Shader Noise

Procedural noise creates natural-looking randomness. Unlike random(), noise is coherent—nearby inputs produce nearby outputs.

Quick Start

// Simple usage
float n = snoise(uv * 5.0);              // Simplex 2D
float n = snoise(vec3(uv, uTime));       // Animated 3D
float n = fbm(uv, 4);                    // Layered detail

// Common range adjustments
float n01 = n * 0.5 + 0.5;               // [-1,1] → [0,1]
float sharp = step(0.0, n);              // Binary threshold
float smooth = smoothstep(-0.2, 0.2, n); // Soft threshold

Noise Types Comparison

Type	Speed	Quality	Use Case
Value	Fastest	Blocky	Quick prototypes
Perlin	Fast	Good	General purpose
Simplex	Fast	Best	Modern default
Worley	Slower	Cellular	Cells, cracks, scales

Value Noise

Interpolated random values at grid points. Simple but blocky.

float random(vec2 st) {
  return fract(sin(dot(st.xy, vec2(12.9898, 78.233))) * 43758.5453123);
}

float valueNoise(vec2 st) {
  vec2 i = floor(st);
  vec2 f = fract(st);
  
  // Smoothstep interpolation
  vec2 u = f * f * (3.0 - 2.0 * f);
  
  // Four corners
  float a = random(i);
  float b = random(i + vec2(1.0, 0.0));
  float c = random(i + vec2(0.0, 1.0));
  float d = random(i + vec2(1.0, 1.0));
  
  // Bilinear interpolation
  return mix(mix(a, b, u.x), mix(c, d, u.x), u.y);
}

Simplex Noise (Recommended)

Best quality-to-performance ratio. Use this as default.

2D Simplex

vec3 permute(vec3 x) { return mod(((x*34.0)+1.0)*x, 289.0); }

float snoise(vec2 v) {
  const vec4 C = vec4(0.211324865405187, 0.366025403784439,
                      -0.577350269189626, 0.024390243902439);
  vec2 i  = floor(v + dot(v, C.yy));
  vec2 x0 = v - i + dot(i, C.xx);
  vec2 i1 = (x0.x > x0.y) ? vec2(1.0, 0.0) : vec2(0.0, 1.0);
  vec4 x12 = x0.xyxy + C.xxzz;
  x12.xy -= i1;
  i = mod(i, 289.0);
  vec3 p = permute(permute(i.y + vec3(0.0, i1.y, 1.0)) + i.x + vec3(0.0, i1.x, 1.0));
  vec3 m = max(0.5 - vec3(dot(x0,x0), dot(x12.xy,x12.xy), dot(x12.zw,x12.zw)), 0.0);
  m = m*m;
  m = m*m;
  vec3 x = 2.0 * fract(p * C.www) - 1.0;
  vec3 h = abs(x) - 0.5;
  vec3 ox = floor(x + 0.5);
  vec3 a0 = x - ox;
  m *= 1.79284291400159 - 0.85373472095314 * (a0*a0 + h*h);
  vec3 g;
  g.x = a0.x * x0.x + h.x * x0.y;
  g.yz = a0.yz * x12.xz + h.yz * x12.yw;
  return 130.0 * dot(m, g);
}

3D Simplex

vec4 permute(vec4 x) { return mod(((x*34.0)+1.0)*x, 289.0); }
vec4 taylorInvSqrt(vec4 r) { return 1.79284291400159 - 0.85373472095314 * r; }

float snoise(vec3 v) {
  const vec2 C = vec2(1.0/6.0, 1.0/3.0);
  const vec4 D = vec4(0.0, 0.5, 1.0, 2.0);
  
  vec3 i  = floor(v + dot(v, C.yyy));
  vec3 x0 = v - i + dot(i, C.xxx);
  
  vec3 g = step(x0.yzx, x0.xyz);
  vec3 l = 1.0 - g;
  vec3 i1 = min(g.xyz, l.zxy);
  vec3 i2 = max(g.xyz, l.zxy);
  
  vec3 x1 = x0 - i1 + C.xxx;
  vec3 x2 = x0 - i2 + C.yyy;
  vec3 x3 = x0 - D.yyy;
  
  i = mod(i, 289.0);
  vec4 p = permute(permute(permute(
    i.z + vec4(0.0, i1.z, i2.z, 1.0))
    + i.y + vec4(0.0, i1.y, i2.y, 1.0))
    + i.x + vec4(0.0, i1.x, i2.x, 1.0));
    
