Computational Simulations: Constructing The Game of Life

Computational simulations are powerful tools used to recreate the behavior of a system. Where such simulations were once science fiction, technology has advanced far enough that the real world can be simulated in a “virtual reality” where all the same physical rules are applied. Many working professionals in industry and academia also use these simulations for a variety of different projects. Simulations are excellent at generating models, visualizing data, and predicting outcomes that would otherwise be infeasible to grasp mentally or create by hand. The growth of computer simulations was simultaneous with the growth of computational power. The first, large-scale simulation was created by John von Neumann to observe nuclear reactions during the Manhattan Project. The simulation made use of a Monte Carlo Algorithm to predict the effects of colliding shock-waves [1]. However, today’s blog will focus on a much simpler system — that of Conway’s Game of Life.

Conway used a Go board, such as this, to track various states while planning Life

Creation

John Conway was a Cambridge mathematician who enjoyed dabbling in recreational mathematics. He was interested in the work of von Neumann and Stanislaw Ulam who had posed the idea of cellular automaton — mathematical models that have simple rules governing the replication and destruction of units. He began working on his model in 1968 and completed it in 1970. The October 1970 edition of the Scientific American presented Conway’s “game” to the world. Upon reception, he was quickly praised for the parallels that existed between his mathematical model and the concept of cellular automation.

Rules of Life

The simulation for Conway’s Game of Life itself is quite simple. There exists a 2D plane that wraps around on itself. This plane is home to cells that maintain two states — populated and unpopulated. Each cell has eight neighbor cells surrounding it. When running the simulation, there are three rules that govern the simulation:

1. Any populated cell with less than 2 neighbors is lonely and dies
2. Any populated cell with more than 3 neighbors becomes overpopulated and dies
3. Any unpopulated cell with 3 neighbors becomes populated

All other cells maintain their current state. The simulation begins in whatever state the user wants by populating or unpopulating various cells and initializing the game. Cells update at time-ticks set by the user with each tick counting as a generation. It can be an entertaining pastime — try it here.

Results

John Conway’s model included plenty of fundamental elements that many computational simulations need — a set of predefined rules, an initial state, multiple components that interact with each other, and data that can be extracted from the model.

A Pulsar Oscillator from the Game of Life

The data that resulted from running this simulation with different starting conditions led to the identification of many patterns that repeat themselves as time intervals passed. Some examples of these include what many people identify as oscillators and spaceships for their apparent movement patterns. There are also still lifes which remain static. The Game of Life is significant because it serves as a proof that complicated behavior is possible in a simple and recursive system. It is a mirror to our reality as understood by science where complicated life arose from recursive molecules that adhere to simple rules. Hence, the game emphasized early on that computers could be used as powerful tools to perform research and visualize data in a very powerful way.

Advancements

Today, computational simulations are often used for other fun projects in coordination with machine learning, such as OpenAI Plays Hide and Seek. The results are fascinating, and again emphasize the key components of computational simulations: predefined rules, an initial state, multiple interacting components, and output data. Macromoltek applies these principles to run computational simulations for a variety of projects in order to create viable antibody designs and accurately see how they interact with the human system.

Links and Citations:

1. Computer Simulation used to predict colliding shockwaves for Manhattan Project http://cms.sjtu.edu.cn/doc/reading/cms/

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