I would once again urge authors not to deluge us with lots of tid-bits, but spend your time (and money) on sending in one or two well prepared articles on disk or in camera ready format that can be fitted into the magazine. Once again, there are some good examples in this issue. It is not just publisher's (my) laziness - this is the best way to avoid errors and enure what you have written is what is printed, and to ensure that readers can input your masterpiece into their systems with the least amount of hassle and error.

Readers are not lazy either - they are often busy people who want a bit of relaxation by playing with programs for a couple of hours on a rainy afternoon. If your program is going to take hours of work to type in and convert, require masses of time because of poor reproduction making some small squiggle indecipherable, then readers won't try it, and your efforts will be wasted.

Announcements

Persecution in

Fractal Translight Newsletter

The editorial in the April 1995 issue of The Fractal Translight Newsletter discussed persecution in science, with particular reference to cold fusion. Roger Bagula thinks that people should look for patterns and connections between events that don't seem connected.

The issue included that story I wouldn't publish in my own magazines, The Face. So if you want to see how badly I write fiction, then you'll have to subscribe to TFTN! On the same page is a reproduction of a letter from Annals of Mathematics which says that a series of Roger Bagula's articles he submitted is "completely without interest" according to their expert.

Whether they are of interest to expert mathematicians does not decry from the attractive and varied patterns they produce, though. This issue includes colour prints of many examples. I cannot help bring to mind Salvador Dali's use of what we now call "technobabble" to support his form of art, and he has earned for more money than any expert mathematician I have heard about!

At the present time, however, Roger Bagula is undiscovered and very much on a budget. Last time I reviewed his work he complained that it cost him money as many people wrote for sample copies but few offered even to remunerate him for print and postage.

I recommend that if you want a sample copy that you enclose 2 1$ notes if you are in the USA or a $5 note if you are outside it.

[Fractal Translight Newsletter $20/yr ($50 overseas) from R.L. Bagula 11759, Waterhill Road Lakeside CA 92949 USA]

News of Contemporaries

The newsletter market still contracts under the relentless onslort of the competition with the Internet for readers' time. Fractal Report survives, and so does REC and Amygdala.

Amygdala's circulation is now 438 with issues 33-34 - less than Fractal Report volume 1, although still about five times or present figure. But as we move into the future the quality of articles in all these newsletters improves, and the smaller readership base is actually getting better value for its expenditure of time and money.

The main article in Amygdala is by the editor and is a heroic piece describing "a remarkable graphic journey, starting from the Mandelbrot set and ending in the quasi-Mandelbrot set associated with z=z³+c". Sound and ceramics gets another airing from two authors - this looks to be a very interested and growing idea. Gabriel Landini included another article on i/f noise (but without the program published in Fractal Report). Another editorial article on The Quicksilver Starship explained an algorithm to produce a moving "warp drive" starfield display and how it may be used to speed up fractal zoom movies. However no hard information was given, and those interested in using the algorithm were invited to write for more information and discuss "conditions of implementation (eg freeware, shareware commercial application), and arrange for permission for you to use my algorithm." There is also a good crop of book reviews in this issue.

Amygdala Box 219 San Christobal NM 87564 USA. $39 pa overseas, $25 US.

REC, or Recreational and Educational Computing has a wider range of subjects, many of them being of greater interest to those of us who are keen on mathematics and number theory first and computer programming second. An active set of readers letters shows a lot of reader participation, and there are a large number of short items some of which are sure to interest any reader.

A large section was devoted to the Pentium Bug, and this is the first time I have seen a listing of a BASIC program to show if your machine has it. It surprises me that while this fiasco was being played out on the Internet (where most of the action happened - the television was two weeks behind and the newspapers a few days later, and the monthlies three months as usual) the Intel share price actually rose to new heights. I suppose the public announcement of the P6 was the reason, but whether a processor designed to guess the next instruction to be sent is a good idea I am not sure! It sound far fetched, but presumably they know what they are doing and there will be another fourfold speed increase which will enable software vendors to save time writing programs which will take four times as long to run ...

REC 909 Violet Terrace Clarks Summit PA 18411 USA, $36 pa worldwide, $28 Canada, $27 USA.

Dr Hugh Daglish

I am sorry to have to announce that long term subscriber and contributor to Fractal Report Dr Hugh Daglish died whilst on holiday in Israel on 24 March 1995. Hugh designed the "Tree" fractal that is on the bottom left hand corner of the front page in every issue. He was also interested in desk top publishing, and was involved with a business newsletter that helped professionals keep up with the latest in telephone technology.

