ISSN 0964-5640
And Innovative Computer Applications
Amgia Program Malcolm Lichenstein 5
Letters 6
Extraterrestial Messages in Our Genes Dr Clifford Pickover 8
A Plotter Hidden in Your Printer Roger Castle-Smith 13
Magic Figures Paul Gailiunas 19
Koan music - A unique new type of music 21
Astronomy with Computers Yvan Bozzonetti 23
International Workshop on Information Processing in Cells and Tissues Ray Paton 24
Skyglobe Mark A. Haney 25
Across My Dreams With Nets Of Wonder G.T. Swain 26
Roger Bagula's Listings Roger Bagula 28
Generating Fractals with Hardware in Real Time Tom Holroyd 31
All at the Press of a Button... Chrissie Loveday 32
Fractal Report is published by Reeves Telecommunications Laboratories,
West Towan House, Porthtowan, Truro, Cornwall TR4 8AX, United Kingdom. CompuServe 100431,3127
Volume 7 no 37 First published March 1995. ISSN 0964-5640.
Editorial
The self similarity of Fractals has claimed a few more "burn-outs" as renewal time came up. However now I have my own photocopying facilities it is possible to maintain a low level of circulation without any economic pressures. Many thanks to all those who took the trouble to write in saying that they no longer propose to subscribe, as opposed to just not subscribing.
New subscribers often take advantage of the bulk rate to buy all back numbers, and this also helps Fractal Report to remain solvent.
Announcements
News of Contemporaries
Can you speak Romanian? If so then you'll want to support this quarterly Fractal newsletter in that language. Fractalia is a 24 page newsletter edited by Marius-F Danca with stiff covers printed in blue and white with the inside in black and white, held together with staples and a PVC tape spine. Presentation is very professional. Some of the articles had programs, some did not. Many of the programs were in BASIC although a few were in C. June 1994 had many familiar fractals, including Sierpinski, Pitagorici, Rossler. The September issue covered cellular automata, 3D Mandelbrots, fractal mountains, and more. I don't suppose it will be long before we see some original work from this group. As far as I can gather it is distributed free at the present time.
Address: Marius_F Danca CP 524 Cluj-Naponca 9 Romania.
[Thanks to Dr Mandelbrot for pointing this group to us.]
I don't know whether Roger Bangula's name originates in Romania, but his newsletter is still being produced. Whatever anyone may say about his mathematical ideas or habits of bombarding people with mail and then chiding them for not replying, there can be no argument that his programs produce many new and interesting patterns that are sure to interest artists and programmers alike. Although they are written for the Amiga, they are easily translatable into other machine formats.
I think that it is a great pity that Roger doesn't get onto electronic mail, as he clearly has a need to tell others of his work which isn't being fulfilled by the ordinary post. The amount of money he must spend mailing this to me would surely pay his subscription!
I wrote (what I consider to be a dreadful) little story, combining a new fractal set with Hitler, God, the meaning of life and everything, that (wearing my hat as editor) I decided not to publish in Fractal Report. As there are stories in FTL and Roger sent me one (about cryonics) I decided to send him mine to see if he would dare publish it. If you want to see how bad a fiction writer I am, you'll have to subscribe and see if he prints it!
Fractal Translight Newsletter
- March 1995
The colourful ink jet cover of The Fractal Translight Newsletter for March 1995 is the best I have seen yet.
The editorial is in Roger Bagula's usual controversial style - this time his editorial looks at History education, making pertinent Orwellian points.
Inside there are cartoons, mathematical speculations and numerous articles and programs in Amiga BASIC, but this is easily translatable to PC BASICS. There are many programs to type in.
If you have seen earlier examples you may have been put off by the poor quality of print and the difficulty of typing in the programs therefrom. This seems to be a thing of the past now.
Subjects covered include:
Discovery of a new prime number distribution formula based on lnln(n) and the hyperbola
Harmonic fractal series approximation
Why Fractals and Chaos really are Outlaw science (by Dick Oliver) Cantor Dimensional Spectrum
Non ideal Dual Riemann Projections
Supercalculus transform
General van Koch fractal
... and more - stories, music art and poetry.
[Fractal Translight Newsletter $20/yr ($50 overseas) from R.L. Baugula 11759, Waterhill Road Lakeside CA 92949 USA]
More Fractal Compression
It has been said that if you buy a hammer, the shop doesn't expect a royalty every time you knock in a nail. Software toolmakers thought differently, but the trend is now firmly away from that sort of legal mumbo jumbo. The latest firm to give up royalties on the use of tools is Iterated Systems, makers of the fractal image compression system used on Compact Disks such as Microsoft's Encarta. People interested in using their software in products are now invited to apply to enter into a partnership scheme, which enables them to use a logo "Genuine Fractal Quality" together with an iterated fern, without any recurring costs.
However the latest range of products for developers don't come cheap - prices range from �2000 to �6500, and the fact that VAT is on top is more likely to be a cash flow problem that an outright expenditure to anyone contemplating buying them. However they will be invaluable to makers of CD ROMs and other multimedia products. The new �4,000 compression board is the fastest ever by a factor of seven, and will "daisy chain" images for producers with large volumes of images for processing.
The company are aware of the need to get the "FIF" compression standard more well known, and are encouraging software producers to include fractal compression in their products. Lotus SmarText is the first product, a desk top publishing system, to display the fern logo and incorporate the system.
Iterated Systems Ltd. Wyvols Court Swallowfield Reading Berks RG7 1PY United Kingdom
Dr Timothy Leary Writes Chaos Book
CHAOS & CYBER CULTURE
by Thmothy Leary, Ph.D.
"The '9Os are here and the doctor is in" - William Gibson
"Yes, he's back. At 72, the ex-Harvard professor who encouraged a generation to "turn on, tune in, and drop out" now counts himself as a cyberpunk. "The PC is the LSD of the 199Os, he says." - Time Magazine
Timothy Leary, the visionary Harvard psychologist who became a guru of the '60s counterculture, has reemerged as an icon if the new-edge cyber culture, a new breed that combines high-technology, art, music, psychedelics, and multimedia to revolutionize communication.
Cliaos & Cyber Culture is Dr. Leary's "cyberpunk manifesto." Here he explores the relationship between the eternal philosophy of Chaos and the future of cutting-edge technology, covering everything from quantum physics to LSD, from cyberpunks to the Woodstock generation, from guerrilla art to virtual reality to high-tech paganism. "This book is a romp through history from Aquaria to Cyberia," wntes actress Susan Sarandon.
Leary's most important book since the 1960s, Chaos & Cyber Culture brings together his provocative, futuristic writings, lively interviews and cogent conversations wfth a variety of writers and celebrities-Winona Ryder, David Byrne, William Gibson, and William S. Burroughs. The focus throughout is on the emergence of a new humanism with an emphasis on questioning authority, independent thinking, individual creativity, and the empowerment of computer and brain technologies.
Chaos & Cyber Culture includes more than a hundred striking illustrations - paintings, drawings, digital art, collages, photographs, icons, and archival materials-from Andy Fritz, Carolyn Ferris, Brummbaer, and other well-known guerilla artists. The book features an innovative design inspired by Wired, Mondo 2000, Boing Boing, and other "zines." Designed by Judy July to appeal to Generation X, this nonlinear layout addresses the question, "Why can't a book be more like a mag?"