  float n_ = 0.142857142857;
  vec3 ns = n_ * D.wyz - D.xzx;
  
  vec4 j = p - 49.0 * floor(p * ns.z * ns.z);
  
  vec4 x_ = floor(j * ns.z);
  vec4 y_ = floor(j - 7.0 * x_);
  
  vec4 x = x_ *ns.x + ns.yyyy;
  vec4 y = y_ *ns.x + ns.yyyy;
  vec4 h = 1.0 - abs(x) - abs(y);
  
  vec4 b0 = vec4(x.xy, y.xy);
  vec4 b1 = vec4(x.zw, y.zw);
  
  vec4 s0 = floor(b0)*2.0 + 1.0;
  vec4 s1 = floor(b1)*2.0 + 1.0;
  vec4 sh = -step(h, vec4(0.0));
  
  vec4 a0 = b0.xzyw + s0.xzyw*sh.xxyy;
  vec4 a1 = b1.xzyw + s1.xzyw*sh.zzww;
  
  vec3 p0 = vec3(a0.xy, h.x);
  vec3 p1 = vec3(a0.zw, h.y);
  vec3 p2 = vec3(a1.xy, h.z);
  vec3 p3 = vec3(a1.zw, h.w);
  
  vec4 norm = taylorInvSqrt(vec4(dot(p0,p0), dot(p1,p1), dot(p2,p2), dot(p3,p3)));
  p0 *= norm.x;
  p1 *= norm.y;
  p2 *= norm.z;
  p3 *= norm.w;
  
  vec4 m = max(0.6 - vec4(dot(x0,x0), dot(x1,x1), dot(x2,x2), dot(x3,x3)), 0.0);
  m = m * m;
  return 42.0 * dot(m*m, vec4(dot(p0,x0), dot(p1,x1), dot(p2,x2), dot(p3,x3)));
}

Worley (Cellular) Noise

Creates cell-like patterns. Great for scales, cracks, caustics.

vec2 random2(vec2 st) {
  st = vec2(dot(st, vec2(127.1, 311.7)), dot(st, vec2(269.5, 183.3)));
  return fract(sin(st) * 43758.5453123);
}

float worley(vec2 st) {
  vec2 i_st = floor(st);
  vec2 f_st = fract(st);
  
  float minDist = 1.0;
  
  // Check 3x3 neighborhood
  for (int y = -1; y <= 1; y++) {
    for (int x = -1; x <= 1; x++) {
      vec2 neighbor = vec2(float(x), float(y));
      vec2 point = random2(i_st + neighbor);
      
      // Animate points
      // point = 0.5 + 0.5 * sin(uTime + 6.2831 * point);
      
      vec2 diff = neighbor + point - f_st;
      float dist = length(diff);
      minDist = min(minDist, dist);
    }
  }
  
  return minDist;
}

// F2 - F1 variant (cracks/veins)
vec2 worley2(vec2 st) {
  vec2 i_st = floor(st);
  vec2 f_st = fract(st);
  
  float f1 = 1.0;  // Closest
  float f2 = 1.0;  // Second closest
  
  for (int y = -1; y <= 1; y++) {
    for (int x = -1; x <= 1; x++) {
      vec2 neighbor = vec2(float(x), float(y));
      vec2 point = random2(i_st + neighbor);
      vec2 diff = neighbor + point - f_st;
      float dist = length(diff);
      
      if (dist < f1) {
        f2 = f1;
        f1 = dist;
      } else if (dist < f2) {
        f2 = dist;
      }
    }
  }
  
  return vec2(f1, f2);
}

FBM (Fractal Brownian Motion)

Layer multiple noise octaves for natural detail at all scales.

