Functions of space can allow us to change how a PDE solution varies in space and time. Here is an example using such a function, given by $I_T(x,y)$, where this function represents a picture. The equations are based on the Schnakenberg model.

  • Load the interactive Turing simulation.

  • You can upload your own image by clicking on Images and then clicking on the image of Alan Turing’s face next to $I_T(x,y)$. 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. Sofya Kovalevskaya also has her own interactive Sofya simulation.

Other images

You can upload a replacement for either of these images under Images. They can each be used as heterogeneities in many parts of VisualPDE. Some examples include: