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.opencode/skills/shader/references/glsl-fbm-fractional-brownian-motion-turbulence-octaves.md

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+# Fractional Brownian Motion (fBm)
+
+Layer noise octaves for natural-looking textures like clouds, terrain, and wood.
+
+## Basic fBm
+
+```glsl
+float fbm(vec2 st) {
+    float value = 0.0;
+    float amplitude = 0.5;
+    float frequency = 1.0;
+
+    // 6 octaves
+    for (int i = 0; i < 6; i++) {
+        value += amplitude * noise(st * frequency);
+        frequency *= 2.0;    // Lacunarity
+        amplitude *= 0.5;    // Gain (persistence)
+    }
+
+    return value;
+}
+```
+
+## fBm Parameters
+
+| Parameter | Effect | Typical Value |
+|-----------|--------|---------------|
+| **Octaves** | Detail level | 4-8 |
+| **Lacunarity** | Frequency multiplier | 2.0 |
+| **Gain** | Amplitude multiplier | 0.5 |
+
+```glsl
+float fbm(vec2 st, int octaves, float lacunarity, float gain) {
+    float value = 0.0;
+    float amplitude = 0.5;
+    float frequency = 1.0;
+
+    for (int i = 0; i < octaves; i++) {
+        value += amplitude * noise(st * frequency);
+        frequency *= lacunarity;
+        amplitude *= gain;
+    }
+
+    return value;
+}
+```
+
+## Turbulence
+
+Use absolute value for sharper valleys:
+
+```glsl
+float turbulence(vec2 st) {
+    float value = 0.0;
+    float amplitude = 0.5;
+    float frequency = 1.0;
+
+    for (int i = 0; i < 6; i++) {
+        value += amplitude * abs(noise(st * frequency) * 2.0 - 1.0);
+        frequency *= 2.0;
+        amplitude *= 0.5;
+    }
+
+    return value;
+}
+```
+
+## Ridged Noise
+
+Inverted turbulence for mountain ridges:
+
+```glsl
+float ridged(vec2 st) {
+    float value = 0.0;
+    float amplitude = 0.5;
+    float frequency = 1.0;
+    float prev = 1.0;
+
+    for (int i = 0; i < 6; i++) {
+        float n = abs(noise(st * frequency) * 2.0 - 1.0);
+        n = 1.0 - n;           // Invert
+        n = n * n;             // Sharpen
+        n *= prev;             // Weight by previous
+        prev = n;
+        value += n * amplitude;
+        frequency *= 2.0;
+        amplitude *= 0.5;
+    }
+
+    return value;
+}
+```
+
+## Warped fBm (Domain Warping)
+
+Feed fBm into itself for organic distortion:
+
+```glsl
+float warpedFbm(vec2 st) {
+    vec2 q = vec2(fbm(st), fbm(st + vec2(5.2, 1.3)));
+    vec2 r = vec2(
+        fbm(st + 4.0 * q + vec2(1.7, 9.2)),
+        fbm(st + 4.0 * q + vec2(8.3, 2.8))
+    );
+    return fbm(st + 4.0 * r);
+}
+```
+
+## Animated fBm
+
+```glsl
+float animatedFbm(vec2 st, float time) {
+    float value = 0.0;
+    float amplitude = 0.5;
+    float frequency = 1.0;
+
+    for (int i = 0; i < 6; i++) {
+        vec2 offset = vec2(time * 0.1 * float(i + 1));
+        value += amplitude * noise(st * frequency + offset);
+        frequency *= 2.0;
+        amplitude *= 0.5;
+    }
+
+    return value;
+}
+```
+
+## Multifractal
+
+Multiply instead of add for different character:
+
+```glsl
+float multifractal(vec2 st, float H, float lacunarity, int octaves) {
+    float value = 1.0;
+    float frequency = 1.0;
+
+    for (int i = 0; i < octaves; i++) {
+        value *= noise(st * frequency) * pow(frequency, -H) + 1.0;
+        frequency *= lacunarity;
+    }
+
+    return value;
+}
+```
+
+See also: `glsl-procedural-textures-clouds-marble-wood-terrain.md`