float fbm(vec2 st, int octaves) {
  float value = 0.0;
  float amplitude = 0.5;
  float frequency = 1.0;
  
  for (int i = 0; i < octaves; i++) {
    value += amplitude * snoise(st * frequency);
    frequency *= 2.0;      // Lacunarity
    amplitude *= 0.5;      // Gain/Persistence
  }
  
  return value;
}

// Configurable FBM
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 * snoise(st * frequency);
    frequency *= lacunarity;
    amplitude *= gain;
  }
  
  return value;
}

FBM Variants

// Ridged FBM (mountains, lightning)
float ridgedFbm(vec2 st, int octaves) {
  float value = 0.0;
  float amplitude = 0.5;
  float frequency = 1.0;
  
  for (int i = 0; i < octaves; i++) {
    float n = snoise(st * frequency);
    n = 1.0 - abs(n);  // Ridge
    n = n * n;          // Sharpen
    value += amplitude * n;
    frequency *= 2.0;
    amplitude *= 0.5;
  }
  
  return value;
}

// Turbulence (absolute value, always positive)
float turbulence(vec2 st, int octaves) {
  float value = 0.0;
  float amplitude = 0.5;
  float frequency = 1.0;
  
  for (int i = 0; i < octaves; i++) {
    value += amplitude * abs(snoise(st * frequency));
    frequency *= 2.0;
    amplitude *= 0.5;
  }
  
  return value;
}

Domain Warping

Distort the input coordinates with noise for organic shapes.

// Simple domain warp
float warpedNoise(vec2 st) {
  vec2 q = vec2(
    snoise(st),
    snoise(st + vec2(5.2, 1.3))
  );
  
  return snoise(st + q * 2.0);
}

// Double domain warp (more complex)
float doubleWarp(vec2 st) {
  vec2 q = vec2(
    fbm(st, 4),
    fbm(st + vec2(5.2, 1.3), 4)
  );
  
  vec2 r = vec2(
    fbm(st + q * 4.0 + vec2(1.7, 9.2), 4),
    fbm(st + q * 4.0 + vec2(8.3, 2.8), 4)
  );
  
  return fbm(st + r * 4.0, 4);
}

// Animated warp
float animatedWarp(vec2 st, float time) {
  vec2 q = vec2(
    fbm(st + vec2(0.0, 0.0), 4),
    fbm(st + vec2(5.2, 1.3), 4)
  );
  
  vec2 r = vec2(
    fbm(st + q * 4.0 + vec2(1.7, 9.2) + 0.15 * time, 4),
    fbm(st + q * 4.0 + vec2(8.3, 2.8) + 0.126 * time, 4)
  );
  
  return fbm(st + r * 4.0, 4);
}

Common Use Cases

Terrain Height

float terrainHeight(vec2 pos) {
  float height = 0.0;
  
  // Base terrain
  height += fbm(pos * 0.01, 6) * 100.0;
  
  // Mountains (ridged)
  height += ridgedFbm(pos * 0.005, 4) * 200.0;
  
  // Detail
  height += snoise(pos * 0.1) * 5.0;
  
  return height;
}

Clouds

float clouds(vec2 uv, float time) {
  vec2 motion = vec2(time * 0.1, 0.0);
  
  float density = fbm(uv * 3.0 + motion, 5);
  density = smoothstep(0.0, 0.5, density);
  
  return density;
}

Fire/Flames

float fire(vec2 uv, float time) {
  // Upward motion
  uv.y -= time * 2.0;
  
  // Turbulent distortion
  float turb = turbulence(uv * 4.0, 4);
  
  // Fade out at top
  float fade = 1.0 - uv.y;
  
  return turb * fade;
}

Water Caustics

float caustics(vec2 uv, float time) {
  vec2 w = worley2(uv * 8.0 + time * 0.5);
  return pow(1.0 - w.x, 3.0);
}

Marble/Stone

float marble(vec2 uv) {
  float n = fbm(uv * 2.0, 4);
  float veins = sin(uv.x * 10.0 + n * 10.0);
  return veins * 0.5 + 0.5;
}

Performance Tips

Technique	Impact
Fewer octaves in FBM	Major speedup
2D vs 3D noise	2D ~2x faster
Bake to texture	Massive speedup for static
Lower frequency = fewer samples	Faster

File Structure

shader-noise/
├── SKILL.md
├── references/
│   ├── noise-comparison.md    # Visual comparison of types
│   └── optimization.md        # Performance techniques
└── scripts/
    ├── noise/
    │   ├── simplex2d.glsl     # Copy-paste simplex 2D
    │   ├── simplex3d.glsl     # Copy-paste simplex 3D
    │   ├── worley.glsl        # Copy-paste Worley
    │   └── fbm.glsl           # FBM variants
    └── examples/
        ├── terrain.glsl       # Terrain generation
        ├── clouds.glsl        # Cloud shader
        └── fire.glsl          # Fire effect

Reference

• references/noise-comparison.md — Visual comparison of noise types
• references/optimization.md — Performance optimization techniques