Add some smoothing to mandelbrot example

examples/mandelbrot/assembly/index.ts

@@ -1,24 +1,41 @@
 // see: https://en.wikipedia.org/wiki/Mandelbrot_set
 
 /** Computes the number of iterations in the rectangle `width` x `height`, limited to `max`. */
-export function compute(width: u32, height: u32, max: u32): void {
+export function compute(width: u32, height: u32, limit: u32): void {
   var translateX = width / 1.6;
   var translateY = height / 2.0;
-  var scale = 4.0 / width;
+  var scale = 10.0 / min(3 * width, 4 * height);
   for (let y: u32 = 0; y < height; ++y) {
     let imaginary = (y - translateY) * scale;
     for (let x: u32 = 0; x < width; ++x) {
       let real = (x - translateX) * scale;
-      let iteration = <u32>0;
-      let ixsq: f64, iysq: f64;
-      for (let ix = 0.0, iy = 0.0; (ixsq = ix * ix) + (iysq = iy * iy) <= 4.0; ++iteration) {
+
+      // Iterate until either the escape radius or iteration limit is exceeded
+      let ix = 0.0, iy = 0.0, ixsq: f64, iysq: f64;
+      let iteration: u32 = 0;
+      while ((ixsq = ix * ix) + (iysq = iy * iy) <= 4.0) {
         let t = ixsq - iysq + real;
         iy = 2.0 * ix * iy + imaginary;
         ix = t;
-        if (++iteration >= max) break;
+        if (iteration >= limit) break;
+        ++iteration;
+      }
+
+      // Do a few extra iterations to reduce error margin
+      for (let i = 0; i < 4; ++i) {
+        let t = (ixsq = ix * ix) - (iysq = iy * iy) + real;
+        iy = 2.0 * ix * iy + imaginary;
+        ix = t;
+      }
+
+      // Renormalize, see: http://linas.org/art-gallery/escape/escape.html
+      let frac: f64 = JSMath.log(JSMath.log(sqrt(ix * ix + iy * iy))) / JSMath.LN2;
+      if (frac > 0) {
+        let norm: f64 = max<f64>(min<f64>((<f64>(iteration + 1) - frac) / limit, 1.0), 0.0);
+        store<u16>((y * width + x) << 1, <u32>(2047 * norm));
+      } else {
+        store<u16>((y * width + x) << 1, iteration * 2047 / limit);
       }
-      // write normalized iterations to [0, width * height], row by row
-      store<u8>(y * width + x, iteration * 255 / max);
     }
   }
 }