Term Paper on "Conway Game of Life"

Term Paper 4 pages (1479 words) Sources: 1+

[EXCERPT] . . . .

Conway Game of Life

The Game of Life (or simply Life) is, briefly, a two-dimensional cellular automata universe governed by a simple set of birth, death and survival rules. It was invented in 1970 by the Cambridge mathematician John Horton Conway. It was publicized by his friend Martin Gardner in his column in the October 1970 edition of "Scientific American." It has been claimed that since 1970, more computer time worldwide has been devoted to the Game of Life than any other single activity.

Each of the cells in the two-dimensional universe can be in one of two states: alive or dead. Beginning with any given initial pattern of live cells, one can employ Conway's rules in order to determine the behavior of the universe over any number of generations or time steps. Whether a cell survives, dies or comes into being is determined by the number of live neighbors the cell has. Each cell has eight possible neighbors (four on its sides, four on its corners). The rules for survival, death and birth are as follows:

Survival: if a live cell has two or three live neighbors, it survives.

Death: if a live cell has less than two or more than three live neighbors, it dies.

Birth: if a dead cell has exactly three live neighbors, it is born.

When one employs these rules to any given initial pattern of live cells, the results can be startling. Complex behavior consisting of various life forms, composed of several or more living cells, often occurs.

Background

John Conway choose the rules carefully after trying many other possibilities, some of which caused the cells to die too fast and others which caused too many cells to be born. Life balances these tendencies, making it hard to tell whether a pattern will die out completely, form a stable population, or grow forever.

Life is just one example of a cellular automaton, which is any system in which rules are applied to cells and their neighbors in a regular grid.

There has been much recent interest in cellular automata, a field of mathematical research. Life is one of the simplest cellular automata to have been studied, but many others have been invented, often to simulate systems in the real world.

In addition to the original rules, Life can be played on other kinds of grids with more complex patterns. There are rules for playing on hexagons arranged in a honeycomb pattern, and games where cells can have more than two states. Life is probably the most often programmed computer game in existence.

Purpose

Conway's Game of Life is a kind of simulation environment; its lifelike nature captures people's attention, and although imitating life wasn't really the goal, in a way, finding artificial life was.

Algorithms

The earliest results in the Game of Life were obtained without the use of computers. The simplest still-life and oscillators were discovered while tracking the fates of various small starting configurations using graph paper, blackboards, physical game boards and pieces, and the like.

During this early research, Conway discovered that the R-pentomino failed to stabilize in a small number of generations.

These discoveries inspired computer programmers the world over to write programs to track the evolution of Life patterns. Most of the early algorithms were very similar. They represented Life patterns as two-dimensional arrays in computer memory. Typically two arrays are used, one to hold the current generation and one in which to calculate its successor. Often 0 and 1 represent dead and live cells, respectively. A double loop considers each element of the current array in turn, counting the live neighbors of each cell to decide whether the corresponding element of the successor array should be 0 or 1. At the end of this process, the contents of the successor array are moved to the current array, the successor array is cleared, and the current array is displayed.

A variety of minor enhancements to this basic scheme are possible, and there are many ways to save unnecessary computation. A cell that did not change at the last time step, and none of whose neighbors changed, is guaranteed not to change at the current time step as well, so a program that keeps track of which areas are active can save time by not updating the inactive zones. In principle, the Life field is infinite, but computers have finite memory, and usually array sizes must be declared in… READ MORE

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