Examples#
This gallery walks through every public feature of mathematicskit.fractals_chaos:
Lyapunov exponent estimation, box-counting fractal dimension, Mandelbrot/
Julia set generation, iterated function systems, and cellular automata.
See also the narrative tutorial:
Each script in this gallery is self-contained and can be run directly with
python examples/fractals_chaos/<section>/<script>.py.
Sections#
lyapunov – Lyapunov exponent estimation for 1D maps and flows.
box_counting – fractal (box-counting) dimension estimation.
mandelbrot_julia – Mandelbrot and Julia set escape-time generation.
ifs – iterated function systems: the Barnsley fern and Sierpinski triangle/carpet.
cellular_automata – elementary (Wolfram rule) cellular automata and Conway’s Game of Life.
Box-counting dimension#
Estimating fractal dimension from a point cloud via box-counting.
Cellular automata#
Elementary 1D cellular automata (Wolfram rule numbering) and Conway’s Game of Life.
Elementary cellular automata and Conway’s Game of Life
Fractal curves#
Nowhere-differentiable and space-filling curves, coastline measurement, and the similarity dimension.
The Weierstrass function: continuous, nowhere differentiable
The Koch snowflake: infinite perimeter, finite area
How long is the coast of Britain? The divider method
Aggregation#
Diffusion-limited aggregation: fractal clusters grown by random walkers.
Iterated function systems#
The chaos game: Barnsley’s fern and the Sierpinski triangle/carpet.
Lindenmayer systems#
Parallel string rewriting and turtle graphics for plants and fractal curves.
Lyapunov exponents#
Estimating the Lyapunov exponent of 1D maps and simple flows.
Lyapunov exponent across the logistic map’s route to chaos
Mandelbrot and Julia sets#
Escape-time generation of the Mandelbrot set and Julia sets.
Discrete maps#
Two-dimensional maps with strange attractors.
