From 61b7b7484e141319479df532c185961eef8edf0c Mon Sep 17 00:00:00 2001
From: Akshay Nair <phenax5@gmail.com>
Date: Sun, 3 Dec 2023 22:57:03 +0530
Subject: improved newton's fractal coloring

---
 sketches/02/newton.frag       |  30 ++++++++++++------------------
 sketches/02/screenshots/1.jpg | Bin 66810 -> 242241 bytes
 sketches/02/screenshots/2.jpg | Bin 147734 -> 230782 bytes
 3 files changed, 12 insertions(+), 18 deletions(-)

diff --git a/sketches/02/newton.frag b/sketches/02/newton.frag
index ac31d73..b905d1b 100644
--- a/sketches/02/newton.frag
+++ b/sketches/02/newton.frag
@@ -21,38 +21,32 @@ vec2 cpow(vec2 z, float n) {
   return pow(r, n) * vec2(cos(n * theta), sin(n * theta));
 }
 
+float fabs(float a) { return a > 0. ? a : -a; }
+
 void main() {
-  float time = mod(1.1 + mod(u_time * 1000.0, 100000.0) / 10000.0, 10.);
-  // float time = 2.0;
+  float time = mod(0.5 + mod(u_time * 1000.0, 100000.0) / 10000.0, 2.);
 
   float ratio = u_resolution.x / u_resolution.y;
   vec2 pos = v_position.xy/vec2(1.0, ratio);
 
+  vec2 prevZ;
   vec2 z = 2.0 * (pos - vec2(0., 0.));
-  int i;
 
-  vec2 prevZ = z;
-  for (i = 0; i < MAX_ITERATIONS; i++) {
+  int iterations = 0;
+  for (int 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;
-    }
+    iterations++;
+    if (fabs(z.x - prevZ.x) < 0.001) break;
   }
 
-  gl_FragColor = vec4(0., 0., 0., 1.);
-
-  float diff = length(z - prevZ);
+  float val = float(iterations) * 10.0 / float(MAX_ITERATIONS);
+  float g = val * 0.5;
+  float b = val * 0.8;
 
-  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.;
-  }
+  gl_FragColor = vec4(0.0, g, b, val);
 }
 
diff --git a/sketches/02/screenshots/1.jpg b/sketches/02/screenshots/1.jpg
index 67a2266..1fb1721 100644
Binary files a/sketches/02/screenshots/1.jpg and b/sketches/02/screenshots/1.jpg differ
diff --git a/sketches/02/screenshots/2.jpg b/sketches/02/screenshots/2.jpg
index da745cb..fd4d4be 100644
Binary files a/sketches/02/screenshots/2.jpg and b/sketches/02/screenshots/2.jpg differ
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