Figure Gallery

Examples of publication-ready visualizations generated by the library.

(This section is under construction. Images from the private repository will be embedded here upon publication).

1. The Fractional Chua Attractor

# Code to reproduce (Requires `hidden_attractors` installed)
from hidden_attractors.workflows.unified_chua import main
# Run with --q 0.98 --output results/

Expected output: A 3D render of a validated non-smooth Chua orbit, overlaid with the $O_+$ , $O_-$ , and $O_0$ equilibria markers.

2. Robustness Overlay Sweep

# Code to reproduce
from hidden_attractors.workflows.robustness_overlay import main
# Run parameter sweep on alpha from 8.0 to 10.0

Expected output: A scatter plot showing the distance of the attractor to the $O_+$ equilibrium across different values of $\alpha$ . The plot clearly shows the bifurcation point where the distance becomes non-zero, indicating the emergence of a hidden attractor.

3. Poincaré Section

# Code to reproduce
from hidden_attractors.analysis import poincare_section
# Intersect the Chua attractor at the x=0 plane

Expected output: A 2D scatter plot revealing the folded, fractal-like internal structure of the fractional Chua attractor.

4. Spectral Power Density

# Code to reproduce
from hidden_attractors.analysis import fft_peak_frequency
# Run FFT on the x-coordinate time series

Expected output: A logarithmic plot of the power spectrum in the frequency domain, demonstrating the broadband chaotic nature of the signal.