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No. 54: Nov-Dec 1987

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Fractals, fractals everywhere

Anyone who follows the popular scientific literature knows that fractals are now "in." Commonly employed to "explain" patterns in nature, fractals are, from a simplistic viewpoint, mathematical ways to predict the development of a growing structure, be it a crystalline mass, a plant, or the universe-as-a-whole.

Yes, the universe-as-a-whole, the clouds of stars and clusters of galaxies, may be mimicked by cellular automata (i.e., fractals). Imagine the universe as a cubical lattice, and start in one corner, adding one layer of cubes after another. Galaxy distribution could be simulated by using a rule telling us which of the added cubical cells had galaxies in them and which did not.

"The rule actually used supposes that the question whether each point in a newly added layer will (or will not) be occupied by a galaxy is mostly determined by the occupancy of the five nearest neighbors in the previous layer, but for good measure, there is a random variable to introduce an element of white noise to the system. To make the process a little more interesting, the determination whether a new site is occupied depends on whether a number characteristic of that site, and calculated by simple arithmetic from the corresponding number for the five nearest neighbors in the preceeding layer, exceeds an arbitrarily chosen number."

Comparing this fractal simulation with the observed universe is startling. The agreement is "spectacularly successful." (Maddox, John; "The Universe as a Fractal Structure," Nature, 329:195, 1987.)

Comment. In biology, too, fractal modelling can be very impressive. But, doesn't it all verge on numerology? The existence of a galaxy at a point in space is simply dependent on its neighbors; and the law of gravitation is not even mentioned. Are the physical laws that we usually assume as controlling the dynamics of matter now "hidden" beneath a more general property of the universe? One is reminded of R. Sheldrake's theory of morphic resonance, in which the mere existence of a certain structure makes it more easy for the same structure to be duplicated elsewhere in the universe!

From Science Frontiers #54, NOV-DEC 1987. 1987-2000 William R. Corliss

Science Frontiers Sourcebook Project Reviewed in:


  • "A sourcebook of unexplained phenomena is therefore a valuable addition to a collection of scientific literature. William R. Corliss has provided this in the past with his source books of scientific anomalies in several subjects, and now he has provided it for astronomy. He has done an excellent job of collecting and editing a large amount of material, taken in part from scientific journals and in part from scientific reporting in the popular or semi-scientific press." -- "The Mysterious Universe: A Handbook of Astronomical Anomalies", reviwed by Thomas Gold, Cornell University, in Icarus, vol.41, 1980

  • "An interesting, systematic presentation of unusual weather [..] This book is recommended for a general audience" --"Corliss, William R., Tornados, Dark Days, Anomalous Precipitation, and Related Weather Phenomena, Sourcebook Project, 1983.", revieweed in Choice, September 1983
  • "..the science is necessarily somewhat speculative, but Corliss's symthesis is based on reputable sources." -- "Corliss, William R. (Compiler). Lightning, Auroras, Nocturnal Lights, and Related Luminous Phenomena" reviwed by Joseph M. Moran, Univ. of Wisconsin in Science Books and Films, Sep/Oct 1983

  • "Before opening the book, I set certain standards that a volume which treads into dangerous grounds grounds like this must meet. The author scrupulously met, or even exceeded those standards. Each phenomenon is exhaustively documented, with references to scientific journals [..] and extensive quotations" -- "Book Review: The moon and planets: a catalog of astronomical anomalies", The Sourcebook Project, 1985., Corliss, W. R., Journal of the Royal Astronomical Society of Canada, Vol. 81, no. 1 (1987), p. 24., 02/1987