Sample chapters include:
Counter Culture traces the evolution of underground culture from the beats and hippies to the cyberpunks and techno-artists, and includes a conversation with Winona Ryder;
Cybernetics discusses artificial intelligence, artificial reality, and the use of technology to empower consciousness and independence. It contains a revealing interview with leading cyberpunk author William Gibson;
Info-Chemicals and Drug Wars examines the failings of the War on Drugs and the reemergence of the intelligent use of psychoactive drugs;
De-Animation/Re-Animation explores death, cryonics, and soul preservation;
Screens is about using new media for personal empowerment and to subvert authority;
Guerrilla Art about the iconoclastic aesthetics of Keith Haring, William S. Burroughs, and Robert Williams, includes a conversation with David Bryne;
Millenium Madness reveals the threat of fundamentalism and monotheism and the emergence of high-tech paganism and digital pdytheism.
CHAOS & CYBER CULTURE
By Timothy Leary, Ph.D.
$19.95 Original Trade Paperback. ISBN: 0-917171-77-1.
8 1/2 x 11. 292 pages. 100+ illustrations, directory, index.
Ronin Publishing. Distributed by
Publishers Group West,
4065, Hillis Street,
Emeryville,
CA 94608
U. S. A.
Individual orders accepted by distributor if your bookshop won't get it.
Visa, MasterCard accepted, no foreign (to USA) cheques. Airmail at cost.
Fax Orders (00) (510) 548-7326
California residents must add sales tax.
Interactive paper available on disk
Chaos, Fractals, and the Semantics of Paradox
Patrick Grim and Gary Mar
Group for Logic & Formal Semantics
Dept. of Philosophy
SUNY at Stony Brook
The disk includes paged text with hypertext footnotes and references, color illustrations in GIF format and buttons which activate .exe files illustrating points in the text regarding paradox, chaos, and fractal organization.
This paper developed from presentations given at the Association for Symbolic Logic meetings at Carnegie Mellon, January 1991, and the joint American Philosophical Association and Association for Symbolic Logic meetings in San Francisco, March, 1991. An earlier form was also available on videotape. Closely related work has appeared in print as Gary Mar and Patrick Grim, "Pattern and Chaos: New Images in the Semantics of Paradox, Nous 25 (1991), 659-694, and Patrick Grim, Self-Reference and Chaos in Fuzzy Logic, IEEE Transactions on Fuzzy Systems 1 (1991), 237-253. See also Patrick Grim, Gary Mar, Matt Neiger, and Paul St. Denis, Self-Reference and Paradox in Two and Three Dimensions, Computers and Graphics 17 (1993), 237-253. Ian Stewart's Mathematical Recreations column on this work appears as A Partially True Story in Scientific American 268, No. 2, February 1993.
The disk operates in DOS on any IBM or clone, although it is of course faster on a 486. Although a mouse is recommended, TAB and ENTER keys can also be used to activate all features.
The paper is not available in a down-loadable format. If you owuld like to be sent a copy of the disk, please send an e-mail message to that effect, with your standard mailing address, to [email protected].
Or write:
Patrick N. Grim Philosophy State University of New York at Stony Brook Stony Brook NY 11795-3750 USA. There is no charge for the disk.
From Mr Michael Batty:
Colleagues may be interested in the following book that has just been published
Michael Batty and Paul Longley (1994) Fractal Cities, Academic Press, London and San Diego, CA: price $49.95 (ISBN 0-12-455570-5) hardcover
From the publishers description:
Fractal Cities is a pioneering study of the development and use of fractal geometry for understanding and planning the physical form of cities, showing how this geometry enables cities to be simulated through computer graphics. It shows how cities evolve and grow in ways that at first sight appear irregular, but which, when understood in terms of fractals, illustrate an underlying order that reveals their complexity and diversity.
The book contains sixteen pages of stunning computer graphics and explanations of how to construct them, as well as new insights into the complexity of social systems. The authors provide an intelligible and gentle introduction to fractal geometry as well as an exciting visual understanding of the form of cities, thus providing one of the best introductions to fractal geometry available for non-mathematicians and social scientists.
Fractal Cities can be used as a text for courses on geographic information systems, urban geography, regional science and fractal geometry. Planners and architects will also find that there are many aspects of fractal geometry in this book relevant to their own interests. Furthermore, those involved in fractals and chaos, computer graphics and systems theory will find important methods and examples which are germane to
their work.
Michael Batty is Director of the National Center for Geographic Information and Analysis in the State University of New York at Buffalo and Paul Longley is Reader in Geography at the University of Bristol
From Mr Arturo (Alex) Thompson
I've spent the last two years working on a project with the Geology dept. at the University of Arizona as a way of gaining an understanding of Fractals and Chaos. In parallel with this research on the fractal dimention of crystal formation we conducted a self course in chaos using the book Chaos and Fractals. I can not remember the authors (there are three) but they were from the Skandinavian countries. Much of the material is of little value but much is very important for any attempt at real orignal research. If you do not excell at mathematics it may be good to ally yourself with someone who is. I presonally am not very good at it.
There was an article published in either Forbes or Inc. abot two years ago that lookaed at the development chaos as a tool in economics. It is mostly a lay person write up and concluded on a somewhat sour note as to the value of chaos in the work of economists.
As for myself I still have not managed to figure out a good framework for using the theory. I am a history/poli. sci. type and do think it would be of inordinate value in modeling but it is still very underdeveloped in my field.
I do have a friend at Biosphere 2 who is working with individuals at the Santa Fe Institute on environmental modelling. I think that this may also be a good resource. There have been numerous articles on the use of chaos driven modeling being used in eco. applicatins. There may be a very nice overlay between that work and complex social modeling.
As a last note my specific areas of intrest are the social history of the American South to about 1968, and revolutionary political activity in secessionist movements.
Feel free to mail me.
PS I am interested in gathering together all acedemics and others looking into this area. Any ideas on a good way to go about it besides just random posting?
-Arturo (Alex) Thompson
University of Arizona, Tucson, Arizona, USA
(People without access to email may send letters as text files on disk to Fractal Report. The contents of the disk will be forwarded by email. If you want your disk back please include an SAE.)
A unique new type of music
Good music has traditionally been thought of as being pre-composed and completely pre-defined. Not so with Koan music. Koan music is created for you as you listen to it or have it playing. It will ebb and flow just like real music too, and this is because of the novel way we have designed it.
Koan music is unique in its approach. For instance, the most commonly used method to create generated music was developed by Mozart. He created a system of automatic composition which required the use of a fairly large set of (generally short) musical phrases of a fixed length. He would roll a dice to determine in which order he should string them together. The result was generally quite reasonable, but fairly limited in expression. Koan Plus does not use the rolled dice principle at all to create its music.
Koan pieces instead can use over 80 specially designed variable controls which influence its music. The values of these controls are written into the Koan piece by its author, who created it with Koan Pro, and they change the notes and melodies played in many special ways. They are what allow the creation of music that it smooth, non-intrusive, and natural sounding. When you play back a Koan piece it interprets all the special information the author has crafted into the piece - there and then, just for you.
