62 lines
3.1 KiB
Plaintext
62 lines
3.1 KiB
Plaintext
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A Noah's Ark Program - by Rudy Rucker.
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From "The Journal of Chaos and Graphics", #3, p.18.
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Dr. Rudy Rucker is author of Infinity and the Mind (Bantam:New
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York, 1982). He is also the author of the 57th Franz Kafka,
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Software, White Light, and Spacetime Donuts (published by Ace
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Books). He can also be reached at the Dept. of Mathematics and
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Computer Science, San Jose State University 95192.
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Today, there are several scientific fields devoted to
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the study of how complicated behavior can arise in systems
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from simple rules and how minute changes in the input of a
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nonlinear system can lead to a large difference in the output;
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such fields include chaos and cellular automata theory.
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"Cellular automata" are a class of simple mathematical systems
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which are becoming important as models for physical processes.
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Usually cellular automata consists of a grid of cells -- and
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the cell's life or death is determined by a mathematical
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analysis of the occupancy of neighbour cells. One popular set
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of rules set forth in what has become known as the game of
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"LIFE". Though the rules governing the creation of cellular
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automata are simple, the patterns they produce are very
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complicated and sometimes seem almost random, like a turbulent
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fluid flow or the output of a cryptographic system.
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The figure on the next page (of the original article)
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was a screen dump of some output from a simple assembly
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language program which runs one-dimentional cellular automata.
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The rule depicted is what is called rule 46 according
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to the notation in the appendices of Steven Wolfram (Theory
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and Applications of Cellular Automata). Instead of using
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graphics capability, my program produces images
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"typographically", using blanks for zeros and solid squares
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(ASCII code DBh) for ones. The pattern starts with a line of
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zeros with a single one.
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In general, a r-2, n-2,1-D CA pattern like this is
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updated according to a rule where a cell C looks at it's left
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neighbor L and right neighbout C to get a three -digit binary
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number LCR. LCR can range through the eight values v from 000
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to 111. The rule depicted is based on the lookup table
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00101110, where the update for value v is the vth lookup value
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from the right. In decimal, the lookup table is number 46.
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What makes this picture interesting is the handling of
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the boundry condition. As it is costumary, we use "cyclic
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boundry conditions", meaning that the rightmost cell is
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regarded as the cell left of the leftmost cell, But in this
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run, I set the leftmost cell always to 0. In effect, the space
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is like a tin can that has a seam running down it.
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The seam acts as a generator that pulses out
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alternating leopard and elephants. The neat thing is that
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these animals then shuffle and mutate to produce giraffes,
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dinosaurs, etc.
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For Further Reading
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1. Peterson, I. (1987) Forest fires, barnacles, and trickling
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oil. Science News. 132:220-221.
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2. Poundstone, W. (1985) The Recursive Universe. William
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Morrow and Company, New York.
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3. Wolfram, S. (1983) Statistical mechanics of cellular
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automata. Rev. Modern Physics. 55,601-644.
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