| Game: Rule 110 |
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Created by W. D. Troyka, 2003-01-25
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5 variants
Educational
Solitaire
download 34 K
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Rule 110 is a cellular automaton, similar to John Conway's Game of Life, which has been scripted by Karl Scherer (Alive and Alive_Auto), as well as by Robert Price (Game of Life). Rule 110 has recently gained attention as a result of a book written by Stephen Wolfram, known in mathematics circles as the author of the software program Mathematica. The book, called a New Kind of Science, suggests that both space and time can be modeled by cellular automata such that a relatively simple set of rules governing the content of a cell might lead to the actual complexity that we experience in the physical world. A cell in this case would be a discrete unit of space, itself spread into discrete units along a time axis, with rules governing its transition from one state to another based on the properties of neighboring cells.
As an example of how simple rules governing cellular automata can lead to complex structures, Wolfram analyzes the basic cellular automata created on a square grid when the rule governing the color of a square (white or black) depends solely on the colors of the three squares above to the northwest, north, and northeast. There are eight possible combinations of colors for these three squares. Because each of these combinations can be defined as causing the cell under consideration to be either white or black, there are a total of 256 (2 to the 8th) possible rules.
Most of these rules do not lead to interesting results. Rule 110, however, if applied to a sufficiently large graph, begins to generate complex irregular structures that do not appear to be predictable from the input row -- the top row of the graph -- or the rule governing coloring. Rule 110 states that a cell remains white if the three squares above are all white, all black, or black-white-white. Otherwise it is colored black. Wolfram purports to show that Rule 110 is a universal computer because it can emulate a universal Turing Machine. (The Turing Machine has also been coded by Karl Scherer). This means that any calculation capable of being performed by any mechanical method, i.e., on any computer, can be performed with Rule 110 using a suitably chosen input row and sufficiently long graph, with the output appearing in a designated bottom row.
This rules file allows you to run iterations of Rule 110, or any of the other 255 rules, with any chosen input row. The graphs come in sizes 10x10, 25x25, 50x50, 80x80, and 100x100. The larger graphs may take several seconds to load. This script departs from the technical definition of Rule 110 because the rows are considered to wrap around the horizontal edges. If you run the default setting once, you will get a technically correct Rule 110 graph through one iteration. For most rules and input rows, however, the first iteration will involve some wraparound effect. Subsequent iterations are always affected. The wraparound is a necessary compromise to make the graph presentable for a large number of rows. The graph also wraps around from bottom to top in successive iterations. This does not affect the accuracy of the rules but merely replaces older rows with newer ones.
For details on how to use this program, please consult the strategy section under the Help menu. |
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