Life Collection: A Mathematical Structures Preservation Organization

Leo Moura


Abstract. There are infinite numbers of Game of Life configurations. The aim of Life Collection is to catalog every possible state of the Game of Life. You can own a particular state. Below is an example of a Game of Life configuration. Although it starts as a seemingly random pattern, it evolves into a stable pattern.

1. Introduction

Game of life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves.

2. The Rules

The universe of the Game of Life is an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, live or dead. Every cell interacts with its eight neighbours, which are the cells that are horizontally, vertically, or diagonally adjacent.

3. Seeds

A seed is a configuration of live and dead cells. The seed evolves from one generation to the next according to the rules of the Game of Life.

We classify seeds into three categories: still lifes, oscillators, and spaceships. Still lifes are configurations that do not change from one generation to the next. Oscillators are configurations that repeat themselves after a certain number of generations. Spaceships are configurations that move across the grid.

Figure 1: A still life seed. It remains the same after a few generations.
Figure 2: An oscillator seed. It repeats itself after a few generations.
Figure 3: A spaceship seed. It moves across the grid.

4. Auction

You can own a particular seed. The auction is a way to acquire a particular seed. The auction starts with a seed and a reserve price. The seed is sold to the highest bidder after 24 hours. The seed is transferred to the winner's wallet.

After you own a seed, you can give it a name. You can also sell the seed in the secondary market. But after you sell, the new owner can override the name.

5. The treasury

The proceeds from the auction are used to fund the organization. The organization is responsible for maintaining the collection. The organization also funds research on the Game of Life.

6. Conclusion

With the Life Collection, we aim to catalog every possible state of the Game of Life. We hope to preserve the mathematical structures of the Game of Life for future generations.

Be a Life Collector and help spread the complexity gospel.