The closest analogy to the Koan products is that of an Aeolian harp, where the wind plucks its strings in an uncertain and changing manner, thus producing quite ethereal music. Koan music can be ethereal or more down to earth, depending on what the author wants. Another comparison we would make of the Koan products would be that they could be seen as the aural equivalent of a log fire - and we all know how entrancing and calming it is to look into a glowing, burning fire.
PC Requirements:
Minimum (for non-rhythmic pieces - 5 included)
386 DX 33MHz PC
2Mb RAM
DOS 3.0 or later
Windows 3.1
Mouse
3.5" 1.44Mb floppy drive for installation
2Mb free hard disk space
A PC sound card/MIDI interface with an
installed Windows MIDI driver
Strongly Recommended (for all pieces - 10 in total)
486 33MHz PC (or greater)
4Mb RAM
DOS 5.0
Windows 3.1
Mouse
3.5" 1.44Mb floppy drive for installation
3Mb free hard disk space
PC soundcard/ MIDI interface with MIDI Mapper support and with the best quality sound synthesizer - Wavetable or LA
Included:
Koan Plus software, 10 Koan pieces and 10 MIDI files, provided on a 3.5" HD floppy disk.
10 studio mastered mood music tracks, recorded whilst saving the Koan pieces output to the MIDI files above, provided on audio CD - plus a free bonus audio track.
Price information:
Koan Plus is retailing at �34.99 and Koan Pro (which is expected to be available in Jan 1995) will be �116.32.
Note: Your software license covers you for all personal use of Koan Plus. However, Non-attended live playing of Koan Plus software or its use for broadcast purposes requires a separate license. Please contact SSEYO for further information.
Koan, SSEYO and the SSEYO Logo are all trademarks of SSEYO Ltd. Other products mentioned may be trademarks or registered trademarks of their respective manufacturers. Specifications may change without notice. Copyright 1994 SSEYO Ltd. All rights reserved.
UK and Republic of Ireland Distributor details:
Koch Media
East Street
Farnham
Surrey GU9 7XX
UK
Tel: 01252 714240
Fax: 01252 711121
For product availability elsewhere contact:
SSEYO Ltd, PO Box 29, Beaconsfield, Bucks, United Kingdom HP9 1EB Tel: +44 (0)1494 671257 Fax: +44 (0)1494 671258
Internet: [email protected]
Compuserve: 100317,302
Koan Pro advance information - 11th Jan 1995.
Koan Pro is a powerful and fun to use Authoring System that allows you to create ever-changing ambient music, be it swirling ambient sounds or more techno in feel. It is visual, easy to navigate and does not require you to have a musical keyboard. Through visual manipulation of the on-screen controls you can create you own Koan pieces. The music these pieces generate when played through the Koan Music Engine (KME) can be used as the basis for the musical content of any number of music or multimedia projects. The Koan pieces you create can also be shipped to others having the Koan Plus player for them to hear and enjoy.
It allows you to play play your .SKD files, the file format in which you create the pieces. These files can be saved in encrypted .SKP format for release to people with the Koan PLus Player. However, Koan Pro cannot play .SKP files, nor does it have an album facility - if you want these then you need to order the player as well.
Creating a Koan piece is straightforward and involves changing a number of parameters you can see on screen. Many of these can real time changeable meaning your changes will take effect as soon as the KME can accomodate them. You can fix some of these parameters throughout the piece, others are defined as envelopes which can provide a varying setting throughout the length of your piece - this is very important for capturing a freshness and subtlety.
Koan Music Engine (KME)
All pieces created with the Koan Authoring
System (Koan Pro) are interpreted and composed in real time by the KME. Whenever a piece is played it can be different. Koan music can also sound very natural and expressive and each piece tends to have its own character. The KME has been designed to be flexible and so does not limit itself to pre-defined style based music, making it ideal for ambient music.
There are over 80 parameters allowing you to do some of the following:
* Control Volume, Pan, Tempo, Velocities and Velocity spreads via envelopes
* Determine the general length of phrases for each voice
* Select the frequency and frequency range of the notes played
* Mutate musical phrases played
* Repeat bars of music played, and choose how far back you can do this
* Select from different voice types, eg. Ambient, Rhythmic, Fixed Pattern or Repeat Bar
* Assign musical rules like Scale, Harmony, Next Note and Rhythm and create your own values for these rules, too
* Set the tempo and metre of the piece
* For Ambient voices set in milliseconds the durations and gaps over which they will play
* Each parameter support lists, where the piece can choose from different values when it starts
* Randomly change the patch(instrument) a voice is playing during the piece
* Select the MIDI channel you want the voice to play on, or leave it up to the KME
* Allow your pieces to play back WAV files, stored externally or even used from a CD ROM
* Define in your piece and auto-load Creative Labs AWE32 SoundFont banks
* Support for GS/ GM
* Controllers like Reverb/ Chorus/ Portamento/Sostenuto/Expression/ Damper/ Softness
* Controllers for SCC1 of Attack/ Decay/ Release
* Create pieces lasting from 1 second to nearly 9 hours
* Automatically change Scale roots during a piece, if required
* Create demo pieces that will stop playing after a pre-determined time
* Import and Export bars from/to MIDI files to use these fragments as seed phrases/pattern used by the piece
* Patterns can be randomly selected during piece playback from a defined list of patterns
* Add pieces notes for others to see when they load your pieces
Other features
* Koan Music Engine with API that can be used for screensavers and games
* A grid to enter/modify any patterns used by your piece, and ability to change them in real time
* Save your Koan pieces is an encrypted Koan Play format (.SKP) so that people with Koan Plus can play them
* Record your Koan piece output to MIDI file
* Draggable piece time marker, position it where you want in your piece
* A set of envelope tools to allow you to make quick changes to the envelopes
* Fast forward/ rewind through your piece as it plays
* Comes with a number of templates
* Full on-line help
Who is it for?
Koan Pro is a creativity tool for the Multimedia user, be they musician or someone with no musical experience - no musical keyboard is required. It is a tool that people may very well find useful to create background music content, as well as experimenting with music creation in general.
Koan Pro is expected to be available in March 95 and a demo version should be available shortly after.
Koan, SSEYO and the SSEYO Logo are all trademarks of SSEYO Ltd. Other products mentioned may be trademarks or registered trademarks of their respective manufacturers. Specifications may change without notice. (c) Copyright 1994 SSEYO Ltd. All rights reserved.
PC Requirements
Strongly Recommended
* 486 33MHz PC (or greater)
* 4Mb RAM
* DOS 5.0 or greater
* Windows 3.1
* Mouse
* 3.5" 1.44Mb floppy drive for installation
* 3Mb free hard disk space
* PC soundcard/ MIDI interface with MIDI Mapper support and with the best quality sound synthesizer - Wavetable or LA
by Yvan Bozzonetti
I think it would be interesting to split the price of a telescope night between some amateurs. The system is usable by single person, astronomy clubs and universities. An informal club seems to me the best solution even if all members are not in the same town or country.
If there are many readers interested, a page in Fractal Report could be devoted to this activity.
First, I think some basic knowledge about CCD pictures are in order. Raw pictures are rarely interesting, they need to be processed. I have some software to do that such MIPS or Hidden Images, so I can process some data for me or anybody interested, the result can be sent on diskette or directly by telephone with a fast modem. My own system accepts a 14400 bauds rate.
