One of the cooler things I discovered recently was that when you google search “Conway’s game of life” google automatically begins to play the game of life in the background of the search results page. It is rather mesmerizing,

The game of life is played on a grid of little squares; squares have two configurations “alive” and “dead” which are usually represented by using two different colours. A single game consists of a initial seed or starting configuration and a set of rules which govern how the grid updates:

(1) Any live cell will remain alive if it has 2 or 3 live neighbors; otherwise it will die.

(2) Any dead cell with 3 live neighbors will become alive.

The rules are roughly motivated by physical considerations; if the population density is too low or too high then individual members of a colony will die before reproducing. However three alive cells may reproduce to create a extra adjacent live cell.

The game is extremely popular because the seemingly overly simple rules can generate extremely complicated patterns. Recently it was demonstrated that certain initial conditions of the game of life can give rise to emergent behavior in the sense that we can aggregate large sections of the grid (consisting of multiple cells) and treat this section as an individual “macroscopic cell” which behaves non-trivially. There are no simple set of rules for how these macroscopic cells behave; all update

rules continue to apply to the small indivisible cells which constitute them. Nevertheless it is possible to  initialize the game of life so that the macroscopic squares effectively appear to evolve according to conditions (1) and (2). There is quite a spellbinding example of this available here. Check it out as it is unbelievable at first sight.