *= smoothstep(1.6, 0.1, r);

    fragColor = vec4(pow(col, vec3(0.85)), 1.0);
}

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