The Arnold Tongue

[AnadyaNair]

Summary:

• Arnold tongues are a concept in dynamical systems theory that visualizes the regions in parameter space where the behaviour of a system switches between periodic and chaotic dynamics.
• They are a resonance zone that emanates out from rational numbers in a two-dimensional parameter space of variables.
• Implementing a visualization tool for Arnold tongues could greatly enhance our understanding of complex systems and their behaviour transitions.
• The tool could be based on interactive plots or graphs, facilitating the analysis of different dynamical systems and aiding in the discovery of underlying patterns.

For the math behind Arnold's tongue, read its dedicated Wikipedia page.

Visualisation: