hypergeometric

const bgCol = "#447abd";
const gCol = "#a2c2e8";
const nGrid = 20;
let gSpace;
let N = 52;
let A = 13;
let n = 10;

function setup() {
  w = max(400, min(windowWidth, windowHeight) * 0.9);
  createCanvas(w, w);
  rectMode(CENTER);
  describe(
    "a hypergeometric distribution with the bars centered horizontally is reflected over the y center of the page and then the sample changes to stretch the reflections in such a way that the two distributions boop."
  );
  angleMode(DEGREES);
  textSize(16);
  gSpace = (w / nGrid) * 0.95;
  prevN = 10;
}

function draw() {
  background(bgCol);
  translate(w / 2, w / 2);
  t = frameCount;
  let targetN = 5 + int(5 * (0.5 + 0.5 * sin(t)));
  n = lerp(prevN, targetN, 0.1);

  prevN = n;
  for (let i = 0; i < n; i++) {
    p = hyperG(i);
    fill(255, 255, 255, 80);
    stroke(255);
    rect(-9 * gSpace + i * gSpace, 0, gSpace, p * gSpace * 30);
    rect(9 * gSpace - i * gSpace, 0, gSpace, p * gSpace * 30);
  }

  noStroke();
  fill(gCol);
  text("hypergeometric", -w / 2 + 10, w / 2 - 5);
  drawGrid();
}

function hyperG(k) {
  if (k > A || n - k > N - A) {
    return 0;
  }
  k = int(k);
  t1 = factorial(A) / (factorial(k) * factorial(A - k));
  t2 = factorial(N - A) / (factorial(n - k) * factorial(N - A - (n - k)));
  t3 = factorial(N) / (factorial(n) * factorial(N - n));

  return (t1 * t2) / t3;
}

function factorial(n1) {
  if (n1 === 0 || n1 === 1) {
    return 1;
  }
  let result = 1;
  for (let i = 2; i <= n1; i++) {
    result *= i;
  }
  return result;
}
function fillRect(x, y, s) {
  push();
  translate(x, y);
  stroke(gCol);
  strokeWeight(2);
  if (s === 1) {
    scale(1, 1);
  } else {
    scale(1, -1);
  }
  for (let i = 0; i <= 6; i++) {
    line(
      -gSpace / 2 + (gSpace / 6) * i,
      -gSpace / 2,
      -gSpace / 2,
      -gSpace / 2 + (gSpace / 6) * i
    );
    line(
      gSpace / 2 - (gSpace / 6) * i,
      gSpace / 2,
      gSpace / 2,
      gSpace / 2 - (gSpace / 6) * i
    );
  }
  pop();
}

function drawGrid() {
  gSpace = (w / nGrid) * 0.95;
  stroke(gCol);
  strokeWeight(0.3);
  for (let i = 1; i <= nGrid; i++) {
    for (let j = 1; j <= nGrid; j++) {
      line(
        -w / 2 + gSpace * i,
        -w / 2 + gSpace,
        -w / 2 + gSpace * i,
        w / 2 - gSpace
      );
      line(
        -w / 2 + gSpace,
        -w / 2 + gSpace * i,
        w / 2 - gSpace,
        -w / 2 + gSpace * i
      );
    }
  }
  noFill();
  strokeWeight(3);
  rect(0, 0, w - 2 * gSpace);
}

function mousePressed() {
  setup();
  draw();
}
function windowResized() {
  setup();
  draw();
}