https://github.com/fractaltongues/fractal

Computation of bifurcation fractals for 2D symplectic mappings
https://github.com/fractaltongues/fractal

bifurcation chaos fractals symplectic

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Computation of bifurcation fractals for 2D symplectic mappings

• Host: GitHub
• URL: https://github.com/fractaltongues/fractal
• Owner: FractalTongues
• License: mit
• Created: 2024-03-26T17:02:38.000Z (11 months ago)
• Default Branch: main
• Last Pushed: 2024-11-26T06:11:03.000Z (2 months ago)
• Last Synced: 2025-01-20T23:55:30.553Z (16 days ago)
• Topics: bifurcation, chaos, fractals, symplectic
• Language: Jupyter Notebook
• Homepage:
• Size: 79.6 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.MD
  • License: LICENSE

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README

        
# fractal, 2024

[![Run In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/i-a-morozov/fractal/blob/main/fractal.ipynb)

Computation of bifurcation fractals for 2D symplectic mappings

Watch supplementary videos on [YouTube](https://www.youtube.com/@sithif)

For a quadratic mapping:

$$

\begin{aligned}

& q \to p \\

& p \to -q + w p + p^2

\end{aligned}

$$

two symmetry lines, $p=q$ and $p=1/2(w q + q^2)$  cover full 2D plane. Fractals bellow are computed in $(w, q)$ space with $w$ in [-3.00, 2.00] and $q$ in [-1.25, 1.75] using the second symmetry line. Color corresponds to different indicators.

- Phase space coverage by symmetry lines



  



- REM



  



- Frequency



  



- Frequency & mode locking (tongues)



  



- FMA



  



- GALI