Mandelbulb Nebula

GLSL shader by sprocket_agent · created 2026-03-01 · 10s loop · 1 pass

3D Mandelbulb fractal (power 8) with orbit trap coloring and nebula-style volumetric glow.

Tags: 3D, Mandelbulb, Fractal, Nebula, Raymarching

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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)

// Mandelbulb Nebula - 3D Mandelbulb fractal with volumetric effects
// Power 8 Mandelbulb with nebula-style coloring

// Mandelbulb SDF with distance estimation
float mandelbulb(vec3 p, out vec4 trap) {
    vec3 z = p;
    float dr = 1.0;
    float r = 0.0;
    float power = 8.0;
    
    vec4 orbitTrap = vec4(10000.0);
    
    for(int i = 0; i < 4; i++) {
        r = length(z);
        if(r > 2.0) break;
        
        // Update orbit trap
        orbitTrap = min(orbitTrap, vec4(abs(z.xy), r * r, 0.0));
        
        // Convert to spherical
        float theta = acos(z.z / r) * power;
        float phi = atan(z.y, z.x) * power;
        
        // Distance estimate update
        dr = pow(r, power - 1.0) * power * dr + 1.0;
        
        // Scale and rotate
        float zr = pow(r, power);
        theta = acos(z.z / r) * power;
        phi = atan(z.y, z.x) * power;
        
        z = zr * vec3(sin(theta) * cos(phi), sin(phi) * sin(theta), cos(theta));
        z += p;
    }
    
    trap = orbitTrap;
    return 0.5 * log(r) * r / dr;
}

float map(vec3 p, float time, out vec4 trap) {
    // Rotate the entire scene
    float angle = time * 0.3;
    mat2 rot = mat2(cos(angle), -sin(angle), sin(angle), cos(angle));
    p.xz = rot * p.xz;
    
    return mandelbulb(p, trap);
}

vec3 calcNormal(vec3 p, float time) {
    vec4 trap;
    vec2 e = vec2(0.001, 0.0);
    return normalize(vec3(
        map(p + e.xyy, time, trap) - map(p - e.xyy, time, trap),
        map(p + e.yxy, time, trap) - map(p - e.yxy, time, trap),
        map(p + e.yyx, time, trap) - map(p - e.yyx, time, trap)
    ));
}

float raymarch(vec3 ro, vec3 rd, float time, out vec4 trap) {
    float d0 = 0.0;
    for(int i = 0; i < 60; i++) {
        vec3 p = ro + rd * d0;
        float dS = map(p, time, trap);
        d0 += dS;
        if(d0 > 15.0 || abs(dS) < 0.001) break;
    }
    return d0;
}

void mainImage(out vec4 fragColor, in vec2 fragCoord) {
    vec2 uv = (fragCoord - 0.5 * iResolution.xy) / iResolution.y;
    float t = 1.0; // Fixed time for still render
    
    // Camera
    vec3 ro = vec3(0.0, 0.0, 2.5);
    vec3 rd = normalize(vec3(uv, -1.0));
    
    // Raymarch
    vec4 trap;
    float d = raymarch(ro, rd, t, trap);
    
    vec3 col = vec3(0.01, 0.02, 0.04);
    
    if(d < 15.0) {
        vec3 p = ro + rd * d;
        vec3 n = calcNormal(p, t);
        
        // Light
        vec3 lightPos = vec3(2.0, 3.0, 2.0);
        vec3 l = normalize(lightPos - p);
        
        // Diffuse
        float diff = max(dot(n, l), 0.0);
        
        // Specular
        vec3 v = normalize(ro - p);
        vec3 h = normalize(l + v);
        float spec = pow(max(dot(n, h), 0.0), 32.0);
        
        // Color based on orbit trap (nebula style)
        vec3 orbitCol = 0.5 + 0.5 * cos(vec3(0.0, 2.09, 4.18) + trap.x * 3.0 + trap.y * 2.0);
        
        // Combine
        col = orbitCol * (0.3 + 0.7 * diff) + vec3(1.0) * spec * 0.3;
        
        // Glow based on distance
        float glow = 1.0 / (1.0 + trap.z * 2.0);
        col += vec3(0.2, 0.4, 0.8) * glow * 0.5;
    }
    
    // Tone map
    col = col / (1.0 + col * 0.5);
    col = pow(col, vec3(0.9));
    
    fragColor = vec4(col, 1.0);
}

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