let angle

let startingAngle

let sequences;

​

function collatz(k) {

  sequence = [];

​

  while (k != 1) {

    if (k in sequences) {

      for (let i = 0; i < sequence.length; i++) {

        sequences[sequence[i]] = [...sequence.slice(i), ...sequences[k]];

      }

      return [...sequence, ...sequences[k]];

    }

    sequence.push(k)

    if (k % 2 == 0) {

      k /= 2;

    } else {

      k = (k * 3 + 1) / 2;

    }

  }

​

  sequence.push(k);

​

  for (let i = 0; i < sequence.length; i++) {

    if (sequence[i] in sequences) break;

    sequences[sequence[i]] = sequence.slice(i);

  }

  return sequence;

}

​

function drawPath(seq) {

  resetMatrix()

  translate(width/4, height - 80)

  rotate(startingAngle)

  let next;

  for (let j=0; j<seq.length; j++) {

      if (j < (seq.length - 1)) {

        next = seq[j + 1]

      } else {

        next = seq[j]

      }

      if (seq[j] * 2 == next) {

        rotate(angle * 2)

      } else {

        rotate(-angle)

      }

      line(0, 0, 0, -offset)

      translate(0, -offset)

    }

}

​

function setup() {

  sequences = {};

  createCanvas(10000, 10000);

  background(0, 0, 0, 0);

  colorMode(HSB)

​

  startingAngle = -PI * 0.6

  angle = 0.08;

  offset = height/100

  weight = offset * 0.9

  N = 10000;

​

  for (let i=4; i<N; i++) {

    let seq = collatz(i);

    let c = [...seq]

    c.reverse()

    stroke(0, 0, 40)

    strokeWeight(weight * 1.3)

    drawPath(c)

    //reds

    //stroke(random(330, 360), random(10,150), random(50,255))

    //blues

    // stroke(random(210, 270), random(10,150), random(50,255))

​

    //greens

    stroke(random(80, 160), random(10,150), random(50,255))

    strokeWeight(weight)

    drawPath(c)

  }

}

​