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| 19th May 2002 | STEPHEN WOLFRAM AND CELLULAR AUTOMATA REVISITED |
Brian Grainger |
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'Is this man bigger than Newton and Darwin', screamed the headline in the Science section of the newspaper this week. That's a pretty tough reputation to live up to. They were talking about Stephen Wolfram, who founded the company that marketed Mathematica, which he also wrote. The guy has a high opinion of himself as well. He did not take his 'A' levels because they were too trivial; left university and did not take his first degree because it was not challenging enough; did not want to submit the ideas of his latest book to peer review because he believed they would be thrown out as they opposed the prevailing opinions. I read the article about his book and then did a web search on his name. There were LOTS of entries. It strikes me this guy knows how to market himself and the book, irrespective of whether he is right. But why am I writing about it? Well, his idea is that the universe is controlled by simple rules, rather than mathematical equations as is the conventional thought. However, what got me interested was that the rules he talks of are the rules of cellular automata. In the article I read it was almost as if he had invented these things himself. He has appeared to do a lot of work in the field, but this was a subject that was all the rage when the first age of personal computing, the Commodore PET, was around. In those days there was a program doing the rounds called the Game of Life. It was not really a game. It was a concept that a Cambridge academic, John Conway, was working on. Starting with a chequerboard pattern, (some squares occupied and some not), and some rules of how to determine the contents of a square in the next generation based on the contents of the neighbouring squares on the current generation, Conway and others investigated the effects of various starting patterns and rules. What they found was the rules of Life created a wide variety of interesting patterns. Some led to a stable state and some didn't. Some patterns oscillated between 2 or more states. Some patterns moved. Intriguingly, some patterns appeared to 'generate' new stable shapes continuously, as if giving life to new objects. This was interesting to us computer owners because the computer was the ideal tool to generate the patterns and see how they changed in each generation. One drawback was that the time taken to create each generation could be quite long, especially if the chequerboard was large. In those days computers were not as powerful as now. I have often wondered why we have not heard more of this work now that we have much more powerful computers. Perhaps now that Stephen Wolfram has put his head above the parapet we are going to. The game of Life is a two dimensional cellular automata. Wolfram has been looking at one dimensional automata. In this scenario you start with a line of squares. The contents of a new line below is determined by applying the rules to the contents of the line above. As you extend the lines downward a pattern can emerge. Wolfram has found that some patterns that can be seen in nature can be generated from appropriate rules. He appears to be arguing, therefore, that all patterns in nature are made up from simple rules. To me, this seems to be arguing that the fact some animals are dogs implies all animals are dogs. Even a non mathematician can pick the holes in that one! Never mind - a bit of controversy should help sales of the book along. Whatever Wolfram's views it is clear that beautiful patterns can be created. A simple example can be created by the following rule: A square in a succeeding line is blank ONLY IF the squares directly above and to the above left and above right are blank. Otherwise the square is filled.
With this rule you can form a pyramid starting from a single occupied square.
This is obviously a simple example but quite beautiful patterns are found with other rules. You might like to dust down your programming skills and get your computer to produce the patterns from the rules you define. However, I guess it is more likely that you will not bother and just look what other people have done. Here is a list of web sites to investigate the world of cellular automata, in particular, Life: http://www.argentum.freeserve.co.uk/life.htm On the first of these site you will find many other links. The last deals with cellular automata in general and is run by the man behind AutoCAD, John Walker. |
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