Conway's Game of Life

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What is Conway’s Game of Life?

Conway’s Game of Life is a cellular automaton, which is a mathematical model consisting of a grid of cells that can exist in different states. The game consists of a grid of cells, each of which can be either “alive” or “dead.” The cells’ states change over time according to a set of rules that depend on the states of their neighboring cells.

 

The rules of the game are as follows:

 

  1. Any live cell with fewer than two live neighbors dies, as if by underpopulation.

  2. Any live cell with two or three live neighbors lives on to the next generation.

  3. Any live cell with more than three live neighbors dies, as if by overpopulation.

  4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.

 

To visualize the game, a two-dimensional grid of cells is drawn. Each cell is either black (representing a dead cell) or white (representing a live cell). The initial pattern of cells is called the “seed.” From this seed, the game progresses in discrete time steps called “generations.” Each generation is created by applying the rules above to each cell in the grid simultaneously.

 

The game has no specific goal, and the patterns that emerge can be highly complex and unpredictable. Some patterns may oscillate or move across the grid, while others may grow or decay over time. The game has been studied extensively in mathematics, computer science, and other fields, and has been used to model various real-world phenomena, such as the growth of biological cells, the behavior of crowds, and the spread of diseases.

Implementation details

Conway’s Game of Life is inherently parallelizable because each cell’s state depends only on the state of its neighboring cells. This means that each cell can be updated independently of the others, making it a good candidate for parallel computing.

 

GPU computing takes advantage of the massive parallelism provided by modern graphics processing units (GPUs) to accelerate the Game of Life. GPUs have thousands of processing cores that can execute many instructions simultaneously, making them ideal for performing computations on large grids. In this approach, the grid is stored in the GPU’s memory, and each processing core updates a portion of the grid simultaneously.

 

This web demo of Conway’s Game of Life uses the GPU in your device to perform the simulation steps. In this implementation, each cell is represented by a pixel in an RGBA texture, where the pixels are either dead or alive. If a pixel has the value (R:1, G:1, B:1, A:1), it is considered alive, and all other values are considered dead.

 

A shader program is used to update the state of the cells in the grid. The shader assigns each core of the GPU to calculate the next state of a single cell. The new states are written to a temporary texture, and then copied over to the main texture representing the next generation.

 

In summary, the implementation of the Game of Life using an RGBA texture involves using a shader program on the GPU to update the state of each cell. The updated states are written to a temporary texture and then copied over to the main texture. This implementation allows for efficient parallel processing on the GPU and can handle large grids with many cells.