Letters

From Mr Edgar Peters

I have written two books:

Chaos and Order in the Capital Markets Wiley, 1991 ISBN 0-471-53372-6

Fractal Market Analysis Wiley, 1994 ISBN 0-471-58524-6

The first book deals with chaos and fractal time series (and self-similar statistics) as alternative models to explain markets. It is primarily conceptual, but I understand that it is a good primer to chaos and fractals in general. In it, I reintroduce the Hurst exponent, and rescaled range (R/S) analysis as a time series tool.

The second book is a more in depth look at rescaled range analysis and how it can be used to analyze time series. In particular, how you can determine whether a series is random, or has long memory. It also uses R/S in analysing chaotic time series.

From: Jon Horner, Editor, FRAC'Cetera.

Binary Decomposition - The Riddle Unravelled

The letter from Roger Castle-Smith in Fractal Report 37, was of particular interest to us. One of our current projects also ran into problems when we attempted to recreate those images from The Beauty of Fractals which used decomposition.

The project was to compile a Fractint .PAR file that would enable a user to recreate ALL the images from the book. Whilst trying to make the black and white decomp images, it became evident that something was amiss. The difficulties, and solution, are outlined in the following synopsis:

The example on page 74 of The Beauty of Fractals, cited by Roger Castle-Smith in his letter, and illustrated in FR 37 p6 (top), is `correct', and uses decomp=2.

The examples in Fractal Creations, both editions, use decomp=8, so are not useful as yardsticks for evaluating images made with decomp=2.

Working with the Fractint developers, and before Roger's letter was published, we established that the decomp=2 code was `broken' in Fractint, so you can't recreate the BoF illustrations. Cases where decomp > 2 worked fine.

decomp=2 code is fixed in Fractint 19.1+ .

The final hooker is that the BoF illustrations use a bailout of 64, rather than the `normal' 4. This isn't documented in BoF.

Using Fractint 19.1+ and bailout=64 it is now possible to re-create the BoF illustrations using Fractint. We suspect that if Roger tries his own code with bailout=64 he will also obtain the correct results. Alternatively, he could obtain the Fractint v19.1+ source and use that code (it's in C).

The current version of Fractint for DOS (v19.2 exe or source), The Beauty of Fractals, and Fractal Creations 2nd ed. are all available from FRAC'Cetera, the electronic (disk-based) fractal/chaos newsletter and home of FRUG, the Fractint User Group.

Readers who order Fractint will also receive a comprehensive Fractint parser tutorial recently published by Bradley Beacham, together with an interesting little IFS program from Wes Loewer that creates IFSs of a character string - keep the neighbours and kids amused for hours - write their names as IFSs.

Fractint exe. + tutorial and IFS prog: �3.50 (UK); �4.00 (EUR); $8 (Rest) Fractint src. + tutorial and IFS prog: �4.00 (UK); �4.50 (EUR); $9 (Rest)

FRAC'Cetera subscription (4 issues): �12 (UK); �13 (EUR); $25 (N.Amer); �16 (RoW). Single issue: �5 (UK); �5.50 (EUR); $10.00 (N.Amer); �6.50 (RoW)

FRAC'Cetera Issue 13 now shipping - it includes the BoF .PAR project, alas, with the `incorrect' decomp entries as it went to press prior to release of the decomp bug fix.

FRAC'Cetera, Le Mont Ardaine, Rue des Ardaines, St. Peters, Guernsey GY7 9EU, CI, UK. 01481 63689 CIS: 100112,1700

HOP - Fractals in Motion

This program, by Michael Peters and Randall Scott, is based on almost 30 new Hopalong type formulas and loads of special effects, produces an unlimited variety of images/animations quite unlike anything you have seen before, and opens the door to a completely new world of fractals!

HOP features Fractint-like parameter files, GIF read/write, MAP palette editor, a screensaver for DOS, Windows, and OS/2, and more. Math co-pro (386 and above) and SuperVGA required.

HOP was originally based on HOPALONG, the Barry Martin creation popularized by A.K. Dewdney in one of his Scientific American articles. The HOP authors have taken Martin's idea well beyond his original concept, and developed it to such a degree that you need to keep reminding yourself of its modest beginnings. This program illustrates compellingly how a fundamentally simple idea can be extended, through the use of various graphics techniques, into something far removed from its humble origins. Don't let the simple name fool you - this is serious, robust, user friendly, IMAGINATIVE software!

