Beautiful, isn't it? It might look complex but it's mathematically quite impressive. Making this pattern wasn't hard but it definitely took a lot of trial and error to get it right and honestly, I don't really know if it's this is the most efficient way to generate this pattern.

This article isn't a tutorial but rather, I'll be talking about the algorithm itself. However, you can check out the source code in my GitHub repository.

How it works?

In order to achieve that "stacked" effect, there are two things to keep in mind:

  1. Generate circles with a random radius
  2. Look for collisions with other circles

The logic is quite similar to the Overlapping Rectangles problem except this is done with circles.

Generate circles with dynamic radius

This method will help generate valid circles with a random radius. Circles that don't overlap or collide with other circles are considered to be valid.

// Generate a valid circle
const generateCircle = () => {
    let newCircle;
    let isValidCircle = false;

    for(let i=0; i<attempts; i++) {
        newCircle = {
            x: Math.floor(Math.random() * width),
            y: Math.floor(Math.random() * width),
            radius: minRadius

        if(checkForCollision(newCircle)) {
        else {
            isValidCircle = true;

    if(!isValidCircle) { return; }

    for(let i=minRadius; i<=maxRadius; i++) {
        newCircle.radius = i;
        if(checkForCollision(newCircle)) {

    drawCircleOnCanvas(context, newCircle, colors[Math.floor(Math.random() * colors.length)]);

Look for collision with other circles

Thanks to some online research, I was able implement the Euclidean Distance equation that helped with calculating the distances between each circle and detect for collisions. Along with that, I also found another article on Touching Circles that was quite useful.

These are the formulas used to detect the collision:

  1. Find the distance between two centres \[ AB = \sqrt{ (x2 - x1)^2 - (y2 - y1)^2} \]

  2. Calculate the radii of both circles. \[R = r1 + r2\]

If the radii is greater than or equal to the euclidean distance of both circles, then it's a valid circle with no collisions.

// Check for collision in a canvas
const checkForCollision = (newCircle) => {

    let x2 = newCircle.x;
    let y2 = newCircle.y;
    let r2 = newCircle.radius;

    // Determine the euclidean distance between two circle
    // using Pythagorean Theorem.

    // Refer to: 

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

        let otherCircle = circles[i];
        let r1 = otherCircle.radius;
        let x1 = otherCircle.x;
        let y1 = otherCircle.y;
        let xx = ((x2 - x1) * (x2 - x1));
        let yy = ((y2 - y1) * (y2 - y1));
        let radii = r2 + r1;
        let euclidDistance = Math.sqrt(xx + yy);

        if(radii >= euclidDistance) {
            return true;

    // Check collision on top
    if(x2 + r2 >= width || 
        x2 - r2 <= 0) {
        return true;

    // Check collision on bottom
    if(y2 + r2 >= width || 
        y2 - r2 <= 0) {
        return true;

    //else return false
    return false;


I'm thinking of implementing more generative patterns like Triangular Mesh and Piet Mondrian's Red, Blue and Yellow composition.

Hope you liked reading this article.

Stay tuned for more!