// see: https://en.wikipedia.org/wiki/Mandelbrot_set /** Number of discrete color values on the JS side. */ const NUM_COLORS = 2048; /** Computes a single line in the rectangle `width` x `height`. */ export function computeLine(y: u32, width: u32, height: u32, limit: u32): void { var translateX = width / 1.6; var translateY = height / 2.0; var scale = 10.0 / min(3 * width, 4 * height); var imaginary = (y - translateY) * scale; for (let x: u32 = 0; x < width; ++x) { let real = (x - translateX) * scale; // 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 ixNew = ixSq - iySq + real; iy = 2.0 * ix * iy + imaginary; ix = ixNew; if (iteration >= limit) break; ++iteration; } // Do a few extra iterations for quick escapes to reduce error margin for (let minIterations = min(8, limit); iteration < minIterations; ++iteration) { let ixNew = ix * ix - iy * iy + real; iy = 2.0 * ix * iy + imaginary; ix = ixNew; } // Iteration count is a discrete value in the range [0, limit] here, but we'd like it to be // normalized in the range [0, 2047] so it maps to the gradient computed in JS. // see also: http://linas.org/art-gallery/escape/escape.html let frac = Math.log(Math.log(Math.sqrt(ix * ix + iy * iy))) / Math.LN2; let icol = isFinite(frac) ? ((NUM_COLORS - 1) * clamp((iteration + 1 - frac) / limit, 0.0, 1.0)) : NUM_COLORS - 1; store((y * width + x) << 1, icol); } } /** Clamps a value between the given minimum and maximum. */ @inline function clamp(value: T, minValue: T, maxValue: T): T { return min(max(value, minValue), maxValue); }