CCD images have many defects but they can be corrected because the signal is a linear function of the light received, this is not the case with ordinary photography.
The first picture to take is a so-called flat field, a short exposure of the twilight sky or a white screen evenly illuminated. The flat field allows to discover dead pixels (giving no output) and sensibility differences between pixels ( up to 20 %). It is best to take at least three flat fields and average them. If they are taken on a screen, the telescope must be displaced between each of them.
Next is the dark frame, a black picture with zero time exposure. It reveals both the hot pixels giving a signal even without input and the reading noise of the system. Because the full array is not discharged instantly, there is a finite exposure time for all pixels beyond the first. Thermal noise builds up in them.
Third, there must be some dark frames with the same exposure time than the planned picture. More than one dark frame is often necessary for each picture, so that the averaged one contains less noise. These frames allow us to take into account the effect of thermal noise on each pixel. Modern CCDs have less sensitivity to thermal effects, so the use of these frame is less essential now compared to some years ago. One every two hours may be sufficient.
Finally, the picture is taken. For a colour exposure, three pictures must be taken with coloured filters. A colour six minutes exposure may well need 45 minutes to complete all stages.
The advantage in buying a full night comes from the economy of scale at the level of the flat field and short dark frames. Longer dark frames remains useful to get a good correction of the residual thermal noise.
I think the first picture may need up to one hour of work and the last in the night end only 15 minutes. This demonstrate the value of dividing the starting costs between many users.
One picture may be useful for more than one person, If twenty pictures are taken, each with three buyers, each buyer pays only $600/60 = $10.
Many scientific activities need some continuity in the work, for example the variable stars observation. If one person must pay half a night for 30 minutes of real data collection, it is not feasible. In the framework of an user groups it looks very different.Second Call for Papers
Information Processing in Cells and Tissues
Liverpool 6th - 8th September 1995
The purpose of this workshop is to bring together a multidisciplinary group of scientists working in the general area of modelling cells and tissues. A central theme will be the nature of biological information and the ways it is processed in cells and tissues. We hope that the workshop will draw together researchers from a range of disciplines including: Computer Science, Cell Biology, Mathematics, Physiology, Biophysics, Experimental Medicine, Biochemistry, Electronic Engineering and Biotechnology.
The workshop is intended to provide a forum to report research, discuss emerging topics and gain new insights into information processing in biological and computational systems.
Subjects areas are likely to include but not be restricted to:
* Cellular information processing systems
* Enzyme networks, Gene networks, Metabolic channeling
* Second messenger systems
* Signal Transduction and Cellular Pattern Recognition
* Automata models
* Parallel Distributed Processing models
* Cellular Automata models
* Single Neuron Computation
* Biomolecular computing
* Inter-cellular communication, Multi-cellularity
* Information Processing in Developmental Systems
* Information Processing in Immune networks
* Endocrine-immune-nervous interactions
* Information processing in neural tissue systems
* Information processing in non-neural tissue systems
* Communication and gap-junctions
* Asynchronous processing, MIMD, SIMD and NIMD systems
* Cell and tissues oscillators
* Fractals and Chaos
* Emergent phenomena and self-organisation
Programme Committee
Georg Brabant Endocrinology (Hanover)
Michael Conrad Computer Science (Detroit)
Roy Cuthbertson Cell Biology (Liverpool)
Claus Emmeche Philosophy of Nature and Science Studies (Copenhagen)
Mike Holcombe Computer Science (Sheffield)
George Kampis Ethology and Philosophy of Science (Budapest)
Hans-Paul Schwefel Computer Science (Dortmund)
Idan Segev Neurobiology (Jerusalem)
Gordon Shepherd Neurobiology (Yale)
W Richard Stark Mathematics (Tampa)
Rene Thomas Molecular Biology (Brussels)
Chris Tofts Computer Science (Manchester)
John Tucker Computer Science (Swansea)
G Rickey Welch Biological Sciences (New Orleans)
Gershom Zajicek Experimental Medicine and Cancer Research (Jerusalem)
Organizing Committee
Ray Paton, Roy Cuthbertson, Mike Holcombe and 'Trina Houghton
Sponsors
GPT
Unilever
Submission Details
All authors must submit 4 copies of the full technical paper by mail or delivery service to:
Ray Paton
Department of Computer Science
The University of Liverpool
Liverpool L69 3BX
UK
Please do not submit papers by fax.
The paper should be in English, double-spaced in 12 point using Times or similar font. The paper should be a maximum of 16 pages including the first page.
The first page must contain: title of the paper, author's names including affiliations, complete mailing address, telephone and FAX numbers, email address, and a 250 word (maximum) abstract.
Important Dates
Submission deadline: Friday April 14th 1995
Acceptance Notification: Friday May 26th 1995
Deadline for final paper: Friday June 23rd 1995
PROCEEDINGS
The papers accepted for the workshop will be bound into an unpublished collection for delegates.
PUBLICATION OF THE PROCEEDINGS
It is intended that a post workshop proceedings will be published by Springer-Verlag and will appear after the workshop.
Enquiries
Enquires should be addressed to Ray Paton at the above address or FAX +44 51 794 3715 or
email [email protected]
by Mark A Haney
SkyGlobe 3.5 is the award-winning desktop planetarium that is fast, fun, and easy to use. A perennial fixture on the Shareware Top Ten, SkyGlobe is the fastest program of its kind available, and it provides a realistic and beautiful display of the splendor of the heavens. You can instantly change your computer view of the cosmos to suit your own tastes, or use one of the many animation modes to simulate celestial motion. Use SkyGlobe to plan a night's viewing, teach yourself about the universe around us, or just to show off the graphics of your computer.
SkyGlobe displays 25,000 stars, constellation lines, the planets, Sun, and Moon, the Messier Objects, the Milky Way, and ecliptic, horizon, and RA-Dec grid lines, for any time and date, from over 230 locations around the world. All display settings can be quickly changed with easy hot-key commands, or through the use of the mouse. Zoom in or out in the blink of an eye, or use the handy Turbo mode with Zoom to create a warp-factor-like effect of racing through the stars. The mouse will constantly tell you the locations and names of bright stars and other objects, or use it to re-center the display at any point of interest. Stars, planets, constellations, and Messier Objects can be located through menus. Try the nifty Sidereal Time mode to preview the move- ments of your favorite planet for the coming months. Learn the constellations by turning the lines on and off, and see if you can see the shapes the ancients saw. There is no better or more beautiful way to use your computer to educate yourself or your children about the wonders of the night sky. Now displays SVGA graphic images!
Requirements:
PC compatible with 512K and graphics. Epson or laser printer optional. SVGA and math coprocessor supported if present.
Winner of the Best Home or Hobby Software category at the 1992 Shareware Industry Awards.
SkyGlobe has been in the Shareware Top Ten for the last 23 months running.
