Coding Challenge 168: The mandelbulb! (#3563)

* mandelbulb challenge code

* voxels example

* starting markdown page

* Fix title mandelbulb page

* Add links and videos to mandelbulb

* Update 168-mandelbulb.md

* Fix spacing in 168 md

* remove space line 36 mandelbulb

Co-authored-by: Kobe Liesenborgs <[email protected]>

Author: shiffman

CodingChallenges/CC_168_Mandelbulb/Processing/MandelBulb_Cloud/MandelBulb_Cloud.pde

@@ -0,0 +1,85 @@
+import peasy.*;
+
+int DIM = 128;
+PeasyCam cam;
+ArrayList<PVector> mandelbulb = new ArrayList<PVector>();
+
+void setup() {
+  size(600, 600, P3D);
+  cam = new PeasyCam(this, 600);
+
+  StringList points = new StringList();
+
+  for (int i = 0; i < DIM; i++) {
+    for (int j = 0; j < DIM; j++) {
+      boolean edge = false;
+      for (int k = 0; k < DIM; k++) {
+        float x = map(i, 0, DIM, -1, 1);
+        float y = map(j, 0, DIM, -1, 1);
+        float z = map(k, 0, DIM, -1, 1);
+        PVector zeta = new PVector(0, 0, 0);
+        int n = 8;
+        int maxiterations = 20;
+        int iteration = 0;
+        while (true) {
+          Spherical c = spherical(zeta.x, zeta.y, zeta.z);
+          float newx = pow(c.r, n) * sin(c.theta*n) * cos(c.phi*n);
+          float newy = pow(c.r, n) * sin(c.theta*n) * sin(c.phi*n);
+          float newz = pow(c.r, n) * cos(c.theta*n);
+          zeta.x = newx + x;
+          zeta.y = newy + y;
+          zeta.z = newz + z;
+          iteration++;
+          if (c.r > 2) {
+            if (edge) {
+              edge = false;
+            }
+            break;
+          }
+          if (iteration > maxiterations) {
+            if (!edge) {
+              edge = true;
+              mandelbulb.add(new PVector(x, y, z));
+            }
+            break;
+          }
+        }
+      }
+    }
+  }
+  
+  String[] output = new String[mandelbulb.size()];
+  for (int i = 0; i < output.length; i++) {
+    PVector v = mandelbulb.get(i);
+    output[i] = v.x + " " + v.y + " " + v.z;
+  }
+  saveStrings("mandelbulb.txt", output);
+  
+}
+
+class Spherical {
+  float r, theta, phi;
+  Spherical(float r, float theta, float phi) {
+    this.r = r;
+    this.theta = theta;
+    this.phi = phi;
+  }
+}
+
+Spherical spherical(float x, float y, float z) {
+  float r = sqrt(x*x + y*y + z*z);
+  float theta = atan2( sqrt(x*x+y*y), z);
+  float phi = atan2(y, x);
+  return new Spherical(r, theta, phi);
+}
+
+void draw() {
+  background(0);
+  rotateX(PI/4);
+  rotateY(-PI/3);
+  for (PVector v : mandelbulb) {
+    stroke(255);
+    strokeWeight(1);
+    point(v.x*200, v.y*200, v.z*200);
+  }
+}