ISSN 0964-5640
And Innovative Computer Applications
Letters 4
Michael Barnsley Collectors Editions 5
Book Review: Frontiers of Scientific Visualisation John de Rivaz 6
Further Models of Gravitational lenses John Topham 7
Forty-one E. W. Shineman, Jr 15
More Amazing Number Arrangements John J. Schraub 15
Kaleidoscope Mal Lichenstein 16
Simulation of Smouldering of Paper Jean van Mourik 17
Migdal-Kadanoff and Ackerman Dual Recursions Roger Bagula 18
Fractals Without Chaos Yvan Bozzonetti 20
Fractal Report is published by Reeves Telecommunications Laboratories,
West Towan House, Porthtowan, Truro, Cornwall TR4 8AX, United Kingdom.
Volume 6 no 33 First published June 1994. ISSN 0964-5640.
Call for Papers
The article pile is nearly empty, so readers are requested to get their thinking caps on again. Remember that we now cover other unusual computer applications, not just fractals. (But no games, business applications etc.)
Graphics Issue of REC
Received just after issue 23 of Fractal Report went to press, REC 8,6 & 8,7 dated Dec 93, Jan/Feb 94 arrived.
This issue contained a large number of graphics and fractal items. Fractal feathers, Christmas Trees, Space Invaders, dynamic circles, "Time Tunnel", "Explosion", and "Sin Tema". The latter is a program written by an Argentinian that produces images described as colourful swirling galaxies on screen.
Of course there is also the usual mixture of mathematical puzzles, magic squares of numbers etc.
We have also received REC 8,8, dated April 1994. In the editorial, Dr Ecker mentions the end of Algorithm, trouble at Amygdala, and Fractal Report's attempts at remaining in publication by expanding its format. However he repeats his lifetime pledge to REC, but exhorts his readers to help as much as possible in getting new subscribers. He will continue even if REC drops to 100 subscribers.
Maybe he already does this, but I recommend getting a photocopier and printing himself. With a modern machine (less than five years old) it is much easier than in the days when Fractal Report started. As you only need print as many copies as you need, a circulation of 30 or even ten is still viable! (Provided you are still interested enough to spend the time.) Printing on double sized paper and folding down the middle gives a better presentation as well as halving the handling time.
Nothing of specific interest in the April issue otherwise - the big item is a "mystery program", a long listing which is some sort of patience problem, leaving the play to figure out what he is supposed to do. Various offers are provided to get the program on a disk. Typing it in and debugging it would be an impossible task. I did publish a program like this years ago for the Spectrum - don't ask for it, it is well and truly lost now - and got over this problem by making the program check itself against a checksum which revealed lines with errors. There was also an interesting article on the theory of e, the base for natural logarithms, and proving it to be irrational (in the mathematical sense.)
Cryonics In Latest TFTN
Roger Bagula published an article I wrote for him on the "outlaw science" of cryonic suspension in his Fractal Translight Newsletter. This was reduced down to one page and the border decorated by fractal doodles.
As well as many of Roger's own articles, the issue contained an article from Gary W. Adamson on a DNA Condon Karnaugh Map. The article did not contain an image, but it points the way to a lot of interesting visualisations, which may go a long way to searching for patterns in the genome. Also similar processes could be used to find "attractors" that indicate style in text.
The "own work" sections included a lot of comments like "What good does it to me if I can show the fractal probability density of particles under different symmetries in multiple dimensions if I am going to get spit in the face for it?" he end the article by saying "... a new way to see dimensionals in fractals has opened up a whole new area of fractal research." I must confess that I have know way of knowing whether these statements are justified, but I can certainly vouch that the images printed are different to others I have seen elsewhere.
Another article claims to draw an "electron simulation". It is very pretty, but whether it has any practical value, eg helping people to make room temperature superconductors, say, or really whether it represents an electron in a useful way I simply can't say.
Finally, if you would like to see Fractal Translight Newsletter there is now another way to get it rather than send money. Send an article! There is still an awful lot of Roger Bagula's own material in it, and if it is to be successful a newsletter has to have variety. Send your article to Roger Bagula Fractal Translight Newsletter 1759 Waterhill Road Lakeside CA92848 USA. (But only when you are sure you have enough work published in Fractal Report!!!)
His newsletter dated August is a special colour edition, featuring poetry, prose and innumerable fractal programs. The colour photocopying process actually improves colour dot matrix prints, as it removes the dottyness. The issue also includes another of my articles, this time on the "outlaw social science" of dating agencies, and how you can set one up all of your own in your local area.