The originator of Hopalong (or Martin's Mappings as he prefers) sent this message to FRAC'Cetera recently:

From: Barry Martin, INTERNET:[email protected] TO: 100112,1700

As you can see I am now on E-mail. Many thanks for the information and FRAC'Cetera disc, Michael Peters and yourself are giving good old HOPALONG (I never did like the name Dewdney gave my mapping) a new lease of life.

HOP has a WWW page: http://rever.nmsu.edu/~ras/hop and a mailing list: write to [email protected]

To subscribe to the HOP mailing list, simply send a message with the word "subscribe" in the Subject: field. For information, send a message with the word "INFO" in the Subject: field.

FRAC'Cetera subscribers may register HOP at a 20% discount.

HOP is available from FRAC'Cetera (address above) on 3.5" DD disk at the following rates: �3.50 (UK); �4.00 (EUR); $8 (Rest)

FRMTUTOR.TXT - AN INTRODUCTION TO THE FRACTINT FORMULA PARSER

"I hope someone comes up with a response to the request of Stephen Leech to produce a clear, definitive `How to program Fractint formulas' ." John Sharp Fractal Report 36/4

"I enjoyed Fractal Report 34, except that I couldn't really translate all those Fractint formulas by Yvan Bozzonetti into Amiga Basic. A short tutorial into the meaning of elements in those statements might be a great idea for a future Fractal Report." Malcolm Lichtenstein Fractal Report 36/3

Whilst this is not the article that Malcolm Lichtenstein wanted, it does bring news of a recently released tutorial, written by one of the Fractint enthusiasts who hang out in the Fractal Sources forum on CompuServe.

The author, Bradley Beacham, developed a fondness for writing his own formulas, but found that the results were not always quite what he expected. Consequently, he began to study the parser in detail and documented his findings. The file, in ASCII, is 2,400 lines long and 115K un-compressed. The resulting major work covers nearly every aspect of parser use, as the following contents list illustrates:

1.0 Legal Stuff

2.0 Acknowledgements

3.0 Limitations

4.0 Introduction

4.1 The Purpose Of This Document

4.2 My Assumptions

4.3 What Is The Formula Parser?

4.4 Formula Files

5.0 A Quote From Fractint.doc

6.0 Some Basics -- A Walk Through The Mandelbrot Set

6.1 Complex Numbers And The Complex Plane

6.2 The Mandelbrot Set

7.0 Anatomy Of A Formula

7.1 A Formula Is A Program

7.2 Elements Of A Formula

7.2.1 Formula Name

7.2.2 Symmetry Declaration

7.2.3 Braces

7.2.4 Variables

7.2.5 Functions

7.2.6 Calculation Expressions

7.2.7 Assignment Expressions

7.2.8 Comparison Expressions

7.2.9 Precedence And Parentheses

7.2.10 The Comma

7.2.11 The Semicolon And Comments

7.2.12 The Colon

7.3 Structure Of A Formula

7.3.1 The Name

7.3.2 Symmetry

7.3.3 Initializing

7.3.4 The Iterated Loop

7.3.5 The Bailout Test

8.0 A Walk Through A Pair Of Examples

9.0 Approaches To Writing Formulas

9.1 Using Mathematical Insights

9.2 Adapting An Existing Algorithm

9.3 Mutating An Existing Formula

9.4 The Monkey-At-The-Typewriter Approach

10.0 Style

11.0 Techniques

11.1 Speed-ups

11.1.1 Avoid Exponentiation And Function Calls

11.1.2 Avoid Unnecessary Calculations

11.1.3 Avoid Unnecessary Iterations

11.2 Simulating The If..Then Construct

11.2.1 How It Works

11.2.2 Pitfalls

11.3 Setting Defaults

11.4 Using Values From Previous Iterations

11.5 Dissecting A Formula With Algebra

11.6 Using A Counter

12.0 Problems

12.1 Potential Problems With Symmetry

12.2 Unparsable Expressions Ignored

12.3 Pathological Formulas

12.4 A Ghost Story

13.0 Where To Go From Here

13.1 Learn More About Complex Numbers

13.2 Learn More About Programming

13.3 Learn More About Fractals

13.4 Find Other Fractal Enthusiasts

14.0 Conclusion

The complete text is included as a complementary add-on to all orders for Fractint v19.2 placed with FRAC'Cetera.