Registration: $20.00 (Plus $5.00 for overseas shipping)
Registrants receive:
1 A copy of the newest version of SkyGlobe, customized with their Home Town as the default city.
2 A professionally printed SkyGlobe manual.
3 A Handy one page Reference Card.
4 A SkyGlobe-like Windows screensaver.
5 A SkyGlobe-like display of our nearest 3800 neighbor stars.
6 Automatic notification of new releases and other products, with discounts on updated versions.
Author: Mark A Haney, KlassM SoftWare, CompuServe 76207,3377
KlassM SoftWare
284 142nd AVE
Caledonia MI 49316
Across My Dreams With Nets Of Wonder
by G.T. Swain
Any survivor of the sixties should have no difficulty recognising the above quotation as part of a hit song entitled, Bright Elusive Butterfly written and performed by American Singer Songwriter Bob Lind. Strangely I was reminded of this by a recent issue of Fractal Report. Rather like a butterfly the exploration of chaos involves selecting an idea expressed mathematically and pursuing it in a disordered fashion.
Now where was I? Butterflies - long before I knew there was such a thing as chaos theory, I was an avid reader of Science Fiction. Arguably the fifties and sixties, when I grew Up, were the golden age for speculative fiction, or perhaps knowing far less about the universe writers were still free to use their imagination. Later when pedantry reared its head the fiction had to take closer account of science fact, so perhaps the readers lost out. The cosmic creations of writers like E 'Doc' Smith, Kurt Vonneught, A E Van Vogt and James Blish, all emanate from the period in question.
Amongst the writers listed above, James Blish came closest to what we now understand as chaos theory. In particular there are several books and stories based upon what the author described as applications of the Lorenz Fitzgerald theory. It may be no more than coincidence, but Lorenz is a name which appears in the pages of Fractal Report quite regularly.
The spindizzy essentially as described at different points in James Blish's various writings incorporated a wave field not dissimilar to the disorganised path of a butterfly. I have to accept this on trust since I have conducted no actual research, Butterfly watching is time consuming, but I have either heard or perhaps read, or maybe imagined the path of a single butterfly is far less chaotic than might appear from casual notice.
Partly it depends on the availability of nectar bearing plants, and on sustaining environments. You do not get many butterflies in the Arctic or in the middle of the Sahara. there is also an element of social behaviour as fritillaries fraternize with each other. Oddly enough another far earlier Science Fiction author, Karel Capek seems also to have been at least partly fascinated by the species as anyone familiar with Insect Play will appreciate.
Just to fill out this article I enclose some images of the Lorenz Attractor created using Fractint. Do they remind you of anything?
These listings are in Amiga True Basic, and Roger Bagula says that they should be easy to convert - just alter the screen settings.
Angtentm.bas
100 set mode "lacehigh16"
110 set window 0,686,0,470
120 print "put in nolet in command window"
130 PRINT " input screen partition:686 for maximum ,70 for fast"
131 INPUT m
132 PRINT " input power of Mandelbrot z'=z^s+c"
140 INPUT s
149 clear
150 let l=1
151 for i = 0.0 to 1 step (1/7)
152 let l = l+2
153 set color mix (l) 1-i,i,i
154 next i
155 let l=2
156 for i = 0.0 to 1 step (1/7)
157 let l = l+2
158 set color mix (l) i,i,abs(1-i)
159 next i
160 let m1=m*470/686
165 let d=0
167 let e=sqr(150)
170 FOR I =-2.5 TO 2.5 STEP 5/(m1+.5)
180 let d=d+1
190 FOR j= -2.5 TO 2.5 STEP 5/(m+.5)
200 let c= c+1
210 let ca=I
220 let cb=j
230 let cc =SQR(ca^2+cb^2)
240 let r=10
250 rem large initial r to prevent early convergence
260 for k=1 to 150
270 IF k = 1 THEN
290 let xx=ca
310 let yy=cb
315 let r=cc
320 END IF
330 let r1=r
350 let x10=xx
355 let y10=yy
360 If X10=0 and Y10>0 Then W=Pi/2
370 If X10=0 and Y10<0 Then W=-Pi/2
380 If X10>0 and Y10>0 Then W=Atn(Y10/X10)
390 If X10>0 and Y10<0 Then W=Atn(Y10/X10)
400 If X10<0 and Y10>0 Then W=Atn(Y10/X10)+Pi
410 If X10<0 and Y10<0 Then W=Atn(Y10/X10)-Pi
420 If Y10=0 and X10>=0 Then W=Pi/2
430 If Y10=0 and X10<0 Then W=-Pi/2
431 let w1=int(abs(w/pi))
435 if mod(w1,2)=1 then w=2*w
436 if mod(w1,2)=0 then w=(2*pi-2*w)
440 let xx=(r^s)*cos(s*w)+ca
460 let yy=(r^s)*sin(s*w)+cb
660 let r = SQR(xx*xx + yy*yy )
690 IF r>e OR ABS(r-r1)<10^(-3) or k=int(e*e) THEN
750 let cr = MOD(k, 16)
780 set color cr
785 goto 800
790 end if
795 next k
800 box area 686*c/m,686*(c+1)/m,470*d/m1,470*(d+1)/m1
820 NEXT j
830 let c=0
840 NEXT I
860 end
Juliafig.bas
100 print "put nolet in command window:input 686 for slow 70 for fast"
110 input m
