GoL 32x32 Torus Quest
The Problem Statement:
Given a 32x32 Game of Life Torus, find the initial configuration that yields the maximum number of unique generations
Without further ado, based on all my search efforts uptodate, here is the configuration with maximum number of unique generations (6261) before repeating:
For a comprehensive understanding of Conway’s Game of Life, refer to this link on Wikipedia. The game takes place on a 32x32 field, set up as a torus. Describing it as a torus implies that it exhibits a ‘wrap-around’ effect on both the x and y axes, including when determining the neighbors needed for rule applications. If you prefer visual learning, check out this neat visualization that illustrates what a Game of Life Torus looks like.
The game commences with a specific initial configuration. The future configuration is dictated by the rules applied to the current state. The existing generation is subsequently replaced by the next.
This process continues until the next computed generation mirrors a previously recorded generation. This can occur under two circumstances: either all activity ceases, leaving only static life forms (from which point all future generations resemble the static life), or we encounter a recurring loop where every X cycles reproduce the same generation. A simple example of this cyclic nature is the placement of a single glider on the grid; despite its continuous evolution, the configuration never stabilizes, resulting in a recurring cycle.