Hexagonal curves

/*

 * Author: Juan Carlos Ponce Campuzano

 * Date: 28/May/2024

 * Site: https://www.dynamicmath.xyz

 * Video: https://youtu.be/vqGeaY188Ew

 */

​

let t = 0, speed = 0.004;

​

function setup() {

  createCanvas(500, 500);

  colorMode(HSB, 1, 1, 1);

}

​

function draw() {

  background(0);

​

  for (let j = 1; j <= 10; j++) {

    let hue = map(j, 1, 10, 0, 1)

    stroke(hue, 1, 1);

    hexagonalCurve(50, 2.5, 3, j, j * t, PI + j * t);

  }

​

  t += speed;

  if(t >= TWO_PI) t = 0;

}

​

/*

  Hexagonal curve

  Defined on the interval [startT, endT]

  Main parameters: n, k, m

*/

function hexagonalCurve(n, k, m, size, startT, endT) {

  noFill();

  strokeWeight(4);

  let view = 12; 

  let x, y;

  beginShape();

  for (let i = startT; i <= endT; i += 0.01) {

    let v = pow(

      pow(cos((m * i) / 2), n) + pow(sin((m * i) / 2), n),

      1 / (k * n)

    );

    x = map(cos(i) * (size / v), -view, view, 0, width);

    y = map(sin(i) * (size / v), -view, view, height, 0);

    vertex(x, y);

  }

  endShape();

}

​