120 set mode "lacehigh16"
130 set window 0,686,0,480
140 m1=m*480/686
150 FOR i =-2 TO 2 STEP 4/(m1+.5)
160 d=d+1
170 FOR j= -2 TO 2 STEP 4/(m+.5)
180 c= c+1
190 ca=-.74543
200 cb=.11301
210 cc =SQR(ca^2+cb^2)
220 FOR k = 1 TO 100
230 IF k = 1 THEN
240
250 xx =i
260
270 yy =j
280 r=SQR(xx^2+yy^2)
290 END IF
300
310 r1=r
320 x10=xx
330 y10=yy
340 xx=(x10^2-y10^2+ca)/4
350 yy=(2*x10*y10+cb )/4
360
370 x0=xx
380 y0=yy
390 r = SQR(xx^2 + yy^2 )
400 IF ABS(r-r1)<1 THEN w=-1
410 IF ABS(r-r1)> 1 THEN w=1
420 th=LOG(ABS((x10*xx+y10*yy+yy*x10-xx*y10)/(r1*r)))
430
440 IF ABS(th)<pi/SQR(5) THEN GOTO 480
450
460 IF r>10 OR ABS(r-r1)<10^(-2) THEN GOTO 480
470 NEXT k
480 REM
490 IF r=0 THEN r=1
500 IF xx=0 THEN xx=1
510 kk=k+ABS(k*LOG(1+cc/(r^2))+w*ATN(xx/yy))
520 IF kk >5*10^3 THEN kk=5*10^3
530
540 cr = 1+ MOD (2.5*kk,15)
550 set color cr
560 box area 686*c/m,686*(c+1)/m,480*d/m1,480*(d+1)/m1
570
580 IF c>=m+1 THEN c=0
590 NEXT j
600
610 NEXT I
620 end
M.bas
100 print "put nolet in command window:input 686 for slow 70 for fast"
110 input m
120 set mode "lacehigh16"
130 set window 0,686,0,480
140 m1=m*480/686
150 FOR I =-2.75 TO .75 STEP 3.5/(m1+.5)
160 d=d+1
170 FOR j= -1.75 TO 1.75 STEP 3.5/(m+.5)
180 c= c+1
190 ca=I
200 cb=j
210 cc =SQR(ca^2+cb^2)
220 r=10*(1+cc/(4*LOG(4)))
230
240 FOR k = 1 TO 150
250 IF k = 1 THEN
260 x0=ca
270 xx=ca
280 y0=cb
290 yy=cb
300 END IF
310 r1=r
320
330 x10=xx
340 y10=yy
350 xx=x10^2-y10^2+ca
360 yy=2*x10*y10+cb
370
380 x0=xx
390 y0=yy
400 r = SQR(xx^2 + yy^2 )
410 IF ABS(r-r1)<1 THEN w=-1
420 IF ABS(r-r1)> 1 THEN w=1
430 IF r>10 OR ABS(r-r1)<10^(-2) THEN GOTO 450
440 NEXT k
450 REM
460 IF r=0 THEN r=1
470 IF xx=0 THEN xx=1
480 kk=ABS(ATN(xx/yy)/ATN(cb/ca))
490
500 IF kk >5*10^3 THEN kk=5*10^3
510
520 cr = 1+ MOD (kk,15)
530 set color cr
540 box area 686*c/m,686*(c+1)/m,480*d/m1,480*(d+1)/m1
550
560 IF c>=m+1 THEN c=0
570 NEXT j
580
590 NEXT I
600 end
O.bas
100 print "put nolet in command window:input 686 for slow 70 for fast"
110 input m
120 set mode "lacehigh16"
130 set window 0,686,0,480
140 m1=m*480/686
150 FOR I =-3 TO 3 STEP 6/(m1+.5)
160 d=d+1
170 FOR j= -3 TO 3 STEP 6/(m+.5)
180 c= c+1
190 ca=I
200 cb=j
210 cc =SQR(ca^2+cb^2)
220 r=10*(1+cc/(4*LOG(4)))
230
240 FOR k = 1 TO 150
250 IF k = 1 THEN
260 x0=ca
270 xx=ca
280 y0=cb
290 yy=cb
300 END IF
310 r1=r
320
330 x10=xx
340 y10=yy
350 aa=-y10+cc^2*COS(ATN(y10/x10))/r
360 bb=-x10-cc^2*SIN(ATN(y10/x10))/r
370 xx=aa^2-bb^2+ca
380 yy=2*aa*bb+cb
390
400 x0=xx
405 y0=yy
410 r = SQR(xx^2 + yy^2 )
420 IF ABS(r-r1)<1 THEN w=-1
430 IF ABS(r-r1)> 1 THEN w=1
440 IF r>10 OR ABS(r-r1)<10^(-2) THEN GOTO 460
450 NEXT k
460 REM
470 IF r=0 THEN r=1
480 IF xx=0 THEN xx=1
490 kk=k+ABS(k*LOG(1+cc/(r^2))+w*ATN(xx/yy))
500 IF kk >5*10^3 THEN kk=5*10^3
510
520
530 cr = 1+ MOD (kk,15)
540 set color cr
550 box area 686*c/m,686*(c+1)/m,480*d/m1,480*(d+1)/m1
560
570 IF c>=m+1 THEN c=0
580 NEXT j
590
600 NEXT I
610 end
O-Fourie.bas
100 print "put nolet in command window:input 686 for slow 70 for fast"
110 input m
120 set mode "lacehigh16"
130 set window 0,686,0,480
140 m1=m*480/686
150 FOR I =-3 TO 3 STEP 6/(m1+.5)
160 d=d+1
170 FOR j= -3 TO 3 STEP 6/(m+.5)
180 c= c+1
190 ca=I
200 cb=j
210 cc =SQR(ca^2+cb^2)
220 r=10*(1+cc/(4*LOG(4)))
230
240 FOR k = 1 TO 150
250 IF k = 1 THEN
260 x0=ca
270 xx=ca
280 y0=cb
290 yy=cb
300 END IF
310 r1=r
320
330 x10=xx
340 y10=yy
350 p=k/150
360 c1=COS(k*ATN(cb/ca)+p)
370 c2=COS(k*ATN(cb/ca)-p)
380 s1=SIN(k*ATN(cb/ca)+p)
390 s2=SIN(k*ATN(cb/ca)-p)
400 aa=c1*c2*x10+c1*s2*y10-y10*c2*s1+x10*s1*s2+cc^2*COS(ATN(y10/x10))/r
410 bb=y10*c1*c2-x10*c2*s1+x10*s1*c2+s1*s2*y10-cc^2*SIN(ATN(y10/x10))/r
420 xx=aa^2-bb^2+ca
430 yy=2*aa*bb+cb
440
450 x0=xx
460 y0=yy
470 r = SQR(xx^2 + yy^2 )
480 IF ABS(r-r1)<1 THEN w=-1
490 IF ABS(r-r1)> 1 THEN w=1
500 IF r>10 OR ABS(r-r1)<10^(-2) THEN GOTO 520
510 NEXT k
520 REM
530 IF r=0 THEN r=1
540 IF xx=0 THEN xx=1
550 kk=k+ABS(k*LOG(1+cc/(r^2))+w*ATN(xx/yy))
560 IF kk >5*10^3 THEN kk=5*10^3
570
580 cr = 1+ MOD (kk,15)
590 set color cr
600 box area 686*c/m,686*(c+1)/m,480*d/m1,480*(d+1)/m1
610
620 IF c>=m+1 THEN c=0
630 NEXT j
640
650 NEXT I
660 end
SO4VG.BAS
100 print "put nolet in command window:input 686 for slow 70 for fast"
110 input m
120 PRINT"input power z^a:a"
130 INPUT a
140 set mode "lacehigh16"
150 set window 0,686,0,480
160 m1=m*480/686
170
180 FOR I =-3 TO 3 STEP 6 /(m1+.5)
190 d=d+1
200 FOR j= -3 TO 3 STEP 6/(m+.5)
210 c= c+1
220 ca=I
230 cb=j
240 cc =SQR(ca^2+cb^2)
250 r=cc
260 FOR k = 1 TO 150
270 IF k = 1 THEN
280 x0=ca
290 xx=ca
300 y0=cb
310 yy=cb
320 r=cc
330 END IF
340 r1=r
420 x10=xx
430 y10=yy
440 IF mod(k,4) = 0 THEN
450 aa= ca+cc^2*x10/(x10*x10+y10*y10)
460 bb= y10+cb-cc^2*y10/(x10*x10+y10*y10)
470 end if
480 IF mod(k,4)= 1 THEN
490 aa= -(x10)+ca+cc^2*x10/(x10*x10+y10*y10)
500 bb=-cb-cc^2*y10/(x10*x10+y10*y10)
510 end if