However I have received a couple of communications which allege that Mr Bagula's articles are "incomprehensible gibberish". What do you think? Is it "The Emperor's New Clothes", or is there some validity in mixing various mathematical formulae to get new fractals? Letters will be published anonymously if you prefer, but it is reasoned argument rather than name calling that interests us.
Colorbox Pro
This is the latest from Iterated Systems Inc., and is a software development kit for DOS and Windows featuring fractal still image compression and decompression. It enables originators of applications to include resolution independent images with significantly smaller files.
Decompression does not require hardware, but compression relies on a card which comes with the kit.
Images can be decompressed to higher resolutions as clients upgrade their equipment. The software is therefore future proof.
The kit costs $2,995 and is obviously out of reach of individuals. However the likes of WordPerfect would find this trivial compared to the advantage of fractal compression and small graphics files in their applications.
Individuals can buy Images Inc which allows the compression and expansion of images in software, and costs a fraction under $400. I have never tried it, but imagine that increases in perceived resolution from video prints may be worthwhile. Maybe a reader who has it or could borrow it would like to write a fuller report. Iterated Systems Inc 5550-A Parchtree Parkway Suite 650 Norcross, GA 30092 USA.
Four Dimensional Ferns
Elsewhere in this issue is an advertisement for Dr Barnsley's books, in signed collectors' editions. His company Springsoft is also producing more recreational software, and the latest offering is to be a program that draws 4D ferns. My mind is boggling as to what these actually are. Ferns blowing in the wind, or growth "speed-up" animations? I have been promised a review copy, so watch for the review in future issues of Fractal Report.
His other company, the abovementioned Iterated Systems, is a separate entity from Springsoft. However I have suggested that one or other of them produce a DOS program that sharpens image files by fractal transformation.
I propose simple DOS program that is run by typing in
FFEXPAND [name of file, factor].
Thus, if you have a file "goose.tif" in your current directory, typing "FFEXPAND goose.tif 4" would result in the file "goose.tif" being re-saved four times as long with an apparent doubling in resolution. The program wouldn't actually produce compressed files, only sharper (and therefore bigger) files, and therefore shouldn't interfere with any other products. Such a program could be sold cheaply, or even as shareware, and should attract volume sales.
Two New Pickover Books
The publisher offers a 20% reduction and NO postage and handling if the books are ordered before 30 November 1994. They are published in a few months. You must clearly indicate "20% discount as advertised in the flyer" when ordering.
The Pattern Book: Fractals, Art, and Nature
Price Before discount: US$51/�38
Price After discount: US$41/�30
Pub Date: August 1994
From Mozambique, to Asia, to all the European countries, the contributors to The Pattern Book range from world-famous cancer researchers to little-known artists, to eclectic computer programmers. Some of the patterns are ultramodern, while others are centuries old. Many of the patterns are drawn from the universe of mathematics. Loads of strange fractals and computer recipes. Pickover, C. ed. World Scientific. ISBN 981-02-1426-X
Visualizing Biological Information
Price Before discount: US$64/�47
Price After discount: US$51/�38
Pub Date: June 1994
Topics: The use of computer graphics to find patterns in DNA and other information containing sequences in biology. Melodic representations of DNA. Unusual graphics of DNA sequences to help the human analyst gain insight and find patterns. Pickover, C. ed. World Scientific. ISBN 981-02-1427-8.
For orders:
World Scientific Publishing,
USA: 1060 Main Street, River Edge NJ 07661.
Fax 201-487-9656.
Tel 201-487-9655,
Toll Free: 800-227-7562.
Europe: 73, Lynton Mead, Totteridge, London N20 8DH UK.
Fax: 081-446-3356.
Tel: 081-446-2461.
You must clearly indicate the words "20% discount as advertised in flyer" on your order. Credit card number OK. Include expiration date and card number.
Frontiers of Scientific Visualisation
Frontiers of Scientific Visualization. Edited by C. Pickover and S. Tewksbury. Wiley: New York, 1994. Wiley-Interscience 605 Third Ave New York NY 10158-0012 USA, $34.95. Colour illustrations. ISBN 0-471-30972-9. Orders: 1 -800-Call-Wiley. Fax: 908-302-2300.
The book explores the art and science of making the unseen workings of nature visible.
Fluid flow, fractals, plant growth, genetic sequencing, the configuration of distant galaxies, virtual reality, artistic inspiration... these are a few of the many unseen phenomena, processes, events, and concepts that can be made visible through the power of modern computers -- including personal computers.
