toolbox_chaos
v0.1.0
Python 3.10+ - PyQt6 GUI - v0.1.0 Stable

Fyskode Chaotic Systems Toolbox

Desktop software for simulating, visualizing, and exploring chaotic dynamical systems.

Download Documentation GitHub Cite

About

Project metadata, archive reference, and build baseline.

Version
0.1.0 (Initial stable release)
License
MIT License
Archive
OSF DOI 10.17605/OSF.IO/GQMJR
Platforms
Windows, macOS, Linux
Built With
Python, PyQt6, NumPy, Matplotlib
Author
Maria Fernanda Moreno Lopez (Fer Moreno) / Xerkkun
Repository
github.com/Xerkkun/Toolbox-chaos

Key Features

Desktop tools for simulation, visual analysis, and reproducible figure generation.

3D
Classical Chaotic Systems
Simulate Lorenz, Chua, Rossler, Sprott flows, maps, delay models, and high-dimensional systems.
SP
Sprott Explorer
Explore compact-code examples with generated maps, flows, projections, and visual presets.
CO
Coexisting Attractors
Compare trajectories produced by the same parameter set under different initial states.
BA
Basins of Attraction
Classify grids of initial conditions by their long-term destinations.
BF
Bifurcation Diagrams
Sweep a control parameter and plot retained long-term values or events.
FT
Time Series and FFT
Compare time-domain trajectories with centered normalized spectra.
LY
Lyapunov Diagnostics
Estimate finite Lyapunov spectra and inspect convergence before interpreting the values.
PDF
PDF Dictionary
Includes local dictionary, Sprott guide, and theory PDFs bundled with the desktop app.
EX
Exportable Figures
Save PNG, PDF, SVG, or JPG figures from the analysis tabs.

Concept-first toolbox

Learning Chaos With Figures

Toolbox Chaos is organized around the same teaching idea as the dictionary PDF: students learn faster when each concept is tied to a concrete graph. The overview shows the available workflows; the documentation explains how to read each graph in detail.

Read the visual theory primer ->

Theory Through Graphics

The dictionary and web documentation connect definitions with reproducible figures, so students can read what each diagnostic is actually showing.

Separate Visual Tasks

A basin map, a coexistence comparison, a bifurcation diagram, and a Lyapunov plot answer different questions. The site keeps those workflows separated.

Reproducible Examples

Examples use explicit systems, parameters, initial conditions, projection choices, and retained windows so students can reproduce the plots.

Recovered exploration workflow

Sprott Explorer

The Sprott Explorer invites students to experiment with compact dynamical-system recipes inspired by J. C. Sprott's strange-attractor work. Load a generated example, change the projection or visual preset, and watch how a short code becomes a map, a flow, or a dense phase-space object worth investigating.

The public page uses reproducible educational examples, while the documentation explains the decoding logic, search filters, plotting choices, and parameter effects.

Open the Sprott guide ->
Generated Sprott-style flow with depth coloring
Depth-colored flow
Generated Sprott-style 3D map with color-coded coordinate
3D map projection
Generated Sprott-style 4D projection with hidden coordinate color
4D color projection

Working Pattern

A practical loop for moving from a first run to a figure worth saving.

1

Choose a visual question

Start from the graph you need: attractor, projection, bifurcation, basin, coexistence, FFT, Lyapunov, or Sprott exploration.

2

Load a coherent preset

Use a registered system so equations, parameters, initial state, and integration scale begin in a known range.

3

Run a low-cost pass

Use coarse grids, shorter sweeps, or fewer points to check whether the selected region is meaningful.

4

Refine one control

Change one value at a time: time step, total time, transient, parameter range, projection, or density.

5

Compare diagnostics

Use geometry, time series, basins, bifurcation, spectra, and Lyapunov estimates as complementary evidence.

6

Export the final figure

Increase resolution after the behavior is clear, then export the figure from the relevant tab.

Visual Output Gallery

Attractors, bifurcations, Poincare sections, basins, coexistence cases, Lyapunov figures, and Sprott-generated graphics.

Animated 3D Lorenz attractor rendered in the Toolbox Chaos visual style
3D attractors

Lorenz 3D rotation

Animated orbit rendered with the toolbox magenta trajectory style.

Chua double-scroll attractor with time-series panels
3D attractors

Chua double scroll

Double-scroll flow with the same phase-and-series layout used by the toolbox.

Lorenz 3D trajectory with 2D phase portraits projected onto coordinate planes
Phase portraits

Projected Lorenz portraits

2D phase portraits overlaid on the planes of a 3D Lorenz figure.

Separate Lorenz 2D phase portraits
Phase portraits

2D projection grid

x-y, x-z, and y-z portraits shown separately for comparison.

Logistic bifurcation diagram generated by Fyskode Chaos Toolbox
Bifurcation

Logistic cascade

Classic period-doubling cascade and dense chaotic bands.

Lorenz bifurcation sweep over rho
Bifurcation

Lorenz rho sweep

Higher-density local maxima of z as rho changes in the Lorenz system.

Lorenz Poincare section showing crossings on a plane
Poincare

Lorenz return section

A 3D flow reduced to crossing points on a selected plane.

Supercritical Hopf bifurcation example with phase portraits
Bifurcation

Hopf example

A stable equilibrium changes into a stable limit cycle.

Lorenz basin map generated by Fyskode Chaos Toolbox
Basins

Lorenz basin map

Grid of initial conditions classified by long-term destination.

Lorenz basin map with representative trajectories
Basins

Basin trajectories

Representative orbits launched from different colored basin regions.

Lorenz coexisting stable states generated from two initial conditions
Coexistence

Lorenz coexistence

Same Lorenz parameters, two initial conditions, two stable destinations.

Animated Lorenz coexisting trajectories
Coexistence

Simultaneous starts

Animation showing both Lorenz coexistence trajectories generated together.

Perturbation expansion and contraction concept diagram
Lyapunov

Perturbation geometry

Expansion and contraction directions behind Lyapunov exponents.

Synthetic Sprott-style flow with depth coloring
Sprott Explorer

Depth-colored flow

A generated Sprott-style flow rendered with depth coloring.

Synthetic 3D Sprott map with coordinate coloring
Sprott Explorer

3D color map

Projection uses color to keep a hidden coordinate readable.

Synthetic 4D Sprott map projected with color
Sprott Explorer

4D projection

A 4D synthetic map projected with the fourth coordinate in color.

Citing Fyskode Chaos Toolbox

If you use this software in research, thesis, or academic workflows, cite the archived OSF release.

Maria Fernanda Moreno Lopez. Fyskode Chaotic Systems Toolbox, version 0.1.0. 10.17605/OSF.IO/GQMJR.

Get BibTeX and CFF files ->