What Happened When We Explore Fractals For Animating Infinity

Every Saturday morning as the autumn air turns crisp and we head into October, a lively mix of curious makers, artists, and code tinkerers gather for our Arts Incubator fall and winter sessions. Some of us show up online with steaming mugs of coffee, others with sketchbooks or half-finished code experiments. The spirit is always the same: no gatekeeping, no high-pressure deadlines … just a few fun hours to collaborate, learn something new, and build playful digital art from scratch.

This past weekend, our curiosity steered us straight into the mesmerizing world of fractals. While a couple of folks had fond memories of staring at vintage screensavers or classic posters of Mandelbrot sets, others were completely new to the concept. We started with a whiteboard and a simple question: How can a single, short math equation generate infinite artistic detail?

The Magic of Fractals: Infinite Detail from Pure Simplicity

At their core, fractals are geometric shapes that display self-similarity. That means no matter how far you zoom in, you keep discovering intricate, repeating patterns that echo the whole structure. You see this everywhere in the natural world: the branching veins of a leaf, the jagged outline of a coastline, lightning bolts striking across the night sky, and the spiraling florets of Romanesco broccoli.

In mathematical art, we feed a starting coordinate into a tiny formula (like classic Mandelbrot equations), take the result, and feed it right back in over and over again. Points that spiral off to infinity get painted one colour, while points that stay trapped within a boundary get painted another. By mapping millions of these calculations directly onto your graphics card with GPU shaders, abstract arithmetic instantly transforms into swirling celestial dragons, glowing neon dendrites, and cathedral-like spires.

Rather than just looking at static pictures, we wanted to build something we could touch, steer, animate, and play with in real time. Over the course of the morning, we prototyped Fractal Fun—a desktop-first, highly responsive digital studio built to let anyone explore and animate fractals without needing a PhD in mathematics.

From classic fractals to 3D animated styles and colours, we had a lot of fun with this experiment. Click the image to try it out!

Here is a glimpse of what we built into the canvas:

  • A Multiverse of Fractal Types: Jump seamlessly between classic 2D complex systems (Mandelbrot, Julia sets, the jagged Burning Ship, and 3-fold Tricorn stars), mathematical physics basins like Newton-Raphson polynomial roots, botanical Iterated Function Systems like the Barnsley Fern, and full 3D raymarched geometric structures like the 8-fold Mandelbulb and Sierpinski Pyramid.
  • Interactive Julia Point Picking: In dynamical Julia sets, the entire universe changes shape based on a single constant point . With our crosshair picker, you can simply click or drag anywhere on the complex plane and watch the fractal blossom and morph in real time under your mouse.
  • Keyframe Animation Sequencer: An intuitive timeline dock lets you set keyframe snapshots at different zoom depths, rotations, and mathematical powers, smoothly interpolating camera movements with silky easing curves to create hypnotic fly-through animations.
  • Audio-Reactive Soundscapes: We hooked up a harmonic ambient synthesizer and frequency analyzer that breathes life into the visualizer—pulsing the fractal zoom, iteration depth, and color waves in time with ambient musical chords or room microphone input.
  • Color & Shading Laboratory: Thirteen custom cosine palettes (from electric neon and synthwave sunset to deep oceanic obsidian) with continuous phase cycling, halo glow, domain warping, and volumetric depth fog.
  • 4K Stills & Video Capture: Export crisp, high-resolution 4K wallpaper posters or record 60 FPS WebM animation loops with a single click.
Click the image to try out our simple Fractal Fun project!

Come Create and Explore With Us!

Building Fractal Fun was a reminder of why we love to explore new things. When you combine playful curiosity with open-ended creative tools, math stops feeling like a dry textbook exercise and becomes an expressive, living canvas. What do you think? Should we keep working on it and improve it?

Our fall and winter programming runs throughout the season, and there is always a seat at the virtual table for you—whether you have been coding for years or have never written a single line of JavaScript in your life. We are all about learning by making, sharing ideas, and exploring the boundless intersections of art, design, and technology.

Come check out what we are up to, view upcoming weekend sessions, and jump into our community projects at artsincubator.ca. Have a question or want to get involved? Drop us a note anytime at info@artsincubator.ca. Let’s make something amazing together!