## "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

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

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* © Copyright 1994-2005
Mario Hilgemeier, email: contact
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