// ip: imaginary part

let minX,

    minY,

    maxX,

    maxY,

    gradWidth;

​

function setup() {

  createCanvas(800, 800);

  minX = -1.5;

  minY = -1.5;

  maxX = 1.5;

  maxY = 1.5;

  gradWidth = 5;

}

​

function draw() {

  background(22);

  axes();

  strokeWeight(5);

  stroke(150, 0, 233);

  figure();

  noLoop();

}

​

function add(n1, n2) {

  return {

    rp: n1.rp + n2.rp,

    ip: n1.ip + n2.ip

  };

}

​

function mult(n1, n2) {

  return {

    rp: n1.rp * n2.rp - n1.ip * n2.ip,

    ip: n1.rp * n2.ip + n1.ip * n2.rp

  }

}

​

function distance(n) {

  return sqrt(n.rp ** 2 + n.ip ** 2);

}

​

function sequence(c) {

  let n = {rp: 0, ip: 0};

  for (let i = 0; i < 100; i++)

    n = add(mult(n, n), c);

  return distance(n) < 10;

}

​

function figure() {

  const delta = 0.002;

  for (let x = minX; x <= maxX; x += delta) {

    for (let y = minY; y <= maxY; y += delta) {

      if (sequence({rp: x, ip: y}))

        drawPoint({rp: x, ip: y});

    }

  }

}

​

function axes() {

  strokeWeight(2);

  stroke(55);

  line(0, height / 2, width, height / 2);

  line(width / 2, 0, width / 2, height);

  for (let x = ceil(minX); x <= maxX; x++)

    line((x - minX) * width / (maxX - minX), height / 2 - gradWidth / 2, (x - minX) * width / (maxX - minX), height / 2 + gradWidth / 2);

  for (let y = ceil(minY); y <= maxY; y++)

    line(width / 2 - gradWidth / 2, (y - minY) * height / (maxY - minY), width / 2 + gradWidth / 2, (y - minY) * height / (maxY - minY))

}

​

function drawPoint(n) {

  strokeWeight(1);

  stroke(233);

  point(width / 2 + n.rp * width / (maxX - minX), height / 2 - n.ip * height / (maxY - minY));

}

​