let pts;

​

function m() {

  // https://arxiv.org/pdf/2302.06230.pdf

  const R1 = random(-1, 1);

  const R2 = random(TWO_PI);

  const R3 = random(TWO_PI);

  const R4 = random(1);

​

  const a1s = [sqrt(1 - sq(R1)) * cos(R2), sqrt(1 - sq(R1)) * sin(R2), R1];

  const a2s = [

    R1 * cos(R2) * cos(R3) + sin(R2) * sin(R3),

    R1 * sin(R2) * cos(R3) - cos(R2) * sin(R3),

    -sqrt(1 - sq(R1)) * cos(R3),

  ];

​

  let s = sqrt(R4);

  const a1 = [a1s[0] * s, a1s[1] * s, a1s[2] * s];

  s = sqrt(1 - R4);

  const a2 = [a2s[0] * s, a2s[1] * s, a2s[2] * s];

​

  const alpha = random(0.001, 0.005);

  const beta = random(0.001, 0.005);

​

  const h12 = a2[0] * a2[1] - a1[0] * a1[1];

  const h21 = h12;

  const h13 = a2[0] * a2[2] - a1[0] * a1[2];

  const h31 = h13;

  const h23 = a2[1] * a2[2] - a1[1] * a1[2];

  const h32 = h23;

  const h14 = a1[2] * a2[1] - a1[1] * a2[2];

  const h41 = h14;

  const h24 = a1[0] * a2[2] - a1[2] * a2[0];

  const h42 = h24;

  const h34 = a1[1] * a2[0] - a1[0] * a2[1];

  const h43 = h34;

​

  const D = cos(alpha) - cos(beta);

​

  return [

    (sq(a1[1]) + sq(a1[2]) + sq(a2[0])) * D + cos(beta), // r11

    h12 * D - a1[2] * sin(alpha) - a2[2] * sin(beta), // r12

    h13 * D + a1[1] * sin(alpha) + a2[1] * sin(beta), // r13

    h14 * D + a2[0] * sin(alpha) + a1[0] * sin(beta), // r14

​

    h21 * D + a1[2] * sin(alpha) + a2[2] * sin(beta), // r21

    cos(alpha) - (sq(a1[1]) + sq(a2[0]) + sq(a2[2])) * D, // r22

    h23 * D - a1[0] * sin(alpha) - a2[0] * sin(beta), // r23

    h24 * D + a2[1] * sin(alpha) + a1[1] * sin(beta), // r24

​

    h31 * D - a1[1] * sin(alpha) - a2[1] * sin(beta), // r31

    h32 * D + a1[0] * sin(alpha) + a2[0] * sin(beta), // r32

    cos(alpha) - (sq(a1[2]) + sq(a2[0]) + sq(a2[1])) * D, // r33

    h34 * D + a2[2] * sin(alpha) + a1[2] * sin(beta), // r34

​

    h41 * D - a2[0] * sin(alpha) - a1[0] * sin(beta), // r41

    h42 * D - a2[1] * sin(alpha) - a1[1] * sin(beta), // r42

    h43 * D - a2[2] * sin(alpha) - a1[2] * sin(beta), // r43

    (sq(a2[0]) + sq(a2[1]) + sq(a2[2])) * D + cos(beta), // r44

  ];

}

​

function makePoints() {

  pts = [];

  for (let ix = 0; ix < 10; ++ix) {

    const x = map(ix, 0, 9, -1, 1);

    for (let iy = 0; iy < 10; ++iy) {

      const y = map(iy, 0, 9, -1, 1);

      for (let iz = 0; iz < 10; ++iz) {

        const z = map(iz, 0, 9, -1, 1);

        for (let iw = 0; iw < 10; ++iw) {

          const w = map(iw, 0, 9, -1, 1);

          pts.push([x, y, z, w]);

        }

      }

    }

  }

}

​

function mul(T, p) {

  return [

    T[0] * p[0] + T[1] * p[1] + T[2] * p[2] + T[3] * p[3],

    T[4] * p[0] + T[5] * p[1] + T[6] * p[2] + T[7] * p[3],

    T[8] * p[0] + T[9] * p[1] + T[10] * p[2] + T[11] * p[3],

    T[12] * p[0] + T[13] * p[1] + T[14] * p[2] + T[15] * p[3],

  ];

}

​

function setup() {

  createCanvas(500, 500);

  makePoints();

  M = m();

}

​

function draw() {

  background(40);

  noStroke();

  fill(255, 100);

​

  for (let idx = 0; idx < pts.length; ++idx) {

    pts[idx] = mul(M, pts[idx]);

​

    const z = pts[idx][2];

    const x = pts[idx][0] / (10 + z);

    const y = pts[idx][1] / (10 + z);

    circle(width / 2 + 1600 * x, height / 2 + 1600 * y, 50 / (10 + z));

  }

}

​

function keyPressed() {

  if (key === " ") {

    M = m();

  } else if (key === "g") {

    makePoints();

    saveGif("out.gif");

  } else if (key === "s") {

    save("jan16.png");

  }

}

​