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"

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
homepage stylized apple blossom



Legal Conditions for Publication or Storage

Thanks for your request of publication rights for copyrighted material (CM) of Dr. Mario Hilgemeier. CM means texts, graphics, sounds, music, data and other media. CM also means codes from which media can be generated.

Depending on the intended usage, publication rights are subject to the following conditions:

Dr. Mario Hilgemeier must be notified of the usage in written form (email or surface mail is sufficient, postal address below). You have to ask before you use any copyrighted material. If Dr. Mario Hilgemeier does not answer within four weeks you may consider the publication rights temporarily granted.
"Temporarily granted" in this document means for one year at maximum and one instance - only for the use you asked for. This publication rights can be withdrawn by Dr. Mario Hilgemeier at any time. Publication rights end on the next January 31 after they have been granted if not contracted otherwise (That is, one year at maximum for temporarily granted publication rights).
In case of withdrawal of publication rights Dr. Mario Hilgemeier will try to notify you via the email address you gave. In any case it is your responsibility to check each year in January if the CM you use is still free. If you cannot contact Dr. Mario Hilgemeier via email you have to use the surface mail address.

If you use copyrighted material without notification you infringe the copyright (with all consequences).


If you want to include the CM in a printed scientific publication (e.g. journal, preprint etc) the rights are given for one instance only - namely your request, provided that you cite correctly "Copyright [year] by Dr. Mario Hilgemeier, [URL]" [insert the appropriate]. In this case, Dr. Mario Hilgemeier would appreciate a copy. Please send it to his postal address.
If you cannot send surface mail for any reason, I'd still like to have a short synopsis of the publication via email for reference purposes (e.g. journal name, name(s) of author(s), article title, one-paragraph summary, date of publication, page)


HTML hint (for newbies only): You can link directly to the CM in question: For a picture just put something like this in your HTML code
<IMG SRC=""> otherwise you can use a normal anchor; for example
<A HREF="">Human Population Growth</A>. Please send Dr. Mario Hilgemeier your URL, even if you only link, Dr. Mario Hilgemeier might backlink eventually.

If you want to include physical bitwise copies of CM on your public(!) site (instead of linking directly via URL) because of speed or performance reasons the publication right is temporarily granted, provided you send Dr. Mario Hilgemeier the URL of every site where you use this CM. If Dr. Mario Hilgemeier does not hear from you, he assumes that you do not accept this condition, and that you will not publish CM in any wise. Non-public sites: see commercial use below.
This also applies to collections of HTML-pages or the information contained therein within databases, for instance, but not limited to, online databases or compact disks (CDs). Databases are considered commercial. If you want to include CM in a database, see commercial use below.


If you want to use CM for course material, reports, presentations etc in schools, universities or other educational organizations that are accessible for the general public: see scientific use above.
Not included in educational use are non-public educational institutions, e.g. private schools, company colleges and the like. When in doubt if this is the case for your institution, see commercial use below.


If you want to use CM for anything outside narrow limits defined above, i.e. something you make money from, or when in doubt, please contact Dr. Mario Hilgemeier via email. Examples for commercial use are

Commercial use is not limited to these examples.
Publicly(!) available search engines (e.g. Altavista, Lycos, Yahoo etc) are considered educational.

Respect copyright - encourage creativity

Dr. Mario Hilgemeier

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