** IN CONSTRUCTION **
Game of life
Introduction
The game of life was invented in 1970 by the mathematician John Horton Conway. It is defined as a cellular automaton, to simplify (and because the author is not an expert on that domain), it’s a system consisting of cells on a 2D grid with a discrete evolution that obey to some rules. In the game of life each cell can be in two different state : alive or dead.
The rules
Each iteration the new system state will change for each cell depending of it’s surrounding (the 8 cells arround it) and following these rules :
- If an alive cell has less than 2 alive neighbours, she dies of loneliness
- If an alive cell has 2 or 3 neighbours, she is happy and stay alive
- If an alive cell has more than 3 neighbours, she dies of pression
- If a dead cell is has 3 alive neighbours (mom, dad and the doctor), she became alive
Exemple of a Game of Life
Here is an exemple of an $(100 \times 100)$ grid with periodic conditions, during $2000$ iterations.
We can see a lot of structures are forming, some of them are static, oscilate or move on the grid. We will describe them in the next section !