数学可视化(08)——分形Fractal

//随机数
float random (in half2 uv)
{
    return frac(sin(dot(uv.xy, float2(12.9898,78.233)))*43758.5453123);
}
float2 random2( in half2 uv )
{
    return frac(sin(float2(dot(uv.xy, float2(127.1,311.7)),dot(uv.xy,float2(269.5,183.3))))*43758.5453);
}
//梯度化噪声
float gradientNoise (in half2 uv)
{
    half2 iuv = floor(uv);
    half2 fuv = frac(uv);
    float a = random(iuv);
    float b = random(iuv + half2(1.0, 0.0));
    float c = random(iuv + half2(0.0, 1.0));
    float d = random(iuv + half2(1.0, 1.0));
    half2 u = fuv*fuv*(3.0-2.0*fuv);
    return lerp(a, b, u.x) +
            (c - a)* u.y * (1.0 - u.x) +
            (d - b) * u.x * u.y;
}
//voronoi噪声，计算最小距离
float voronoiNoise(in half2 uv)
{
    half2 iuv = floor(uv);
    half2 fuv = frac(uv);
    
    float minDist = 1.;  //最小距离
    
    for (int y= -1; y <= 1; y++) {
        for (int x= -1; x <= 1; x++) {
            // 邻居网格节点
            float2 neighbor = float2(float(x),float(y));
    
            // 在网格内从current+neighor位置来随机位置
            float2 pt = random2(iuv + neighbor);
                    
   // 移动特征点
            pt = 0.5 + 0.5*sin(time + 6.2831*pt);
                
   // 像素到特征点的矢量
            float2 diff = neighbor + pt - fuv;
                
            // 计算到特征点的距离
            float dist = length(diff);
                
            // 计算最小距离
            minDist = min(minDist, dist);
        }
    }
    // 返回最小距离
    return  minDist;
}

//分形布朗运动
 #define OCTAVES 6 // 定义有几级噪声函数
 float fbm (in half2 uv) {
     // Initial values
     float value = 0.0;
     float amplitude = .5;
     
     // Loop of octaves
     for (int i = 0; i < OCTAVES; i++) {
         //value += amplitude * gradientNoise(uv);
         
         //湍流
         value += amplitude * abs(voronoiNoise(uv)*2 - 1);
         //
         uv *= 2.;
         amplitude *= .5;
     }
     // Sharpness
     //value = 1.0 - clamp(0, 1, value); 
     //value = value * value;
     //
     return value;
 }
 //翘曲域
 #define IterNum 3
 float domainWarping(in half2 uv)
 {
     float value = 0.0;
     for (int i = 0; i < IterNum; i++)
         value = fbm( uv +value );
     return value;
 }
 half3 PixelColor(float2 uv)
 {
     half3 c = half3(0, 0, 0);
     //
     uv = uv*10;
     //分形布朗运动
     //c = fbm(uv + time);
     //翘曲域
     c = domainWarping(uv + time);
     //
     return c;
 }