sample a complex number for membership in julia sets

samplePointJulia.js

const MAX_SAMPLES = 1000;
const MAX_RADIUS = 2 ** 4;

/**
 * a complex number, c, belongs to The Mandelbrot Set if the iterative application
 * of the function f(z)=z^2+c, starting at z=0, does not result in divergence
 * beyond a specified radius before a specified number of iterations
 *
 * a complex number, z, belongs to The Julia Set if the iterative application
 * of the function f(z)=z^2+c, where c is a constant, does not result in divergence
 * beyond a specified radius before a specified number of iterations
 *
 * @param {Number?} zr the real part of the complex number
 * @param {Number?} zi the imaginary part of the complex number
 * @param {Number?} cr the real part of the complex number
 * @param {Number?} ci the imaginary part of the complex number
 * @param {Number?} maxRadius the maximum distance an orbit point may be
 * @param {Number?} maxSamples the maximum number of samples to take before assuming the orbit does not diverge
 */
export function samplePointJulia(zr = 0, zi = 0, cr = 0, ci = 0, maxRadius = MAX_RADIUS, maxSamples = MAX_SAMPLES) {
  let inSet = true;

  let escaped = false
  let orbitDistance = 0;
  let orbitPoints = [{ escaped, orbitDistance, zr, zi }];

  //sample the entire range rather then aborting upon escape to maximize data
  while (orbitPoints.length < maxSamples) {
    let escaped = false

    //this is literally just the FOIL method
    //we subtract the Last terms from the First because `i**2===-1`, and they are
    //no longer imaginary, then we combine the Inside and Outside because they are
    let tempR = zr ** 2 - zi ** 2 + cr;
    zi = 2 * zr * zi + ci;
    zr = tempR;

    orbitDistance = zr ** 2 + zi ** 2; //pythagoras
    escaped = orbitDistance > maxRadius ** 2;
    inSet = inSet && !escaped;

    orbitPoints.push({ escaped, orbitDistance, zr, zi });
  }

  return { orbitPoints, inSet };
}