Chapter Titles:
Scientific Visualization of Fluid Flow
Visualization of Scroll Waves
Visualization of Chemical Gradients
Visualization of Biological Information Encoded in DNA
Visualizing Droplet Coalescence Phenomena
Computer Simulation of Plant Growth
Scientific Display: A Means of Reconciling Artists and Scientists Architecture and Applications of the Pixel Machine
Brave New Virtual Worlds
Exploring the art and science of making the unseen workings of nature VISIBLE ...
Fluid flows, fractals, plant growth, genetic sequencing, the configuration of distant galaxies, virtual reality, artistic inspiration ... these are a few of the many unseen phenomena, processes, events, and concepts that can be made visible through the power of modern computers including personal computers. Frontiers of Scientific Visualization explores the many ways in which computers are now used as tools for simulation, art, and discovery. It presents the most important recent work of some of the best minds in computer-visualization research. It also puts forth a vision of the future in which current limitations on computer graphics dissolve, opening great new frontiers, vast new landscapes of knowledge, creativity, and even entertainment that, today, remain unseen.
Many of the patterns provided in the book can be reproduced using a personal computer. Supplemented with a special 16-page insert of riveting colour computer-generated illustrations, this clear and accessible text will be of equal interest to the scientist and the artist, the mathematician and the video technician, the educator, the student, and the general reader interested in computer graphics.
CLIFFORD A PICKOVER is a research staff member at IBM's T. J. Watson Research Center in Yorktown Heights, New York. He is also the Associate Editor of Computers in Graphics, and an editorial board member of Computers in Physics and Speculations in Science & Technology. He is the author of Mazes for the Mind: Computers and the Unexpected and numerous other books on the blending of art and science.
STUART K. TEWKSBUBY (retired from AT&T Bell Laboratories) is a professor in the Department of Electrical and Computer Engineering at West Virginia University. He has written or edited several books dealing with the general interplay between advances in technologies and opportunities for new architectures and applications, and is Editor of the Journal of Microelectronic System Integration.
WILEY INTERSCIENCE John Wiley & Sons, Inc. Professional, Reference and Trade Group 605 Third Avenue New York N.Y. 10158-0012 USA
Journal of Chaos of Graphics
Dr Clifford Pickover's Journal of Chaos and Graphics is no longer in print, but he has kindly sent me a complete set and says that I can supply readers of Fractal Report with copies for a reasonable copying fee if anyone wants it. The total number of pages is 108 and therefore the cost would be the same as a volume of Fractal Report, ie �20 (cheque to RTL) or $34 (cheque to J. de Rivaz) anywhere. Copies will be made individually when time permits, so allow a week or so for delivery, please.
Many of the articles are of the "OOOH! look what I have done!" type rather than "Here is what I have done and here is how you can do it." as preferred by Fractal Report. Nevertheless, as with all of Dr Pickover's publications there is much to amuse interest and fascinate, and maybe provide ideas for future more explicit articles in Fractal Report.
Physics Courseware Communicator
This is a quarterly newsletter for physics teachers and those interested in physics software and hardware. The Winter 1944 issue features sonic ranging, a new method of analysing objects in motion that is said to be starting a revolution in physics education. Kits start from $75 and I would expect that they have more uses than mere physics education. A sonic ranger could turn a laptop into an electronic tape measure, for example. Imagine an estate agent using such a device to measure a house and print the sales details on the spot for the client to see.
There are articles on other subjects, such as "gophers" to burrow through Internet collecting specified information, an e-mail course on special relativity, software reviews, and low cost LCD displays for classrooms.
Physics Courseware Communicator is available from
Physics Courseware Evaluation Project Department of Physics North Carolina State University Raleigh NC 27695-8202 USA.
The cost is $35 ($15 USA) for four issues. It is of interest to physics teachers and also individuals interested in using their computers for physics experiments. Apple IIs, Macs and PCs are supported. Letters
From Mr Dick Oliver
re: Nonlinear Nonsense/Fractal Report
Thanks for your kind words about my newsletter in the last issue of yours. I'll return the favour (because your newsletter is worthy of mention, not because you mentioned mine) in my next issue.
Some of the facts about my offerings were a bit mixed-up, but most of them weren't off the mark far enough to warrant any correction. One detail I would ask you to print a correction to, though: Polyray is not "Cedar's latest," but a ray-tracer written by Alexander Enzmann and included by permission in my recent book, Tricks of the Graphics Gurus. I don't want Xander thinking that I'm claiming to have written his program!
