This is a relaxation-method solver for Laplace's equation with motion of the lattice. Forked from (https://github.com/deltaGPhys/TheGoodLaplace) -> (https://github.com/deltaGPhys/ForestFire) -> (https://github.com/deltaGPhys/ConwayGameOfLife) -> (https://github.com/Zipcoder/ConwayGameOfLife)
See https://github.com/deltaGPhys/TheGoodLaplace for background on the equation and the relaxation method for finding numerical solutions.
In this implementation, the cells in the array are simulated as if they are discrete parts of a moving lattice. Each element feels an average force exerted by its neighbors, based on its position relative to theirs, modeled via Hooke's Law (force proportional to displacement and opposite in direction). The velocity of each element is stored and updated using this acceleration as well as a damping factor, which allows the system to come to equilibrium in the long- time limit. The positions are changed according to the velocity at each step.
As a result, the lattice moves like an elastic sheet, overshooting the equilibrium position and oscillating, eventually damping down to the steady state. The 'height' of each cell is illustrated by color, but this time by HSB colors, instead of RGB, to better show the height contrast.
For a system with two "high" and two "low" corners:
An animation of the relaxation process with a large damping factor and lower lattice resolution
Higher resolution and much lower damping, allowing a great deal of oscillation before settling down to the steady state
