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!

\[\begin{aligned}\pd{πŸ€}{t}&=D_πŸ€\vnabla\cdot (\vnabla πŸ€-g(πŸ€)\vnablaπŸ§€)+f(πŸ€,πŸ§€),\\ \pd{πŸ§€ }{t}&=D_πŸ§€ \nabla^2πŸ§€ +g(πŸ€,πŸ§€)\end{aligned}\]