You have probably heard of Game of Life. It is popular cellular automata simulation game where you create simple structures in infinite plain and watch the life evolve. All this is achieved by implementing several basic rules. By implementing different rules, you can simulate biological processes, model structure behavior and program robot swarms.
Building cellular automata is fairly simple. You can start with Arduino Nano and 128×64 OLED to get pretty interesting results. In this following project the Game of Life has been implemented. There are only two rules applied to pixels to make it work:
1. A cell which is dead and is surrounded by exactly 3 alive cells, will be born
2. A cell which is alive and has either 3 or 2 alive cells will remain alive, else it dies
The source code is hosted on GitHub which can be analyzed and used for your purposes. In order to compile for Arduino you will need two additional libraries – Adafruit GFX, which handles graphical display (draws graphs and displays text) and second is Adafruit SSD1306 which is the actual driver for OLED chip. Probably you will find one thing that limits the fun – small LCD.