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
Requires Python 3.14 or newer.
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 4, the default x0 = 0.5 is preperiodic
exponent = logistic.lyapunov(r=4.0, x0=0.2) # -> log 2, a generic x0 gives the attractor's exponent
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 --python 3.14
uv pip install -e ".[dev]"
uv run pytest
License
Apache-2.0. Copyright 2026 Ricardo A S Frantz.
1 maintainer
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