For FRAC'Cetera address details and subscription information, see above.

From Dr. Cliff Pickover

You are cordially invited to submit interesting, well-written articles for the "Chaos and Graphics Section" of the international journal Computers and Graphics (Pergamon Press). I edit this section which appears in each issue of the journal. Topics include the mathematical, scientific, and artistic application of fractals, chaos, and related. Your papers can be quite short if desired, for example, often a page or two is sufficient to convey an idea and a pretty graphic. The journal is peer-reviewed. I publish colour, where appropriate. Send papers to Dr. Cliff Pickover, IBM Watson Research Center, Yorktown Heights, New York 10598.

Thanks, Cliff [email protected]

Goals

The goal of my section is to provide visual demonstrations of complicated and beautiful structures which can arise in systems based on simple rules. The section presents papers on the seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created from simple rules, and aesthetic graphics drawn from the universe of mathematics and art.

Catastrophic Chaotic Attractor

by Mal Lichtenstein

This program combines a catastrophe derivative equation with a Lorenz butterfly. Does this contain the seeds of an idea of how the two might be used to control one another?

screen 12

defdbl a-z

frac=8/3:h=.01

x=.1:y=.1:z=.1

a=-.4:b=-.5:c=-.2

while not instat :' ie while inkey$="" in other BASICs

rem Lorenz Butterfly

xnew=x+10*h*(y-x)

ynew=y+h*(28*x-y-x*z)

znew=z+h*(x*y-z*frac)

x=xnew:y=ynew:z=znew

rem catastrophe equations

xc=3*x*x+a+c*y

yc=3*y*y+b+c*x

rem subtract Catastrophe from Lorenz

rem to form Catastrophic Chaotic Attractor

x=x-xc:y=y-yc

px=x*1000:py=(y+1)*300-100

pz=point(px,py)+1

pset (px,py),pz

wend

N-Color Decompositions

Jules Verschueren

Binnenstraat 53, B-3020 Veltem, Belgium

E-mail: [email protected]

The article below is an answer to the 'Help - Binary Decomposition' question from Mr Roger Castle-Smith in Fractal Report 37, page 6.

His methodology and algorithm are correct and the only difference is in the bailout value: |z|=2 in his figure and |z|=4 in the Beauty of Fractals or default Fractint setting.

Fractint allows decompositions of powers of 2 (up till 2⁸ or 256) and clearly indicates in the help section on decompositions that higher bailouts give more accurate plots, explaining already the above difference. However, the 'quadrant' testing gets rapidly complicated for decompositions exceeding the binary.

An easy and much more flexible decomposition method can actually be quite simple when we view Z in its polar form Zeⁱ with the angle of the complex number from the origin and thus =Tan^-1(ZImag/ZReal). If we normalize for we can assign a color according to the decomposition angle.

The following general coloring algorithm (in Pascal) can be used whenever the bailout value is reached:

[with 'Decomps' the no. of decompositions (2-eg. 999) and 'DecompCol' the calculated color]

IF ZReal = 0 THEN Kolor := 0 ELSE BEGIN { overcome /0 error }

DecompCol := Round(ArcTan(ZImag/ZReal) / Pi * Decomps - 0.5);

IF DecompCol < 0 THEN DecompCol := Decomps + DecompCol;

{ArcTan<0 =>use higher half of color spectrum }

IF (MaxColor = 15) OR (Decomps < 16) THEN { 16 colors used }

Kolor := Abs(16 - DecompCol) Mod 16 { start with bright colors }

ELSE Kolor := DecompCol Mod (MaxColor + 1); { normal color pattern}

END;

[ line 2 in Basic: DecompCol = INT(ATN(ZImag/ZReal) / Pi * Decomps) ]

A good advise: don't decompose too close to the set as the delicate fractal structure might get lost into the very quickly changing decomposition colors, eg. decomposition for a bailout number of iterations of 10-20 is usually sufficient for the best effect, while you color higher iterations white and the set black. For the rest the bailout number has no effect on the decomposition color.

Note that also the internals of the Mandelbrot/Julia sets can be decomposed in the same way.

Below some Newton type 'internal' decomposition examples.

