A-maze-ing PDEs

This is a simulation of a chemotaxis-like system which tries to solve a maze by gobbling up all the food as it goes. There is a source of food at the edge of the maze, and some initial (but slowly decaying) food spread throughout the maze. Will the population make it to the end? Can a web-based PDE solver help complete such puzzles?

Find out in the interactive simulation!

\[\begin{aligned}\pd{🐀}{t}&=D_🐀\vnabla\cdot (\vnabla 🐀-g(🐀)\vnabla🧀)+f(🐀,🧀),\\ \pd{🧀 }{t}&=D_🧀 \nabla^2🧀 +g(🐀,🧀)\end{aligned}\]

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