For your information (no printed correction needed unless you feel one is necessary), the following statements were also inaccurate:
"The Fall issue for 1993 features the Windows version of FractalVision. This is available both in disk and CD versions."
Actually, the Windows version comes with both floppy disk and CD.
"The CD version costs only $29, or $44 if you send for an instruction and user manual published by Sams."
Actually, the $29 version comes with both floppy & CD, and includes a 56-page instruction and user manual. The $44 version is the same, but with a 550-page book instead of the 56-page one.
"The disk version costs $39 with the book."
It's the DOS version which costs $39 with the book. The DOS version does have a disk, but so does the Windows version. " The book includes a chapter on programming. . . but apart from this, all the other information in the book is on the CD."
None of the text of the book is on the CD. What the newsletter states is that all the information from the DOS version of the book is also in the Windows version of the book, with the addition of the programming chapter and CD.
"Also in the fall issue is a 'how to' with Povray listing from the Sams book Tips of the Graphics Gurus ..."
The listing is for Polyray, not POV-ray, and the book is entitled Tricks of the Graphics Gurus.
Your review showed me that I need to find a way to make the variety of product options in my newsletter much more clear! In any case, thanks again for the review and best of luck with Fractal Report and your other endeavours.
Cedar Software Pleasant Valley Road Wolcott VT 05680 U.S.A.
Voice:802-888-5275 Fax: 802-888-3009
From Mr John Horner
Frac'cetera subscribers also complain bitterly about the lack of time. I often wonder if the root problem is that the relationship between man's activities and the day length and his lifespan have been distorted as he develops more ways of occupying himself. Early man had a very limited choice when it came to deciding how he would spend his time. Nowadays just the opposite is true.
Frac'cetera 10 promises to be on time, and I've made serious inroads into my correspondence.
On the Bozzonetti disk some of the formulae had line breaks in them, stopping them from running. It may be worth publishing this fact, as not everyone will know how to fix the broken formulae.
[Frac'cetera Le Mont Ardaine Rue des Ardaines St Peters Guernsey GY 9EU CI]
Music Mandala
The more retentive readers may recall a brief mention of this program in the last issue.
Unfortunately I grew less enthusiastic about it as I played with it. I had hoped that it could produce different kinds of music by fiddling with the controls, but a lot of what it produced just wasn't musical. The settings provided by the manufacturers did produce a sort of Eurovision instantly likeable quickly boring result, hence my initial enthusiasm.
Its algorithm produced music on the sound card (set up via Windows) whilst drawing patterns on the screen, hence the name. If you try and break out of the program a message reveals that it was written in BASIC, presumably compiled. (Not VisualBasic.) However even on a 20MHz 386/7 it did not run unbearably slow for a Windows programme.
The control panel was well set out with very intuitive and logical control. You could even change some settings as the music runs.
It is also possible to have the pattern completely fill the screen, but if in your enthusiasm not to read the instructions (supplied on disk only) you don't know how to escape, then you will probably have to "reset" out to stop it!
Newtronic, 62b Manor Avenue, London SE4 1TE. (�31 req Windows. Atari ST version also available).
Maybe some more musically minded reader will buy it and send in his/her opinions in a review article or letter.
Book review:
Frontiers of Scientific Visualisation
Pickover & Tewksbury (editors)
by John de Rivaz
I have to review this book in the light of its usefulness to readers of Fractal Report, and these are defined by self selection as people who want to do things on their own computers. From this standpoint it will be a disappointment to many, as there is very little that one can immediately implement. However it is a "frontiers" book and therefore it is looking at the cutting edge of the subject. People are often unwilling to give too much away in such situations, either for personal, contractual or corporate reasons. The book follows the usual Pickover formula, of a number of long articles by different authors.
The chapter that most interested me was the one on visualising DNA sequences, as although I don't know a lot about this (well, vanishingly little really) I do understand the importance of the subject. DNA is organised as a sequence of four different chemicals, or nucleotides, (A,G,C,T), therefore it can be represented in a space of five directions (also confusingly known as "dimensions"), one for each of the chemicals and one for position along the chain. The writers of this chapter propose a visualisation model as a curve in five directions, a,b,c,d,e. If the first nucleotide is an A we move along the a-axis by one unit. In order to increment the position, we move along the e axis by one unit. Thus the point is 1,0,0,0,1. If the next nucleotide is T we move along the d axis by one unit and the e axis by another unit and the next point is 1,0,0,1,2. The curve can then be projected into two dimensions by the computer. As a wiggly line the result is hardly stunning graphics, but they do claim it to be of value.
