precision highp float; uniform vec2 resolution; uniform float time; uniform vec2 mouse; uniform sampler2D backbuffer; #define iResolution resolution #define iTime time #define iMouse mouse const float PI = 3.141592653589793; vec3 hsvToRgb(float h, float s, float v) { // h: -π - +π, s: 0.0 - 1.0, v: 0.0 - 1.0 h = (h + PI) / (2.* PI) * 360.; float c = s; // float c = v * s; float h2 = h / 60.0; float x = c * (1.0 - abs(mod(h2, 2.0) - 1.0)); vec3 rgb = (v - c) * vec3(1.0, 1.0, 1.0); if (0.0 <= h2 && h2 < 1.0) { rgb += vec3(c, x, 0.0); } else if (1.0 <= h2 && h2 < 2.0) { rgb += vec3(x, c, 0.0); } else if (2.0 <= h2 && h2 < 3.0) { rgb += vec3(0.0, c, x); } else if (3.0 <= h2 && h2 < 4.0) { rgb += vec3(0.0, x, c); } else if (4.0 <= h2 && h2 < 5.0) { rgb += vec3(x, 0.0, c); } else if (5.0 <= h2 && h2 < 6.0) { rgb += vec3(c, 0.0, x); } return rgb; } // hsvToRgb borrowed from // https://qiita.com/sw1227/items/4be9b9f928724a389a85 // (slightly modified by Kanata) //operations on complex numbers borrowed from //https://shadertoyunofficial.wordpress.com/2019/01/02/programming-tricks-in-shadertoy-glsl/ #define re(a) vec2((a).x, 0.) #define im(a) vec2(0., (a).y) #define cmul(a,b) ( mat2(a, -(a).y, (a).x ) * (b) ) #define conj(a) vec2( (a).x, -(a).y) #define cinv(a) ( conj(a) / dot(a, a) ) #define cexp(a) ( exp((a).x)* vec2(cos((a).y), sin((a).y)) ) #define clog(a) vec2( log(length(a)), atan((a).y,(a).x) ) #define cpow(a,n) cexp( float(n)* clog(a) ) void mainImage(out vec4 fragColor, in vec2 fragCoord); void main(void) { vec4 col; mainImage(col, gl_FragCoord.xy); gl_FragColor = col; } void mainImage( out vec4 O, vec2 u ) { vec2 res = iResolution.xy, z = ( u* 2. - res) / min(res.x, res.y); float t = iTime; float scale = 1.5; z *= scale; const float delta = 0.1; #define f(w) (cpow(w, 5) + cmul(cpow(w, 4), cexp(vec2(sin(t), t))) + tan(-0.3* t)* cpow(w, 3) +tan(0.21* t)* cpow(w, 2) + cmul(w, cexp(vec2(0., t))) + cexp(vec2(0., -1.47* t))) #define df(w) (f(w + vec2(delta, 0.)) - f(w - vec2(delta, 0.))) / (2.* delta) #define ddf(w) (df(w + vec2(delta, 0.)) - df(w - vec2(delta, 0.))) / (2.* delta) #define dddf(w) (ddf(w + vec2(delta, 0.)) - ddf(w - vec2(delta, 0.))) / (2.* delta) float l = length(f(z)); float ld = length(df(z)); float ldd = length(ddf(z)); float lddd = length(dddf(z)); O = vec4(vec3(.01/ abs(l - 1.)) + vec3(.01/ abs(ld - 1.), .01/ abs(ldd - 1.), .01/ abs(lddd - 1.)), 1.); }

Complex derivative