Exploring Chaos: Drawing Lines from Dynamical Systems
Lines Through Chaos
This post explores a set of visual experiments based on classic chaotic systems—plotted as continuous lines. Each is rendered in the browser using basic JavaScript and canvas drawing. You can try them directly using the embedded JSFiddles below.
These attractors aren’t new, but tracing their paths as single connected lines reveals a meditative beauty that’s fun to explore.
The sections below are links to jsfiddles which show an animation of the chaotic system.
The system is defined by a bunch of equations you can find the javascript. They are fairly simple equations and the js iterates through them, plotting successive points. Points from the ends are removes which shows it like a ribbon moving along the path of the system.
🌀 Lorentz Line
One of the most iconic systems in chaos theory. The Lorentz attractor is based on simplified models of atmospheric convection.
🔄 Rossler Line
The Rossler system produces smoother, spiraling chaos - a contrast to the Lorentz system’s butterfly structure.
🔀 Lorentz-Rossler Hybrid
This sketch combines the behaviors of both the Lorentz and Rossler attractors. It holds both systems in memory and at every iteration progresses both and takes an average of each of the XYZ co-ordinates of both systems.
The result is a hybrid pattern—somewhere between flight and swirl.
🔁 Rikitake Line
A lesser-known but fascinating system inspired by the dynamics of Earth’s magnetic field reversals. The Rikitake attractor creates loops that feel like unstable orbits.
Closing Notes
Each system starts from a simple set of equations, but the lines they draw feel alive—never repeating, always moving forward. There’s a quiet satisfaction in seeing them emerge in real time.
If you’re curious about the math, these are numerical integrations of ODEs using Euler’s method with a light touch of aesthetic tuning.
Let me know if you remix or build on these—I’d love to see what lines you follow.