Newton (Julia type) z⁶-1=0, Decomps=12

Newton (Mandel type) z⁵-z(c-1)-c=0, Decomps=10

(note the miniature Mandelbroids of type z^m-1)

Conference News

The Legacy of George Boole

University College, Cork in celebration of its 150th anniversary will be hosting a 3-day conference on June 28th-30th in honour of George Boole, who was professor of mathematics there. The details follow:

28th-30th June 1995.

University College, Cork. IRELAND

The Conference will open at 9.30 a.m. on Wednesday, 28th June and close at lunchtime on Friday, 30th June.

The following are a list of Conference speakers and their titles:

G.K. Batchelor (Cambridge University) Geoffrey Taylor's Share in the Legacy.

Robert L. Devaney (Boston University) The Fractal Geometry of the Mandelbrot Set.

Keith Devlin (St. Mary's College of California) - Beyond Logic: The Mathematics of Everyday Communication.

Ivor Grattan-Guinness (Middlesex University) - Operations of Thought: Boole's Inheritance from French Mathematics.

Theodore Hailperin (Lehigh University) Boole and Probability.

Desmond MacHale (UCC) - George Boole and Sherlock Holmes.

John McCarthy (Stanford University) - More Laws of Thought.

Roger Penrose (Oxford University) -

An Investigation of Physical Laws and Conscious Thoughts.

There will be an afternoon tour to places of Boolean interest, and there will be a Conference Dinner on the Thursday night in the Aula Maxima. (�25 per person).

The Conference fee will be $30 (�20) for early registration before the end of May, or $50 (�30) for registration in June. This fee includes opening reception, lectures and coffee breaks. Accompanying persons' fee will be $15 (�10).

Thank you for your interest, and we look forward to meeting you in Cork.

Professor Jim Bowen, Dr. Donal Hurley, Professor Desmond MacHale, Lucette Murray - Committee.

For more information, contact the UCC150 Office

(e-mail [email protected]) or

Donal Hurley

(e-mail [email protected])

If you wish to attend please write or email for a registration form.

International Conference on "Future of Fractals" 25th-27th July 1995 Aichi Prefecture Labourer Center, Seto, Aichi, Japan

Topics

The meeting is devoted to discuss Future of Fractals, which is seemed to have accomplished the first stage progress up to the present time. Therefore we will distribute enough time to debate the future aspects and dreams of fractals. The topics include formation of fractal structures (kinetics of aggregation and gelation, depositions, cluster growth, chemical reactions, fractures, self-organized criticality, etc.), physical properties of fractals (transport, vibrations, magnetism, etc.), and applications of fractal concepts in materials science, geoscience, biology, etc. Due to the interdisciplinary character of the field, all participants from whole above mentioned fields as well as from mathematicians to engineers and medical doctors are invited to take part in. The registration fee is 15,000 yen (before March 31) and includes a banquet. The proceeding will be given to all speakers.

Location

The Conference will take place in

Aichi Prefecture Labourer Center,

Kawahiracho 78, Setocity,

Aichi 489, JAPAN,

Fax : 81(Japan)-561-48-3146

Phone : 81(Japan)-561-48-2611

which is located on the top of the hill.

Conference Language

The Conference language is English.

Partial List of Invited Speakers

( will be confirmed)

A. Aharony, S. Buldyrev, E. Bouchaud, A. Bunde, H. van Damme B. Duplantier, F. Family, J. Feder, A. Goldberger, S. Havlin H.J. Herrmann, K. Honda, P. Jensen, K. Kawasaki, J. Kertesz M. Kolb, B.B. Mandelbrot, P. Meakin, L. Pietronero, I. Procaccia L. Sander, B. Sapoval, Sernetz, H.E. Stanley, D. Stauffer T. Viscek, Y.C. Zhang, H. Takayasu

Program

Invited and contributed papers will be presented from Tuesday, July 25, 9:00 till Thursday, July 27, 17:00. To avoid parallel sessions, most of the contributed papers will be presented in Poster Sessions. The maximum size of each poster is 130 cm high by 95 cm wide. There will be a welcoming reception (with beer, wine, and sandwiches) on Monday evening, July 24, 19:00, at the hut 5 min. walk from the center. A banquet will be held on Wednesday, July 26, 19:00, at the Cafeteria of Women's College, Chubu University.

Papers

The Conference Proceedings will be published as a regular issue of Fractals, to appear before December 1995. (The rest of this runs to several pages, and may be obtained by fax or post -ed.)