520 IF mod(k,4) = 2 THEN
530 aa= (-x10)+cc^2*x10/(x10*x10+y10*y10)
540 bb= y10+cb -cc^2*y10/(x10*x10+y10*y10)
550 end if
560 IF mod(k,4)= 3 THEN
570 aa= (-x10)-ca+cc^2*x10/(x10*x10+y10*y10)
580 bb= y10 -cc^2*y10/(x10*x10+y10*y10)
590 end if
600 IF aa>0 AND bb>0 THEN t2=ATN(bb/aa)
610 IF aa>0 AND bb<0 THEN t2=ATN(bb/aa)
620 IF aa<0 AND bb>0 THEN t2=ATN(bb/aa)+pi
630 IF aa<0 AND bb<0 THEN t2=ATN(bb/aa)-pi
640 IF bb=0 AND aa>=0 THEN t2=pi/2
650 IF bb=0 AND aa<0 THEN t2=-pi/2
660 r2=SQR(aa^2+bb^2)
670 xx=((r2^a)*COS(a*t2)+ca)
680 yy=((r2^a)*SIN(a*t2)+cb)
690
700 x0=xx
710 y0=yy
720 r = SQR(xx^2 + yy^2 )
730 IF ABS(r-r1)<1 THEN w=-1
740 IF ABS(r-r1)> 1 THEN w=1
750 IF r>10 OR ABS(r-r1)<10^(-2) THEN GOTO 770
760 NEXT k
770 REM
780 IF r=0 THEN r=1
790 IF xx=0 THEN xx=1
800 kk=k+ABS(k*LOG(1+cc/(r^2))+w*ATN(xx/yy))
810 IF kk >5*10^3 THEN kk=5*10^3
820 cr = 1+ MOD (kk,15)
830 set color cr
840 box area 686*c/m,686*(c+1)/m,480*d/m1,480*(d+1)/m1
850
860 IF c>=m+1 THEN c=0
870 NEXT j
880
890 NEXT I
900 end
O-TWIST.BAS
100 print "put nolet in command window:input 686 for slow 70 for fast"
110 input m
120 set mode "lacehigh16"
130 set window 0,686,0,480
140 m1=m*480/686
150 REM double twist with cqp monitor
160
170 FOR i =-3 TO 3 STEP 6/(m1+.5)
180 d=d+1
190 FOR j= -3 TO 3 STEP 6/(m+.5)
200 c= c+1
210 ca=i
220 cb=j
230 cc =SQR(ca^2+cb^2)
240 r=10*(1+cc/(4*LOG(4)))
250
260 FOR k = 1 TO 150
270 IF k = 1 THEN
280 x0=ca
290 xx=ca
300 y0=cb
310 yy=cb
320 END IF
330 r1=r
340 x10=xx
350 y10=yy
360 p=k/150
370 x20=x10^2-y10^2
380 y20=2*x10*y10
390 r2=x20^2+y20^2
400 ca2=ca*x20-cb*y20
410 cb2=cb*x20+ca*y20
420 aa=(-1-ca2/cc)*(p)+cc^2/r+(1-p)*(-1+ca2/r2)
430 bb=(-cb2/cc)*(p)-cc^2/r +(1-p)*(-cb2/r2)
440
450 xx=((aa^2-bb^2)+ca)/4
460 yy=(2*aa*bb+cb)/4
470 x0=xx
480 y0=yy
490 r = SQR(xx^2 + yy^2 )
500 IF ABS(r-r1)<1 THEN w=-1
510 IF ABS(r-r1)> 1 THEN w=1
520 IF r>10 OR ABS(r-r1)<10^(-2) THEN GOTO 540
530 NEXT k
540 REM
550 IF r=0 THEN r=1
560 IF xx=0 THEN xx=1
570 kk=k+ABS(k*LOG(1+cc/(r^2))+w*ATN(xx/yy))
580 IF kk >5*10^3 THEN kk=5*10^3
590
600 cr = 1+ MOD (1.5*kk,15)
610 set color cr
620 box area 686*c/m,686*(c+1)/m,480*d/m1,480*(d+1)/m1
630
640 IF c>=m+1 THEN c=0
650 NEXT j
660
670 NEXT I
680 end
Rarenburg.bas
100 print "put nolet in command window:input 686 for slow 70 for fast"
110 input m
120 set mode "lacehigh16"
130 set window 0,686,0,480
140 m1=m*480/686
150
160 FOR I =-3 TO 3 STEP 6/(m1+.5)
170 d=d+1
180 FOR j= -3 TO 3 STEP 6/(m+.5)
190 c= c+1
200 ca=I
210 cb=j
220 cc =SQR(ca^2+cb^2)
230 r=10*(1+cc/(4*LOG(4)))
240
250 FOR k = 1 TO 150
260 IF k = 1 THEN
270 x0=ca
280 xx=ca
290 y0=cb
300 yy=cb
310 END IF
320 r1=r
330
340 x10=xx
350 y10=yy
360 yy=(-(x10^2-y10^2)+cb -2*y10/(r^2))/1.5
370 xx=(-2*x10*y10+ca +x10/(r^2))/1.5
380
390 x0=xx
400 y0=yy
410 r = SQR(xx^2 + yy^2 )
420 IF ABS(r-r1)<1 THEN w=-1
430 IF ABS(r-r1)> 1 THEN w=1
440 IF r>10 OR ABS(r-r1)<10^(-2) THEN GOTO 460
450 NEXT k
460 REM
470 IF r=0 THEN r=1
480 IF xx=0 THEN xx=1
490 kk=k+ABS(k*LOG(1+cc/(r^2))+w*ATN(xx/yy))
500 IF kk >5*10^3 THEN kk=5*10^3
530 cr = 1+ MOD (kk,15)
540 set color cr
550 box area 686*c/m,686*(c+1)/m,480*d/m1,480*(d+1)/m1
560
570 IF c>=m+1 THEN c=0
580 NEXT j
590
600 NEXT I
610 end
SW-SHADOW.BAS
Standing Wave Cycloidal :Shadowbox
print "put nolet in command window:input 686 for slow 70 for fast"
input m
set mode "lacehigh16"
set window 0,686,0,480
m1=m*480/686
PRINT "standing wave cycloidal :shadowbox"
PRINT "by R.L.Bagula march 1988 translated to true basic 3 Feb 1995 "
PRINT " cycloid numbers of 0,and 1 are forbidden"
PRINT " low negative cycloid numbers also don't work well"
PRINT " input first cycloid number try 6 or 2 or -4 or larger neg"
INPUT n
PRINT "second cycloid number"
INPUT n2
clear
g =-30
h=70
lx=-5
ly =-5
lz =-5
vx =-1
vy =-1
vz =1.2
DIM x(11),y(11),z(11)
x(1)=0
y(1)=0
cr =1
DEF FNc(x,n)=(2-1/n)*COS(x)/2+COS(x*(n-1))/(2*n)
DEF FNs(x,n)=(2-1/n)*SIN(x)/2+SIN(x*(n-1))/(2*n)
ss=0
d=0
FOR i = -pi/2 TO pi/2 STEP pi/(m1+.5)
d=d+1
FOR j=-pi TO pi STEP 2*pi/(m+.5)
c=c+1
di=2*pi/(m+.5)
dj=2*pi/(m+.5)
o=1
FOR l =-1 TO 1
FOR p = -1 TO 1
o =o+1
x(o)=FNc(j+dj*l,n)*FNs(i+di*p,n2)
y(o)=FNs(j+dj*l,n)*FNs(i+di*p,n2)
z(o)=FNc(i+di*p,n2)
NEXT p
NEXT l
nx=(x(6)*y(10)-x(10)*y(6))*(z(9)*x(7)-z(7)*x(9))-(z(6)*x(10)-z(10)*x(6))*(x(9)*y(7)-x(7)*y(9))
ny=(y(6)*z(10)-y(10)*z(6))*(x(9)*y(7)-x(7)*y(9))-(x(6)*y(10)-x(10)*y(6))*(y(9)*z(7)-y(7)*y(9))
nz=(y(6)*z(10)-y(10)*z(6))*(z(9)*x(7)-z(7)*x(9))-(z(6)*x(10)-z(10)*x(6))*(y(9)*z(7)-y(7)*y(9))
nn=SQR(nx^2+ny^2+nz^2)
ll=SQR(lx^2+ly^2+lz^2)
cr=(nx*lx+ny*ly+nz*lz)/(1+ll*nn)
cr=1+MOD (abs(cr*300),30)
set color cr
box area 686*c/m,686*(c+1)/m,480*d/m1,480*(d+1)/m1
IF c>=m+1 THEN c=0
NEXT j
NEXT I
end
Note - these programs are as received. Queries to Roger Bagula, please! He'd love to hear from you and correspond on the ideas behing his programs.
