Kovalevskaya on chaos

Functions of space can allow us to change how a PDE solution varies in space and time. This page explores an example using an image of Sofya Kovalevskaya encoded as the function $I_S(x,y)$. The system uses the complex Ginzburg–Landau equation.

• Load one of the interactive simulations demonstrating dark soliton pinning, localised chaos, or fireflies.

• You can upload your own image by clicking on → Images and then clicking on the image of Sofya Kovalevskaya’s face next to $I_S(x,y)$. The image will be effectively treated as a greyscale function $I_T(x,y)$, which will be approximately 1 when the image is close to white and approximately 0 when the image is close to black.

• Change $I_T$ to $I_S$ in   → Definitions to see another famous mathematical face: Alan Turing.

• You can upload a replacement for either of these images under → Images. They can each be used as heterogeneities in many parts of VisualPDE.