Prof. Sasuke Miyazima

Department of Engineering Physics

Chubu University

Kasugai,

Aichi 487,

Japan

Phone : 81-568-51-1111

Fax : 81-568-52-0134

Fractal Image Encoding and Analysis

a NATO Advanced Study Institute

July 8-17, 1995 at the

Reso Royal Garden Hotel

Trondheim, Norway

See http://inls.ucsd.edu/y/ASI/ for a more complete announcement.

OBJECTIVES: The Advanced Study Institute (ASI) is an expository meeting in which invited speakers present new advances in fractal image encoding and analysis. The meeting has two main objectives: First, the ASI will focus on presenting material that is not taught elsewhere and that is not available from any one source. Second, researchers with fractal image analysis and encoding backgrounds will demonstrate their techniques to each other in order to advance both fields. Workshops in both areas will discuss specific implementation issues and generate a list of interesting unsolved problems.

SCOPE: Topics to be covered include, but are not limited to:

* Fractal Analysis and * Video and Colour encoding. Modelling of 2D data. * Multiresolution analysis. * Encoding methods: VQ, classification, * Multifractal image segmentation breaking the time complexity, * Vectorspace models. search strategies. * Analysis and Implementation * Decoding methods: pixel chasing.

Workshops.

finite step decoders,

pyramid representation, matrix inversion.

INVITED SPEAKERS

Z. Baharav (Technion, Israel). M. Barnsley (Iterated Systems, Inc., USA).

M. Dekking (Delft University, Netherlands). F. Dudbridge (University of California, San Diego, USA). C. Evertsz (Bremen University,, Germany). K. Falconer (St. Andrews University, Scotland). Y. Fisher (University of California, San Diego, USA). B. Forte (University of Verona , Italy). A. Jacquin (AT&T Bell Labs, USA). J. Levy-Vehel (INRIA, France). D. Monro (University of Bath, UK). G. Oien (Rogaland University Center, Norway). D. Saupe (University of Freiburg , Germany). C. Tricot (Ecole Polytechnique, Montreal, Canada). E. Vrscay (University of Waterloo , Canada).

Other speakers: L. Lundheim, S. Lepsoy, R. Voss, G. Vines.

SPONSORS

* The North Atlantic Treaty Organization.

* Iterated Systems, Inc.

* Institute for Nonlinear Science, University of California, San Diego.

CONTACT INFORMATION

NATO Fractal Image Encoding and Analysis ASI

Institute for Nonlinear Science 0402 Phone: (619) 534-5599 University of California, San Diego Fax: (619) 534-7664 9500 Gilman Drive E-mail: [email protected] La Jolla, CA 92093-0402, USA WWW: http://inls.ucsd.edu/y/ASI/

Is the world a superbrain ?

by Yvan Bozzonetti

Today, physics is explained in terms of group symmetry, for example U(1) for electromagnetism, SU(2) for spin in three dimensions or electroweak force field, and so on. On the other hand all symmetries must merge at least at the so called Planck's elementary scale, near 10-33 cm. from quantum mechanics, the smaller the scale the larger the energy. So, the planck's unit is something as 10^29 times (ten billions of billions of billions) more energetic than the simple photon of visible light.

From modern physics experiments, it seems the electroweak force field must fuse with nuclear force at a scale near 10 000 Planck's units. A light radiated at that level would not see an Universe with an infinite number of directions, for it the world would be a sphere made from small Planck's unit surfaces. The surface of a sphere is given by the formula: 4 x Pi x R^2, or 1 256 000 000 for R = 10 000. The biggest possible energy for a photon gives it a view of the Universe with something as one billion possible directions.

Quantum mechanics produces a strange phenomena: the so called state superposition: A photon radiated at the elementary scale will goes in one billion directions at the same time! It will get to one billion different places after one crossing time, the time it take to travel at light speed a distance equal to R ( 10 000 Planck's units). Such a quantum process can works with virtual particles using no net energy at large scale. That is to say, it will take place continuously everywhere in each space element 10^-29 cm long and on a time scale near 10^-39 second. This is mere physics, now I put my personal idea:

This structure looks as a biological neuron firing a signal at one billion nearby neurons 1 000 billions of billions of billions of billions times a second. If that process could be mastered, it would becomes the ultimate hypercomputer. An human brain could be copied in a space 1 000 000 times smaller than the smallest length measured today in physics. AT ten neuron firing per second and ten billion second life span, an entire life would takes 10^-27 second : 10 000 less than a typical nuclear reaction in a nucleus. That would nevertheless amount to 300 years of psychological time, nearly the age Newton would have today. Even the longevity of the Big Bang Universe would amount only to a glimpse at the scale of particle physics.

