SmoothLife (Continuous Game of Life)

A continuous-space, continuous-state generalization of Conway's Game of Life, proposed by Stephan Rafler in 2011.
Instead of binary cells on a rigid grid, cells have continuous float values from 0.0 to 1.0. Neighborhoods are calculated using continuous integration (rings/discs) instead of discrete neighbors.
This creates beautiful, organic, fluid-like behaviors such as gliding amoebas, pulsing blobs, and cellular mitosis.