Bangle.js: displays the famous Mandelbrot set

Bangle_MandelbrotSet.js

  Bangle.setLCDMode();                                // use normal display mode
  g.clear();

  const Width  = g.getWidth();
  const Height = g.getHeight();

/**** color mapping (especially for Bangle.js) ****/

  function rgb565 (r,g,b) {
    return (r << 11) | (g << 5) | b;
  }

  let ColorMap = [0];      // not part of Mandelbrot set? then leave pixel black
    for (let i = 1; i <= 4; i++) {       // make low escape times distiguishable
      ColorMap.push(rgb565(4*i,4*2*i+1,31));
    }
    for (let i = 4*4+1; i < 32; i++) {            // extend map for more details
      ColorMap.push(rgb565(i,2*i+1,31));
    }
  const ColorCount = ColorMap.length;

/**** EscapeTimeOf ****/

  const maxIterations = ColorCount;
/*
  function EscapeTimeOf (x,y) {                                   // unoptimized
    let re = x, imag = y;
    for (let i = 0; i < maxIterations; i++) {
      let newRe   = re*re - imag*imag + x;
      let newImag = 2*re*imag + y;
      
      re = newRe; imag = newImag;
      if (re*re + imag*imag > 2) { return i }
    }
    return 0;
  }
*/
  function EscapeTimeOf (x,y) {                            // slightly optimized
    let re = x, imag = y;
    
    let r2 = x*x, i2 = y*y, z2 = (x+y)*(x+y);
    for (let i = 0; i < maxIterations; i++) {
      let newRe   = r2 - i2 + x;
      let newImag = z2 - r2 - i2 + y;
      
      r2 = newRe*newRe;
      i2 = newImag*newImag;
      z2 = (newRe+newImag)*(newRe+newImag);
      
      if (r2 + i2 > 4) { return i }
    }
    return 0;
  }

/**** draw Mandelbrot set ****/

  const xOffset = -1.9;  const Zoom = 100;
  const yOffset = -1.2;

  for (let y = 0; y < Height; y++) {
    for (let x = 0; x < Width; x++) {
      let EscapeTime = EscapeTimeOf(
        xOffset + x/Zoom, yOffset + y/Zoom
      );
      if (EscapeTime > 0) {
        g.setPixel(x,y,ColorMap[EscapeTime]);
      }
    }
  }