Now, all of that is for electroweak SU(2) symmetry, what if we restrict to mere U(1) electromagnetism? We know it is limited by the Z boson mass, near 90 GeV or a corresponding length scale near 10^- 15 cm. Everything I have said before could be restated with a 10^11 space and time expansion. This is the level two natural brain structure.

Assume now we are somewhat bigger than that scale so it look as our ground. We could for example dwell in the molecular domain. What if we use all kind of possible physical symmetries ? Soon or late, we will hit the domain called superstring by current physicists. Superstrings are complicated objects with one interesting property here: They rest on modular symmetry, a module is a mathematical object built from three groups, but that is of no concern. On the other hand, modular symmetry has a simple behaviour: it symmetrizes in scale everything about a pivotal unit length. Brain 2 at 10^-15 cm is the unit, at a 10^-11 factor is brain 1 so modular symmetry will build a mirror brain structure at 10^-15 / 10^-11 = 10^-4 cm. All of that is rather tortuous physical reasoning with crude approximation, nevertheless it fall at only a factor ten of the true length of a biological neuron.

The physicist Roger penrose has stated in two book this feeling about a connection between consciousness and quantum mechanics. The modular properties of quantum superstrings would do indeed the job. We have now three brain-like structures, each one stacked on the other with a length factor near 10^11. This look as the fractal scale invariance. Is the next step in physics, after super symmetry, built on fractal geometry ? Who will ponder about it ?

THE THERMODYNAMICAL SIDE.

Thermodynamics is often seen as the science of heat engine, it is more! There are three so called thermodynamics laws: The first is simply the mass-energy conservation. The second introduces entropy, the logarithm of the number of states a system can occupy in a "phase space" with coordinates built from ordinary space and impulsion. The second law states that entropy remains the same in a reversible shift from a state to another and grow if the move is not reversible. Entropy and disorder are different words for the same thing in thermodynamics. The third law puts the entropy zero level for a crystalline material at the absolute zero temperature: - 273 degrees C.

Now enter information theory. If a data set has its maximum information content, is must looks as a random set of digits, if not, there may be a compression algorithm reducing the set without loss of information. A simple example is given by a fractal picture: The picture itself may be many MB long, on the other side a simple formula supplemented by some parameters can code for it. This is a compressed form of the fractal image without lost of content. A random set of digit with its maximum information content is simply a closed thermodynamic system at equilibrium with maximum entropy. From information theory to thermodynamics the words are not the same, the reality IS the same.

To extract useful information from an encoded data set, we need to decipher it with a computing system, a computer or a brain for example. The deciphered data set contains now some redundancies, it is no more in thermodynamic balance with its surrounding, some work can be extracted from it. In theory, information processing needs not to consume energy, so a brain can extract work from a thermodynamics system at equilibrium without any energy input; That look as a perpetual motion system. More precisely, this is a perpetual motion of the third kind: What it violate is the 3rd thermodynamics law. What does the brain is to shift to zero point of entropy.

What we call technological civilization is the use of brains 3 ( biological brains) to process information and apply it to thermodynamics controlled by brain 2. Now assume we could use the scale invariance properties of fractal or the modular symmetry of superstrings to do brain 2 computing, we could fool all ordinary thermodynamic systems. Well, there would not be really perpetual motion, the third law would be working at brain one to forbid that. On the other side, brain one deals with extraordinary high energy and for all practical purposes a brain 2 control would violate the third law, at least everything would look as if that was the case. Must I say this could be a strong incentive to study fractal systems ?

THE TOPOLOGY SIDE.

Topology is a mathematical branch dealing with fundamental properties of spaces, or in simple cases, of surfaces. Contrary to geometry, topology allows any continuous transformations, for example a token can be turned into a marble or a cup into a doughnut. One important topologically conserved property is space orientability. Our space is orientable because whatever the path you choose to follow, a right handed screw will never turn to a left handed one.: A right hand frame can't transform into a left one. On a Moebius strip, this is not true: left and right can be exchanged..

