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

© Copyright 1994 Mario Hilgemeier

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.

Figure (7.)1

Audioactive decay explained
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

Tree-generating L-System
Abundance computation
Conversion of GZR to "time-series"

Pointers to other media

Conway's elements
Numerical interpretation of the GZR

Partial map of fractal land and adjacent countries
Lengths of the iterates of the GZR
The first stages in the development of the "1"
"Development scheme" of Conways elements
Abundances of Conway's elements, ordered by element number
Abundances of Conway's elements, ordered by magnitude
The tree-generating L-system described in the text
GZR(49) interpreted as time-series
Conway's element 4Be as "protein"
Cipher abundances in iterates of the GZR

Circular diagram of iterated audioactive decay (Gleichniszahlenreihe)

Self-similarity of GZR at beginning and end shown by a Taiwanese study. Enables immediate computation without iteration (July 2005).

Henry Bottomley provides

Hilgemeier's Likeness Sequence, from The Teacher Handbook, an introductory exploration on how to do mathematics research (2003).

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

There is 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

FAQ on copyright and publication rights

© Copyright 1994-2005 Mario Hilgemeier, email: contact
homepage stylized apple