Chaos Atlas

Iterated maps, coupled map lattices, and Lyapunov exponents for chaotic dynamical systems. NumPy arrays in, NumPy arrays out.

This is the Python companion to the Chaos Atlas web explorer, which visualises the same systems interactively.

Install

pip install chaos-atlas

Use

Every map shares the same surface, so switching systems is a one-word change.

from chaos_atlas.maps import logistic, henon

orbit = logistic.trajectory(r=3.9, x0=0.5, iterations=1000)
exponent = logistic.lyapunov(r=4.0)          # -> log 2, the Bernoulli shift

points = henon.attractor(a=1.4, b=0.3, iterations=10_000)   # (10000, 2)

Bifurcation diagrams come back as paired flat arrays, ready to scatter:

import matplotlib.pyplot as plt

r, x = logistic.bifurcation(r_min=2.5, r_max=4.0, r_steps=2000)
plt.plot(r, x, ",k", alpha=0.25)

Coupled map lattices return a (time_steps, lattice_size) space-time array:

from chaos_atlas import cml

spacetime = cml.diffusive(r=3.9, epsilon=0.4, lattice_size=256, time_steps=512)
plt.imshow(spacetime, aspect="auto", cmap="magma")

Pass rng= (or initial=) when you need a run to be reproducible.

Maps

Module System Notes
logistic x → rx(1−x) period doubling, bifurcation, cobweb
tent piecewise linear λ = log α exactly, symbolic dynamics
henon (1−ax²+y, bx) strange attractor, λ₁ ≈ 0.419
standard Chirikov area preserving, KAM islands
ikeda optical cavity spiral attractor
arnold cat map area preserving, finite recurrence period
bakers baker's transformation entropy = log 2 exactly
tinkerbell quadratic 2D multi-loop attractor
duffing double well fixed points in closed form
complex_quadratic z² + c Julia and Mandelbrot escape-time

Lyapunov exponents for the nonlinear 2D maps evolve a tangent vector under the analytic Jacobian with renormalisation each step. Where a map has an exact exponent — tent, baker's, Arnold, logistic at r = 4 — the test suite pins the numerical result to it.

Development

uv venv && uv pip install -e ".[dev]"
pytest

License

Apache-2.0. Copyright 2026 Ricardo A S Frantz.

Project links

Data verified by PyPI on Jul 25, 2026
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Newer release available (0.3.0)

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Credits

Author: Ricardo A S Frantz

GitHub Statistics

Data verified by PyPI on Jul 25, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License expression

Apache-2.0
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Requires

Python >=3.10

Provides Extra

dev

Tags

bifurcation-diagrams chaos-theory coupled-map-lattices dynamical-systems fractal-geometry lyapunov-exponents strange-attractors

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