Fractal Particles

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Fractal Particles

Project Overview

Animated 3D fractals made of particles (100,000 per frame, accumulated over many frames), rendered on the CPU in C++. I saw Acerola make something like this, thought it looked cool, and wrote my own version from scratch, focusing on making it fast.

A wispy fractal cloud

How It Works

The fractal is an iterated function system, drawn with the "chaos game":

  1. Pick a few random 3D affine transforms (scale, rotation, shear, translation).
  2. Start with a cloud of random points. Every step, move each point by one of the transforms, picked at random.
  3. After a few iterations the points settle onto the fractal that those transforms define.

To animate it, the program smoothly interpolates each transform toward a new random target, then picks another target when it gets there. The fractal keeps morphing into new shapes.

Rendering

I tried a few different renderers:

  • Point splatting: Project every particle onto the screen and accumulate how many land on each pixel, then map that density to brightness. Accumulating over several frames smooths out the noise.
  • Ray marching: Treat the fractal as a volume of density, march a ray through it for each pixel, and attenuate light as it passes through (Beer-Lambert absorption), so the fractal looks like glowing smoke instead of points.
  • Discrete ray marching: First bin the particles into a 3D grid of densities, then ray march through the grid, which is much cheaper to sample.

Everything runs on the CPU, compiled with aggressive optimization flags (-O3 -march=native -ffast-math), with per-frame values precomputed outside the hot loops. There is also an offline mode that renders frames to disk to stitch into a video with ffmpeg.

Fern-like fractal Branching fractal Spiky fractal Soft fractal cloud

What's Next

I've learned a lot more about CPU optimization since I wrote this (SIMD, cache-friendly memory layouts, multithreading), and I could make it much faster now. It would also be a good project for learning Vulkan to run it on my laptop's GPU, since OpenCL doesn't handle its unified memory well.

Technology Stack

  • C++
  • GLM (vector math)
  • SFML (window and display)
  • ffmpeg (video export)