I would suggest that the field is still wide open for other visualisation techniques to be discovered!
The chapter on simulation of tree development may also appear by title to be of interest to Fractal Report readers. Indeed it will, if you are interested in the theory behind plant growth simulation. But if you are looking for something to try, then look elsewhere. Another chapter is entitled Scientific Display: A Means of Reconciling Artists and Scientists. This introduces and discusses many interesting ideas, but again doesn't have anything for the reader to do. (Although most of you will have done some of the things discussed via articles in Fractal Report.)
There is some coverage of virtual reality, and it is very well presented and interesting to read. However in "real reality" it may be some years before individuals can afford the equipment required to carry out meaningful experiments.
One of the uses of virtual reality techniques is in presenting information to operators of equipment.
I was particular impressed with a mention of the fact that in presenting data to equipment operators, whether they be surgeons or pilots, one had to be aware of the possibility of sensory overload. This is often overlooked, I fear, even in domestic equipment. Lots of knobs, buttons, lights and dials may impress techies, but they put off many potential customers, particularly amongst the more conservative elderly class. The latter have more time and money to buy and use such products, if they can be motivated. An operator can be in an environment where (s)he is just coping with a high level of sensory input, and after a while will develop health problems because of this overload. (eg migraines, sick building syndrome, ME etc.) This doesn't have to be electronic input, an environment such as a stock or commodity exchange provides the problem. Indeed, in the domestic environment excessive input (baby, animals, telephone, door bells all at once) sensory overload can occur. Note that the latter two items are technical in origin. Do we need more?
The VR chapter suggested that future telephones will have a "presence" control, which ranges from "off" to "full". The former is obvious, the latter is where a full VR simulation of the caller is provided, as if they were in the same room. In between steps would include text only (modem), fax, voice, ordinary picture. This is vaguely similar to my "Virtual Travel" idea, (see Electronics World and Wireless World May 1994 page 420, also in Venturist Monthly News and Inventors Report.)
As with all books edited by Dr Pickover, Frontiers of Scientific Visualisation gives you plenty to think about. As I said, it may give you less to do than some of his others, but that will vary with the ability and perseverance of the reader. It is published by John Wiley and Sons Inc 1 Wiley Drive Somerset New Jersey 08875-1272 USA at $34.95, ISBN 0-471-30972-9.
by Yvan Bozzonetti
The first property of fractals is the scale invariant peculiarity of these objects. Whatever the magnification you impose, there is always something new to see. To be sure, computers have their own limit and we can use arbitrairy large magnification on a software such Fractint. Neverthless, this limitation has nothing to do with the true nature of fractals.
In mathematical therm, fractals are an illustration of spaces without metric, the mathematical tool defining distance. The scale invariance property come with chaos, and there is a common view than fractals need in some way a chaotic system. The Mandelbrot set is the simplest and most known example of this situation: It is the chaotic display of the iterated second degree equation.
In quantum physics there is always a metric (defined as the integral of the squarre of a complex function, a difficulty without interest here). So, we can assume there is no quantum chaos, something true but difficult to demonstrate. Without chaos, there must be no quantum fractal and this is the common idea.
Now, in exploring the near endless worlds of Fractint I have seen many time some display or even mini mandelbrot bordered by a set of spike boundaries. At each new color the number of spikes was doubling without end. As far as I have zoomed in these screens, I have never seen the true chaotic limit. They seem to be "quasi fractals" with only an endless set of period doubling never turning to chaos and so true scale invariance. neverthless, the mini mand produced in this way looked perfectly normal and so, chaotic.
What may be the usefulness of that observation? Think for example about nonlinear optics: A photon can be absorbed and its energy split between two new photns with correlated wave functions. Mineral converters generate 2, 4 or 8 photons from a single one. Organic dyes can produce up to 128 or 256 correlated photons. At this level we can think of the radiative medium as a quasi fractal quantum space.
Now, masseless photons are by far the simplest particle to handle, so any quantum property starts to display itself in a photonic system. If we have quasi fractal quant-um space for the photon, the same thing must be true for any material particle. The scale invariance of fractals, even limited by quasi fractal states, would bring to us at any chosen scale the quantum properties of our choice. If, for example, the nuclear force radius of action could be extended 30 times, a simple electric arc in a magnetic field would start a controled fusiou process.
Looking at fractint may, after all, bring interesting ideas with potential applications. If you are prone to lost your time at looking for fractals, please store any example of quasi fractals and tell me about your findings, I am interested in such pictures.
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