Fundamental Chaos

About this site

This is a personal notebook. The material here is informal — short essays, reading notes, and computational sketches around topics that I find beautiful or instructive in the study of dynamical systems. Topics drift between continuous flows (the Lorenz and Rössler systems), discrete maps (logistic, Hénon, standard map), and basic ergodic theory.

Nothing here is original research. Everything is either a re-derivation of standard material, a numerical illustration, or a paraphrase of textbook content for my own understanding.

Recent notes

• 2026-03 The logistic map and its bifurcation cascade — period-doubling, Feigenbaum constants, and the universality of the route to chaos.
• 2026-02 Numerical integration of the Lorenz system — fourth-order Runge–Kutta, sensitivity analysis, and visualization of the strange attractor.
• 2026-01 Symbolic dynamics on the unit interval — coding orbits via partition refinement and the link to information-theoretic entropy.
• 2025-12 Lyapunov exponents from time series — practical estimation by the Wolf and Rosenstein algorithms with worked examples.
• 2025-11 A short introduction to ergodic theory — measure-preserving transformations, Birkhoff's theorem, and a few illustrative counterexamples.

Tools

Most numerical work uses NumPy and SciPy with custom integrators where stiffness matters. Plots are rendered with Matplotlib. Where animations help, I export short MP4s using FFmpeg. Source for individual notebooks is kept locally; nothing here depends on a hosted service.

Contact

If you spot a mistake or want to discuss something, you can reach me at contact at fundamentalchaos.xyz. I read mail when I have time but do not promise quick replies.