All nonorientable spaces can be built from glued together elementary bricks, that basic brick is the so called projective plane. To get a picture of it, think about the following recipe: Take a sphere, cut it at equator, glue here a moebius band, for each point not on the equator, identify each point in the northern hemisphere with its antipode point in the southern part. You have a projective plane, something impossible to build in three dimensions. Another picture of the same object yet: Look at a sea urchin and think of all points along a needle as the same one. This is a projective plane when the number of needles get to infinity. A neuron with its dendrite forest is a topological picture of the projective plane similar to the sea urchin.

A brain, at level 1, 2, or 3 is so a very complicated, very large dimensional nonorientable space, it is a device using a large space to make order. That is, lowering entropy in a smaller dimensional domain. Topological orientability is the property used to tag each kind of space. Well, entropy looks reduced in the low dimensional, orientable space and that violate the thermodynamics second law. In fact, the closed system includes the high dimension number, nonorientable space and entropy get simply diluted in all possible dimensions. That reduce it for each dimension, not the sum for all dimensions. You could have guessed it: Computing don't violate the thermodynamics second law.

Now, assume we can build a fractal structure inducing computations in brain 2, a whole range of new technology would fall in our hands. Before that, we need to simulate what a system could be. A computer is a realization of a Turning machine, itself a system able to simulate any computing device, including nonorientable hyperdimensional spaces. A sea urchin neuron must be relatively simple to programme, connecting many of then build an simulated hyperspace. Can we start to explore computing by simulated entropy dilution ? Before giving my solution, I would be interested to see the result of other readers work on sea urchin neuron.

Can you programme one of them?

Beyond Measure Theory

Into the Vacuum

By R. L. Bagula

It occurred to me that my game value matrix probability could be applied to Lorentz-Fitzgerald transforms. The problem of what the second transform would actually mean hits hard at both philosophy of science questions and the conserved measure doctrine. I can calculate this codependant transform with some work from the matrix probability equation, but what are these "extra" variables I come up with? To me they represent the dual Riemannian type of noneuclidean geometry, a matter-antimatter like way of seeing geometry. This approach gives a different class of answers to Lorentz-Fitzgerald transforms than does the Jacobian determinant cubic root form.

The transform is:

1) v'=M0*v : v'=(x',t');v=(x,t)

2) M0= | 1 -v | : det M0=1

|-v/c^2 1 |//(2+v(1+1/c^2))=gvM0

The matrix probability equation is:

4) gvM0+gvM1=1

with transform:

5) v1'=M1*v1 ;v1=(x1,t1)

With a little trouble and thought I derived:

6) x1'=(x1-v*t1)/(1+v*(1+1/c^2)/2)

7) t1'=(t1-v*x1/c^2)/(1+v*(1+1/c^2)/2)

What these transforms give is for our expanding universe there is an equal and opposite contraction. This contracting space is necessary for conservation of the matrix probability. Look at it as the Lorentz-Fitzgerald transform being how the gravity field works: then, these are a field of what has been called antigravity. The resulting equations behave as if a repelling force between masses existed, I think. This geometry is what the dual Riemannian geometry also would point toward. The question is: "Where are these masses and how come we don't see or measure such actions?"

In a measure preserving universe Lorentz-Fitzgerald transforms are "perfect" and leave entropy unchanged. Actually, entropy tends to a maximum and that agrees with an expanding universe as a nonlinear Lorentz-Fitzgerald expansion. So if the Jacobian determinant that gives special relativity is actually different than one by just a very small amount over time and continued transforms, the universe will tend to increased entropy. The idea is that our universe is connected to an unseen universe at each point with it's own codependant laws that can not be measured from here. It seems not necessary that we know more than the data of our universe, since the other would be codependent in all aspects. The idea of the tau time of antimatter that we can measure by observing antimatter particle and their decay was only a beginning that brings the other universe into view by higher energy reactions of the total space time.

The quest for antigravity is old and not an easy field with gyro-mechanical monsters and strange ideas of all sorts. If fractal matter/radiation can exceed the speed of light, then, it may also be able to bring a gravity repelling field into being. As long as you feed the entropy engine, translight, antigravity and time travel should all be possible to a well understood fractal quantum theory. I have demonstrated translight from measure conservation theory and antigravity from matrix/game theory ideas, can time travel be very much further down the line? The vacuum of space time behaves as a resisting fluid to result in magnetic and electric permiabilities that determine the speed of radiation. In fractal radiation these permiabilities have a Julia quality.

R.L.BAGULA 7 MARCH 1995 -

This page hosted by

Get your own Free Home Page

Hosted by www.Geocities.ws