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CoveringtheTerrain of Cellular Automata By Colin Fields
from The Inquirer
Cover ing the Ter r ain of Cellular Automata
By Colin Fields
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Introduction
In the abstract world of mathematics and computation, there exists a branch of knowledge devoted to studying what is called cellular automata. Cellular automata are defined as discrete rewriting mathematical systems that change in time and space over a grid of cells. Simply put, a cellular automaton (singular form) is the structure created when a specific rule set is applied to a sequence of binary values (e.g.,1s and 0s, black and white, dot and dash, etc.). Sometimes the rules create stable, repeating structures, and other times the results are chaotic. In some cases, cellular automata show that a simple set of starting nodes, when acted on by a few conditions, can lead to extremely complex results.
ATwoStepsBack Cellular Automaton
Histor y of Cellular Automata Even though the basic ideas behind cellular automata are simple, a major study of their properties did not begin until the 1950s. The ideas behind the cellular automata that we know today were largely discovered through the work of John von Neumann, one of the most prolific mathematicians of the 20th century. Back then, he was working on a mathematical model of self-reproduction in biology, which led him to the idea of a self-reproducing binary set. Likewise, Stanislaw Ulam, a mathematician and nuclear physicist who worked with von Neumann at the Los Alamos National Laboratory, studied crystal growth and also discovered many of theunderlying principlesof cellular automata.
At the end of the 1950s, cellular automata began to be thought of in terms of parallel computers. Parallel computing is a method of computation where multiple processes can be executed at the same time and, thus, ?in parallel.? In 1968, John Conway, an English mathematician, did experiments on a PDP-7computer with cellular automata. Then, in 1970, he came up with a set of rules titled ?The Game of Life,? one of the most famous examples of cellular automata. An intense effort has gone into finding specific initial conditions that when applied to his rules generateinteresting patterns. The rules of The Game of Life are the following: (1) Any live cell with two or three live neighbors survives to the next generation; (2) Any dead cell with three live neighbors becomes a live cell in the next generation; and (3) All other live cells die in the next generation, and, similarly, all other dead cellsstay dead.
Generation 0 Generation 78
In 1981, Stephen Wolfram independently began working in the field of cellular automata, specifically studying one-dimensional cellular automata, also known as elementary cellular automata. The rules of elementary cellular automataare defined in asingle row of binary values, not amultidimensional structure.
One-Dimensional Cellular Automaton
Applications of Cellular Automata Many applications of cellular automata can be found in the natural sciences. For example, certain types of cellular automata have been created to model neurons, and even behaviors like learning can be demonstrated. Other examples are found in the worlds of music and video game design, with the application of procedural music generation for the former and procedural terrain generation for the latter. Multitudes of applications can also be found in physics, computer science, and chemistry. For instance, in video game design, procedural generation of levels and landscape can be a problem. Fortunately, with cellular automata, game designers can automatically generate thousands of levels with landscapes based off of cellular automatapatterns. Overall, cellular automatons may be one of the most fundamental building blocks in the universe, and it may help explain some of the most profound questions about nature.
Cellular Automata Terrain
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