Conway's Game of Life is one of the most well-known examples of cellular automata. It is a simple model where each cell on an infinite 2D grid can either be alive or dead. Its state changes depending on the state of its eight neighbors and predefined rules. Despite these rules being extremely simple, they lead to fascinating dynamic patterns simulating seemingly 'living' behavior.
These simple principles lead to complex structures such as oscillators (patterns that repeat periodically), 'spaceships' (patterns that move across the grid), or even stationary structures known as stable objects. Though the Game of Life may seem like a simple simulation, it is, in fact, computationally complete, meaning it can simulate any computation. Some researchers have even demonstrated that functional logic circuits and simple computers can be created in the Game of Life.
However, when exploring these patterns, the question arises: What if we move away from the binary system (alive/dead) and introduce fuzzy logic into the game? Such fuzzification could open up new possibilities for exploring dynamic processes and perhaps uncover patterns that do not appear in the classic game. This is a natural approach because in real life, states are often continuous and fluid, while sharp binary divisions are more of an exception than a rule.
Implementing fuzzy logic into the Game of Life represents both a challenge and an opportunity. How can we modify the rules for fuzzy states? What new patterns would emerge with continuous transitions? Could fuzzy configurations show new oscillators, stable patterns, or even something akin to analog computation?
This thesis, therefore, focuses on the intersection between the classic Game of Life and fuzzy logic. Our goal is to extend these basic rules and explore how fuzzy logic affects this model.