feat: mandelbrot + newton fractals

1 files changed, 54 insertions, 1 deletions

diff --git a/sketches/02/newton.frag b/sketches/02/newton.frag
index 9cbf92c..ac31d73 100644
--- a/sketches/02/newton.frag
+++ b/sketches/02/newton.frag
@@ -1,5 +1,58 @@
+varying vec4 v_position;
+uniform vec2 u_resolution;
+uniform float u_time;
+uniform float u_mouse;
+
+#define MAX_ITERATIONS 100
+
+vec2 cmul(vec2 a, vec2 b) {
+  return vec2(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x);
+}
+
+vec2 cdiv(vec2 a, vec2 b) {
+  float denominator = b.x*b.x + b.y*b.y;
+  if (denominator == 0.) return a;
+  return cmul(a, vec2(b.x, -b.y)) / denominator;
+}
+
+vec2 cpow(vec2 z, float n) {
+  float r = length(z);
+  float theta = atan(z.y, z.x);
+  return pow(r, n) * vec2(cos(n * theta), sin(n * theta));
+}
 
 void main() {
-  gl_FragColor = vec4(1.0, 0.0, 0.0, 1.0);
+  float time = mod(1.1 + mod(u_time * 1000.0, 100000.0) / 10000.0, 10.);
+  // float time = 2.0;
+
+  float ratio = u_resolution.x / u_resolution.y;
+  vec2 pos = v_position.xy/vec2(1.0, ratio);
+
+  vec2 z = 2.0 * (pos - vec2(0., 0.));
+  int i;
+
+  vec2 prevZ = z;
+  for (i = 0; i < MAX_ITERATIONS; i++) {
+    prevZ = z;
+    vec2 value = cpow(z, 3.0) + vec2(1., 0.);
+    vec2 value_der = 3.0 * cpow(z, 2.0);
+    z = z - time * cdiv(value, value_der);
+
+    if (length(z - prevZ) > 30.0) {
+      break;
+    }
+  }
+
+  gl_FragColor = vec4(0., 0., 0., 1.);
+
+  float diff = length(z - prevZ);
+
+  if (diff > 10.0) {
+    gl_FragColor = vec4(97., 42., 191., 255.0) / 255.;
+  } else if (diff > 1.0) {
+    gl_FragColor = vec4(150., 191., 69., 255.0) / 255.;
+  } else if (diff > 0.0) {
+    gl_FragColor = vec4(27., 14., 50., 255.0) / 255.;
+  }
 }