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<title>The Story of Life</title>
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<DIV ALIGN="center"><H2>The Story of "The Game of Life"</H2></DIV>
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<TD ALIGN="center"><IMG SRC="Conway.jpeg" WIDTH="91" HEIGHT="109" BORDER="0" ALT="John Conway"></TD>
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<TR><TD ALIGN="center">John Conway</TD></TR>
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<P>The Life simulation was developed in 1970 by the English mathematician John Horton Conway, a distinguished mathematician at the University of Cambridge. Conway became interested in a problem in group theory proposed by mathematician John Leech having to do with the symetry group of a particular dense packing of spheres in 24 dimensions. Conway found some remarkable properties and published the results in 1968. Conway was also interested in a problem presented in the 1940s by renowned mathematician John von Neumann. Von Neumann tried to find a hypothetical machine that could build copies of itself and succeeded when he found a mathematical model for such a machine with very complicated rules on a cartesian grid. Conway tried to simplify von Neumann's ideas and eventually succeeded. Coupling his previous success with Leech's problem in group theory with his interest in von Neuman's ideas concering self-replicating machines resulted in the Game of Life.</P>
<P>Originally, "acres of squared paper" (probably not literally) were used for the grid, "and he and his admiring entourage of graduate students shuffled poker chips, foreign coins, cowrie shells, Go stones or whatever", about the paper according to the rules for birth, death, and survival that Conway designed. </P>
<P>Conway showed the game to his friend Martin Gardner who described it in the October 1970 column which he wrote in Scientific American. The game became an instant success and Conway became a household name. The game is particularly suited to computer science students since it presents an informative challenge to optimize the coding of the basic algorithm in order to process the huge number of calculations that must be performed between succesive generations in the shortest possible time. It has often been claimed that since 1970 more computer time world-wide has been devoted to the Game of Life than any other single activity. Gardner wrote:</P>
"The game made Conway instantly famous, but it also opened up a whole new field of mathematical research, the field of cellular automata... Because of Life's analogies with the rise, fall and alterations of a society of living organisms, it belongs to a growing class of what are called "simulation games" - games that resemble real-life processes."
<P><STRONG>Rules of Life</STRONG><BR>
Conway chose his rules carefully, after a long period of experimentation, to meet three criteria:<BR>
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<LI>There should be no initial pattern for which there is a simple proof that the population can grow without limit. </LI>
<LI>There should be initial patterns that apparently do grow without limit.</LI>
<LI>There should be simple initial patterns that grow and change for a considerable period of time before coming to an end in the following possible ways:<BR>
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<LI TYPE="a">Fading away completely (from overcrowding or from becoming too sparse)</LI>
<LI TYPE="a">Settling into a stable configuration that remains unchanged thereafter, or entering an oscillating phase in which they repeat an endless cycle of two or more periods. </LI>
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<P>In other words, the rules should be such as to make the behavior of the population both interesting and unpredictable. </P>
<P>The rules are simple and elegant:<BR>
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<FONT COLOR="#0000FF"><LI>Any live cell with less than two neighbors dies of loneliness. </LI>
<LI>Any live cell with more than three neighbors dies of crowding. </LI>
<LI>Any dead cell with exactly three neighbors comes to life.</LI>
<LI>Any live cell with two or three neighbors lives, unchanged, to the next generation.</LI></FONT></OL></P>
<P>It is important to understand that all births and deaths occur simultaneously. Together they constitute a single generation or, we could call it, a "tick" in the complete "life history" of the initial configuration.</P>
<P><STRONG>The Game</STRONG><BR>
The basic idea of the "game" is to start with a simple configuration of living (organisms) which are placed on a 2D grid by various methods (e.g. see <a href="select.html" TARGET="main">Initial Cell Placement</a>), one to a cell. This constitues the first generation. Conway's "genetic laws" for births, deaths and survivals (the four rules above) are the applied to the pattern and the next generation pattern is placed accordingly. Generation by generation the "player(s)" observe the various patterns that emerge.</P>
<P><STRONG>Life Goes On... and on... and on...</STRONG><BR>
From an initial pattern of living cells on the grid, you will find, as the gerations tick by, the population constantly undergoing unusual, sometimes beautiful and always unexpected, change. In a few cases the society eventually dies out (all living cells vanishing), although this may not happen until after a great many generations. Most initial patterns either reach stable figures - Conway calls them "still lifes" - that cannot change or patterns that oscillate forever. Patterns with no initial symmetry tend to become symmetrical. Once this happens the symmetry cannot be lost, although it may increase in richness.</P>
<P>Conway originally 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 at the time. 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" (a configuration that repeatedly shoots out moving objects such as the "glider" or a "puffer train" (a configuration that moves but leaves behind a trail of "smoke"). The prize was won in November of the same year by a team from M.I.T. The initial configuration (shown below) 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.</P>
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<TD><IMG SRC="glider_gun.gif" WIDTH="349" HEIGHT="122" BORDER="0" ALT=""></TD>
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<TD ALIGN="center">An initial configuration for a glider gun</TD>
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