# Conway Game of Life the Term Paper

#### Excerpt from Term Paper :

This leads to problems when the active area encroaches on the border of the array. Programmers have used several strategies to address these problems. The simplest strategy is simply to assume that every cell outside the array is dead. This is easy to program, but leads to inaccurate results when the active area crosses the boundary. A more sophisticated trick is to consider the left and right edges of the field to be stitched together and the top and bottom edges also. The result is that active areas that move across a field edge reappear at the opposite edge. Inaccuracy can still result if the pattern grows too large, but at least there are no pathological edge effects. Techniques of dynamic storage allocation may also be used, creating ever-larger arrays to hold growing patterns. Alternatively, the programmer may abandon the notion of representing the Life field with a two-dimensional array, and use a different data structure, like a vector of coordinate pairs representing live cells. This approach allows the pattern to move about the field unhindered, as long as the population does not exceed the size of the live-coordinate array. The drawback is that counting live neighbors becomes a search operation, slowing down simulation speed. With more sophisticated data structures this problem can also be largely solved.

Implementation and Software Issue

Most initial patterns which Conway calls still-life (patterns that oscillate forever) either reach stable figures. Patterns with no initial symmetry tend to become symmetrical. Once this happens the symmetry cannot be lost, although it may increase in richness. Conway conjectured that no pattern can grow without limit. Put another way, any configuration with a finite number of counters cannot grow beyond a finite upper limit to the number of counters on the field. This was probably the deepest and most difficult question posed by the game. Conway offered a prize of \$50 to the first person who could prove or disprove the conjecture before the end of 1970. One way to disprove it would be to discover patterns that keep adding counters to the field: a "gun" or a "puffer train." The prize was won in November of the same year by a team from M.I.T. The initial configuration grows into such a gun, emitting the first glider on the 40th generation. The gun emits a new glider every 30th generation from then on.

Summary

In 1970, John Conway published his "Game of Life." It is meant to represent living cells. The system supposes that new life arises near a group of existing individuals of a lifeform, if there is enough room left. In to heavily crowded areas or areas not crowded enough, life dies. Game of Life is a two-dimensional with some very simple rules. These rules concern the birth, survival and death of the artificial creatures that roam the two-dimensional.

The result of these simple rules is astonishing. Starting from a certain pattern, there is no easy way to predict whether a pattern ultimately will perish or remain in existence. The behavior of this system is again chaotic: adding one point can make the difference between dying and staying alive for an infinitely large pattern.

References

Bosch, R. (n.d). Constraint Programming and Hybrid Formulations for Three Life Designs. Retrieved July 5, 2005, from mat.gsia.cmu.edu Web site: http://mat.gsia.cmu.edu/LIFE/cpaior.ps

Gardner, M. (2002). Mathematical Games. Retrieved July 5, 2005, from ddi.cs.uni-potsdam.de Web site: http://ddi.cs.uni-potsdam.de/HyFISCH/Produzieren/lis_projekt/proj_gamelife/ConwayScientificAmerican.htm

Koblitz, D. (1997). Artificial Life. Retrieved July 5, 2005, from Alife

Web site: http://www.sra.uni-hannover.de/forschung/koblitz/alife-1.htm

Matthews, J. (2004). Conway's Game of Life Project. Retrieved July 5, 2005, from Generation 5 Web site: http://www.generation5.org/content/2000/life.asp

Thomas, R. (2002). Games, Life and the Game of Life. Retrieved July 5, 2005, from Plus Magazine Web site: http://plus.maths.org/issue20/features/conway/

Game of Life. (2005). Retrieved July 5, 2005, from Achim Flammenkamp Web site: http://wwwhomes.uni-bielefeld.de/achim/gol.html

It's the name of the game. (1998). Retrieved July 5, 2005, from John Saeger Web site: http://www.whimsey.com/Life.html

The Game of Life. (2000). Retrieved July 5, 2005, from www.reed.eduWeb site: http://www.reed.edu/~paramors/science/gamelife.html

The Game of Life. (n.d). Retrieved July 5, 2005, from kleinesysterne.de

Web site: http://www.kleinesysteme.de/game_help.html

Virtual Life. (n.d). Retrieved July 5, 2005, from users.pandora.be Web site: http://users.pandora.be/tijs.vermeulen/english/TELAI/cell_aut_virt_life.html

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