R.L. Baugula 11759, Waterhill Road Lakeside CA 92949 USAGenerating Fractals with Hardware in Real Time
by Tom Holroyd
Here's a way to generate fractals with video hardware in real time.
First, create a video feedback loop. Do this by aiming the video camera at the monitor. The monitor and camera settings are important, try the following general setup: monitor brightness all the way down, or at least very low (not completely black, obviously). Contrast set somewhat higher than normal. Zoom the camera in so that the *image* of the monitor on the monitor is about the same size as the monitor (in other words, aspect ratio close to 1:1).
Also, some rotation is desirable, else you just get a blob that is hard to stabilize. Hint: turn the monitor upside down, or put it on its side - this is much easier than trying to mount a camera upside down on a tripod! Oh yeah, tripods are good. Adjust the tripod so you can rotate the camera about the viewing axis.
At this point you should be able to create lots of swirling, spinning stuff. Try messing with the color, (B&W is usually easier to start with), phase, focus, zoom, iris, etc. If the camera and or monitor has automatic features, turn them all off, you get better control that way. Try poking your fingers in, or shining a flashlight on the screen.
The patterns that you see can exhibit spatiotemporal oscillation and chaos, and can be quite hypnotic. But there is usually a single fixed point on screen (that is either stable or unstable, depending on the zoom). To get more complicated patterns like fractals, you need to mix in another transform. The simplest way to do this is with a mirror. The setup should look like this:
monitor
| video camera
| ___
+-->| >___|----+
| | ------------------------ |
| | mirror |
| |
+---------------------------------------------+
The mirror is positioned so that the camera sees *both* the monitor screen directly, and a reflected view of it. Now you have two transforms of the image to play with: the non-linear transform provided by the electronics of the camera+monitor, and the simple reflection of the mirror. With the setup above I have been able to create colorful, pulsating, fractal ferns, and some 'jellyfish' like shapes. Quite different from the usual video feedback fare, because of the break from circular symmetry. Almost like life-forms.
Another way to do this (that I have not tried yet) is with a video mixer. Point two cameras at the screen, mix their output together and display it on the screen. With different rotation angles and zoom settings it should be possible to create lots of cool visual effects. Unfortunately, I do not have access to a video mixer, so I can't try this myself. I have tried to do it with the poor man's video mixer, a half-silvered mirror. I've been able to get some interesting patterns, but there are some serious constraints on this method.
Video feedback is cool in general, and I encourage anybody with a camcorder to point it at the monitor screen! (Remember to rotate it, and zoom in to close to 1:1.) It is a great way to demonstrate nonlinear, self-organizing pattern formation. I have had people look at the screen and say "where does the pattern come from?" This is a great excuse to start telling them all about dissipative structures, reaction-diffusion systems, etc. etc.. Once I even got a pattern of spiral waves that looks a little like the BZ reaction. The WWW page with framegrabbed images is, alas, still "currently under construction" :-(
There are several sources for more information about video feedback. One is this paper, which discusses the mathematics (there is a video tape to go along with this paper, I don't know if it's still available): J.P. Crutchfield, Space-time dynamics in video feedback, 229-245 Physica 10D (1984).
Another is the book by H.-O. Peitgen, H. Juergens, and D. Saupe, Fractals for the Classroom (vol. 1) 1992, Springer-Verlag, New York. This book has some pictures of video feedback, as well as quite a lot of information about pattern formation through iterated mappings. It was Dr. Peitgen's suggestion to use a mirror, by the way.
Some more mathematics and inspired musings can be found in the excellent book by A.V. Gaponov-Grekhov and M.I. Rabinovich, "Nonlinearities in action: oscillations, chaos, order, fractals 1992, Springer-Verlag, Berlin.
Program in Complex Systems and the Brain Sciences
Florida Atlantic University, Boca Raton, FL 33431 USA
"The basis of stability is instability".
The 9th Amendment of the U.S. Constitution:
"The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people."
All at the Press of a Button...
by Chrissie Loveday
Wherever I go these days, someone seems to be talking about E-Mail, Internet or Super-Highways. I must say, it is a wonderful idea, even if it does scare me to death. For a start, I am very much an amateur when it comes to using a computer. I have become fairly adept with my own little word-processor, typing away at a rate fast enough to satisfy me, even if I don't use all the right fingers for every key. I was told by an expert typist and teacher recently, that as long as I use more than two fingers, I shouldn't contemplate learning to type properly. (I think she may have been referring to the fact that I'm now too old to learn and have too many bad habits!) Besides, I don't want to waste my precious time learning about all the clever things computers will do ... I want to spend the time available doing what I know already and John is usually close at hand when anything goes disastrously wrong!
Back to the Internet. The first paragraph should have shown that I am not a candidate for grasping the concept of modems and down-loading, up-loading or anything else. (Free-loading, maybe?) What I have discovered, frightens me almost more than pressing the wrong key on the computer ... there are thousands of people who have got to grips with it all and they all have most interesting information to offer. Why this scares me, is all a matter of time. It's like seeing that TV programme advertised that you know is exactly what you should be looking at for the next course you are taking ... that it will doubtless contain the last vital links to set your thoughts on the right lines. The trouble is, there's never enough time to watch, so you record it and consign it to the pile of other worthy programmes you really intend to watch soon. By then, you're on to the next course, the next subject and the old one is out of date.
But not so the Internet. By the time you get round to reading your messages, there are probably half a dozen more, complete with replies from another batch of like-minded people, all saying exactly what you believed in the first place. I asked a question (through my resident expert, of course) about the topic of autism (yes, my next course, in preparation). I am staggered by the number of things people have said and contributed. I am also doing some work on a project concerned with the employment of disabled people. I already have a folder full of wonderful information from highly eminent people in the field. I have read papers delivered to a conference held in Melbourne (Australia) only this week. Brilliant information and very interesting, if only I had time to respond!
So basically, it all comes back to John's so often quoted, "evil of time". There is simply never enough of it. I positively balk at the idea of four or five hundred messages a day, knowing I should never have the self control to skim through them and only read the most interesting. I should want to read the lot and probably reply to at least half. Still, I am the sort of person who scrapes every bit of silver off any card that comes my way, just to see if I would have won the prize, if I had time to enter the competition.
Because he feels so strongly about the huge power of the Internet, John now syphons off the most important messages for me and only gives me those I find most interesting. This is truly a service! Perhaps when the next book is finished, and the college work has been off-loaded, and ... why bother? It's becoming obvious why I need another go at life... I shall need cryonic suspension just to give me time to read all the interesting stuff on Internet. I suppose by then it will have turned into yet something else and I won't have time for that either!
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