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Off Topic » in reply to Is there really any chaos in the game of life?

Conway’s Game of Life is the starting point
Gary — (archived)

alcaray said:

>From a given start, one and only one outcome can be calculated.
>Everything is precisely pre-ordained by starting conditions.

This is correct. Conway’s Game of Life is the starting point in trying analyze the hyperspherical surface causation problem. Years ago, I wrote a life game in assembly language (there's nothing to it). There's a 2-D matrix of say 100x100 cells. At every time step the cells are raster scanned. If a cell is occupied then a simple rule is invoked concerning whether the cell's occupant reproduces, lives or dies based upon the state of adjoining cells. This model is obviously causation driven because it is time stepped and then raster scanned to test each cell. A computer model of a hyperspherical surface driven by chaos can not be time stepped or use any sort of synchronous raster scan. Instead there would have to be a stream of random numbers passing through each cell. As new numbers appeared in each cell, a test would be performed concerning the cell's value in relation to the values of adjoining cells. Rules such as those used in Conway’s Game of Life would be applied to the cell. One of the rules would have to be if a given condition was satisfied then the cell ceased to be suceptible to chaos (the random number stream). In essence, I'm proposing a hybrid of Conway’s Game of Life with a Monte Carlo simulation.

This would actually be a fun little project to code up. The algorithmn would be very sensitive to the model's dimensionality. The random number generator would have to be absolutely clean of pattern forming or fractals, e.g. the digits of Pi would do the trick. One would have to play around with cell rules in order to get the model to do interesting things. Hopefully, setting a particulat set of rules would cause a "Big Bang" inside the compute. The simulation of that universe would only last a few trillionths of a femtosecond until all the cells in the computational hypercube were filled up by the expanding hypersphere. The trickiest problem would be imaging the surface of the growing hypersphere onto the computer stream. I'd have to start the problem as a 3-D cube to get my feet wet and then go to a hypercube. This could keep me busy for a couple of years. Too bad there's no money to do a fun project like this.

Gary

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