You're probably familiar with the Game Of Life: create a grid sparsely populated with "cells"; apply a couple of simple rules (cells "die" if they have too few or too many neighbours; dead cells spring into life if they have exactly three); watch complex behaviour spontaneously emerge. This video explains the traditional Game of Life in more detail (watch to the end so see come interesting "creatures" that emerge from these simple rules).
This Game of Life is based on a discrete world: cells live squarely in grids with exactly 8 neighbours, and time moves step by step instead of as a continuous flow. (This digital quality made the GoL ideal for implementation on early computers, and is one of the few non-utility programs with implementations dating all the way back to the 60's.) But what if you implemented the Game of Life in a continuous world?
That's what SmoothLife does. Rather than working with discrete square cell, it works at the level of points in a continuous 2-D space. A cell lives or dies depending on how much of a small disk in its immediate neighbourhood is filled, and also the density of a ring surrounding the cell. This diagram (from these slides) contrasts the discrete Game of Life with the continuous SmoothLife:
Implementing SmoothLife in a computer takes some doing, as computers are still digital after all. But with some clever approximations (described in this paper by Stephan Rafler) of the continuous field in a grid, and using technique similar to antialiasing to count the areas in the inner and outer ring that drive life and death, beautiful behaviours such as those in this animation by Tim Hutton emerge:
(An open-source program to implement SmoothLife — sadly, Windows-only — can be downloaded at SourceForge.) Smoothlife can easily be extended to 3-D as well, by considering spheres and shells instead of discs and rings. And when you do that, you get something that's, well, lifelike:
What amazing creatures might we discover inside this SmoothLife to parallel the traditional Game of Life's glider guns and puffer trains? From simple rules, life, reproduction, and death all emerge spontaneously ... at scales both small and large. Something to contemplate over the weekend. Enjoy!