Colorized Conway’s Game of Life

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Cellular Automata and Conway's Game of Life

Cellular automata are mathematical models that consist of a grid of cells, where each cell can have a simple state (like alive or dead). These cells interact based on predefined rules, evolving over discrete time steps. Cellular automata can create complex patterns and behaviors from simple rules, making them fascinating tools in mathematics, computer science, and art.

One of the most famous examples is Conway's Game of Life, created by mathematician John Conway in 1970. The Game of Life is a zero-player game, meaning that once it’s set up, it evolves automatically without further input. The game's simplicity and emergence of complex patterns make it an iconic exploration of how complexity arises from simplicity.

Rules of Conway's Game of Life

In the Game of Life, each cell on a grid can be either "alive" or "dead," and its future state depends on its current state and the states of its eight neighbors:

Birth: A dead cell with exactly three live neighbors becomes alive (simulating reproduction).
Survival: A live cell with two or three live neighbors remains alive.
Death: A live cell with fewer than two live neighbors dies from underpopulation. Similarly, a live cell with more than three live neighbors dies from overpopulation.

How the Game Evolves

The grid evolves over time, with each new generation calculated based on these rules. Various patterns emerge, such as:

Still lifes: Stable patterns that don’t change from generation to generation.
Oscillators: Patterns that cycle through a sequence of states and return to their original form after a fixed number of generations.
Spaceships: Patterns that repeat themselves as they move across the grid.

In this interactive Conway's Game of Life, you can adjust the initial pattern by clicking individual cells. The Auto Animation Switch and color options introduce a chance for intricate and random cell inversions for an added visual effect, creating evolving, unpredictable animations.