The Game of Life is a cellular automaton. It was devised by the British mathematician John Horton Conway in 1970. It is the best-known example of a cellular automaton. The "game" is a two-dimensional zero-player game, meaning that its evolution is determined by its initial state, requiring no further input from humans. Each cell of the automaton has two states, "alive" or "dead". The program reads an initial configuration and displays how it evolves.
Here is a YouTube video of Dr. Conway’s invention of the game:
Originally, Conway played the Game of Life on a Go Board, but we will code it using Object – Oriented Principles. 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, alive or dead. Every cell interacts with its eight neighbors, which are the cells that are horizontally, vertically, or diagonally adjacent. This is called a Moore neighborhood.
For the Conway Cell, the flow of the game is that at each generation, for each cell, the number of live neighbors is counted. The following transitions occur:
- Any live cell with fewer than two live neighbors dies, as if caused by under-population.
- Any live cell with two or three live neighbors lives on to the next generation.
- Any live cell with more than three live neighbors dies, as if by overcrowding.
- Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
The initial pattern constitutes the seed of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed—births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a tick (in other words, each generation is a pure function of the preceding one). The rules continue to be applied repeatedly to create further generations.
First, we will build a program to create a file containing the initial pattern. It will be called PatternMaker, and will create text files with one pattern at a time for the grid of 45 rows and 78 columns. It will begin by filling the 2_D grid with '.', which means that the cell is dead. Then code an initial pattern of live cells by placing ‘*’ in those cells. Create a text file, naming it something descriptive, like “bar.txt” or “cross.txt.” The first line of the file will be the number of rows and the number of columns in the grid, with a space in between (45 78). Then write out the grid. This file will provide the initial pattern for your Game of Life.
These are other cell models that we will use:
I. The Fredkin Cell was developed by Edward Fredkin, a physicist at Carnegie Mellon University. It is a replicator where a cell survives or is born if there is an odd number of neighbors. Under this ruleset, every pattern self-replicates; furthermore, every pattern will eventually produce an arbitrary number of copies of itself, all arbitrarily far away from each other. Instead of the Moore neighborhood, it uses the Von Neumann neighborhood, which consists of four directions: up, down, right, and left. The rules are:
- A dead cell becomes a live cell if 1 or 3 neighbors are alive.
- A live cell becomes a dead cell if 0, 2, or 4 neighbors are alive.
- Otherwise, the cell stays the same.
II. The Modified Fredkin Cell also keeps track of the age of the cell. The rules are the same as for the Fredkin cell, except that if a cell survives to the next generation twice, it becomes a live Conway cell. All of the Conway rules apply to that cell.
III. The Seeds Cell is in the same family as the Game of Life, initially investigated by Brian Silverman and named by Mirek Wójtowicz. In Game of Life terminology, a pattern in which all cells that were on turn off at each step is called a phoenix. Nearly every pattern in Seeds explodes into a chaotic mess that grows to cover the entire universe. The rules are:
- A dead cell becomes a live cell if exactly 2 neighbors are alive.
- All other cells become dead.
We will model these five cells using the abstract class LifeCell, below. The Conway Cell, the Fredkin Cell, and the Seeds Cell all derive from the Life Cell. The Modified Fredkin Cell derives from the Fredkin Cell. Do some research. Either select a different Cell type and Rules or create one yourself. This last one will be selection 5.
In main, reset the window size to its largest size for your screen.
Create an array of LifeCell pointers, and create objects of each kind of derived class. Then set the addresses of the derived objects into the pointers
This sets up the polymorphic array. Display information that introduces the game of Life (probably using a function). Next, open a do-while or while loop for the user to play repeatedly. Describe the different cells to the user and ask the user to choose a Cell Type. Show the user a menu of patterns and ask the user to choose an initial pattern. Set the pattern into the cell type object chosen by the user.
Open another do-while or while loop that will set the game in motion and roll the generations forward. Call the derived class object through the base class array pointer to access the class method:
