book cover 1st edition


"One Metaphor Fits All" :
A Fractal Voyage With Conway's Audioactive Decay


This is chapter 7 from "FRACTAL HORIZONS: The Future Use of Fractals", by Clifford Pickover, editor, St. Martins Press, 1996

Reproduced by Henry Bottomley with permission
Copyright 1994 Mario Hilgemeier

Part 1 Part 2

Fractals seem to provide a unifying metaphor for many phenomena in science, art, management and other disciplines. In this chapter, an informal collection of essays, I will show some structural similarities between DNA, the weather, robots and plants using "audioactive decay" as an example. The topic of aesthetics is also discussed. Finally, fractals are presented as a stage in the evolution of mathematical models of reality.


Page 1:
Audioactive decay explained

Page 2:
Circular diagram of evolving audioactive decay (Gleichniszahlenreihe)
Similarity to L-systems
From chaos to robots
Two faces of intelligence
DNA and protein folding
Nearly infinite paradise of images
Traveling the ocean
Art unlimited & return of Pythagoreans
Models and metaphors
A look beyond the event horizon
Pseudocodes: Tree-generating L-System ; Abundance computation ; Conversion of GZR to "time-series"
References


Have a look at chapter 4 of "FRACTAL HORIZONS: The Future Use of Fractals", by Clifford Pickover, editor, St. Martins Press, 1996.
J.C.Sprott, The Computer Artist and Art Critic
Strange attractors - dimension and Lyapunov exponent as measure of aesthetics

Proof of Conway's lost cosmological theorem, a TeX article by Shalosh B. Ekhad, 1997-08-21

Theres more on the net about the Maple package accompanying the above paper: HORTON modification by Doron Zeilberger, which can also be found at the ETH, Zurich

Conway's Constant, an article by Eric W. Weisstein in the online CRC Concise Encyclopedia of Mathematics

Another page on Conway's Constant 1.30... Gives the polynomial of which it is the largest zero (plus references and links).

Torsten Sillke's index of Martin Gardner's book with further references, 1998-04-22, gives several German journal references.

essays page

Also Henry Bottomley's Look and Say Java Script, Evolution of Conway's Elements and Seven Complete Orderings



Reproduced by Henry Bottomley with permission
Copyright 1993-1999 Mario Hilgemeier, email: contact
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These three web pages reproduced by Henry Bottomley with permission:
Extract from e-mail from Dr Mario Hilgemeier to Henry Bottomley 16 August 1999:
"You may want to copy from my website what you need, since it will probably go down this September ... If you wish (and include the Copyright info) you may even publish my "Fractal Voyage" chapter (on your public website only).

Henry Bottomley's Look and Say Java Script, Evolution of Conway's Elements and Seven Complete Orderings