RuntimeProject made a tutorial to create a little cellular automata on a small 126×64 OLED using Arduino Nano.

He worked on one type of cellular automata, the Game of Life by John Conway, which has a grid of cells each having 2 states True or False/on or off/alive or dead. These cells are governed by 2 simple rules:

Rule 1: A cell which is dead and is surrounded by exactly 3 alive cells, will be born

Rule 2: A cell which is alive and has either 3 or 2 alive cells will remain alive, else it dies

The Arduino-based Cellular Automata works using 2 libraries the,  Adafruit GFX library  to handle all graphics and text displayed on the OLED;
Adafruit SSD1306 library which is the driver for the OLED.

You can read more info on how to make it on his blog and download the sketch on Github.