FRACTAL REPORT 35

And Innovative Computer Applications

Letters 6

On Penny Saving/collecting As An Experimental Observation R. L. Bagula 10

Lorenz Butterfly Music Malcom Lichenstein 11

Lorenz Music for Tympani, Shakuachi, Piano and Pipe Organ John de Rivaz 12

The Sound of Chaos Dr Gabriel Landini 15

Fishtank Cecil J. Freeman 16

Pondering on a Bifurcation Yvan Bozzonetti 17

The Bagula Set Roger Bagula 19

Rabbits, Foxes and Oppossums Roger Bagula 19

Patterns of Repulsion Paul Gailiunas 20

Fractal Report is published by Reeves Telecommunications Laboratories,

West Towan House, Porthtowan, Truro, Cornwall TR4 8AX, United Kingdom.

Volume 6 no 35 First published October 1994. ISSN 0964-5640.

Editorial and Announcements

The article pile is nearly empty, so readers are requested to get their thinking caps on again. Remember that we now cover other unusual computer applications, not just fractals. (But no games, business applications etc.)

Editorial

Your editor is now on CompuServe, no 100431,3127. The box is usually emptied at about 10pm, and replies posted the following day at the same time. Sometimes there is another access, resulting in a quicker response, but this should not be relied upon. Text files only, please. Other files have to be encoded with UUENCODE (download it from the IBM Communications Forum in Library 2 under UU521.ZIP)

It is hoped that CompuServe will offer full Internet service soon, or failing that it is hoped that I can get a local call connection to a full Internet service.

If you have a computer with a serial port but no modem, then M & B Electrical Supplies Pilgrim Works Stairbridge Lane Bolney Sussex RH17 5PA have some Amstrad 2400 baud SM2400 modems for sale at �6 each. They are customer returns, and you need to ask for the lead and instructions. There are no power supplies - the reason the customers returned them is probably because Amstrad aren't very good at designing power supplies. You have to get a 9V 1A power supply and fit the appropriate connector. Actually M&B sell a Sinclair 9V 2.1A power supply for �3 that should do nicely - the modem will, of course, only take as much current as it needs. If you don't know how to do it yourself you will need to find a local person to fit the appropriate connector to connect the power supply to the modem. M & B charge �3 postage per order. (0444 881965) This modem costs a little under �100 from normal suppliers. I suggest you get two at the price of �6 to be sure that one is working. Overseas readers may need to change the phone plug on the modem, and should not that the Sinclair power packs are for 240 volts mains. (You do all of this at your own risk, of course!)

If you are not a member of CompuServe and would like to join, then you can get 40% off if you telephone 0800 289378 (USA people please ring 800-848-8990) and ask for the member referral scheme. You have to quote my name (John de Rivaz) and number (100431,3127) to get the discount. You membership pack will then cost you �15.50 instead of the regular price of �26.45.

Quarterly Publication

There has been no howl of protest over the idea to add extra pages to each volume but reduce the frequency to quarterly, so as to get better value from international airmail. Complaints of slow delivery of up to 12 weeks are coming in with regards to surface mail, and this service is obviously almost useless. Sending a 60g packet by air is now prohibitively expensive as the minimum printed papers rate is 100g.

Therefore the more pages but quarterly regime will be introduced for the next volume.

Yes

You should find enclosed with this issue another application form for a free copy of Yes magazine. I have recently started sending them articles about all and sundry, and hopefully this will lead to a few new readers for my publications. Maybe some of you would like to write as well. They pay �35 for 1,500 words, and as you may gather if they accept my stuff they'd probably take about anything!

Pay Once

On the reverse side of your address sheet you should find details of yet another multi-level scheme, "Pay Once". On the face of it this appears daft - you pay �24 for a �12 book! But the other �12 enrols you into a scheme that, if you make regular mailings anyway, should earn you some extra money. You only need three people to join to break even on your enrolment costs, and another three to pay for the book. After then, it is profit, and the matrix is a deep one!

Some people may well be wondering why I am getting involved in these schemes. The reasons is that I am investigating new ways to promote Fractal Report. Simple advertising is just too expensive, and weighed down by VAT.

Announcements

Chaos in Wonderland

Clifford A. Pickover's new book Chaos in Wonderland was published at the end of July. He says that the colour plates look great. The full title is Chaos in Wonderland: Visual Adventures in a Fractal World and it is published at a shade under $30 by St Martin's Press, New York. ISBN is 0-312-10743-9, and there are 300 pages with 200 illustrations.

If we get a review copy, or if someone else send in a review article, we will print more about this book in this or a later issue. But I have no doubt that if you have liked Dr Pickover's previous works this one will be no exception.

News of Contemporaries

The Fractal Translight Newsletter dated November 1994 was received here late in July, and contained the usual mixture of Amiga programs, articles, poems, stories etc. and comment on "outlaw science". The programs are short and can be typed in if you understand enough about programming to sort out difficulties of the small print and poor copying. Mr Bagula is struggling to overcome these difficulties, and says that he needs more support to continue. In the editorial to his December 1994 issue he lists problems he has had in producing the last year's 12 issues, and says he made a loss of about $1,000. However he is to continue publishing monthly rather than go quarterly as have so many newsletters in the face of international mail pricing changes. This issue printed most programs in normal text and only used a small typeface for articles. Every subscriber gets some pages in colour, not just review copies. ($20 USA, $50 overseas. 11759 Waterhill Road, San Diego, CA92040 USA)

REC on the other hand has better fortune. Dr Mike Ecker has acquired a new laser printer, and the production quality of the newsletter has improved substantially as a result. In the editorial he asks for donations towards the costs of the improvements. [Don't panic, Fractal Report readers, we won't catch this American habit - which is just as well as computer equipment is much more expensive over here.] It is also an interesting issue, with new Mathemagical Black Holes and other numerical fun.

I was interested in a computer simulation of a zero sum game. Game theory has been used by Dr Richard Dawkins and Dr Eric Drexler in discussing the abuse of power by the professions and government in relation to the individual.

There is also an article on mathematical methods for calculating PI, but there was little information on computer implementation for large numbers of decimal places.

An analysis of trends in computing is an irregular feature of REC, as are product reviews. This may be helpful to people considering whether to introduce some new gadget to their computer system. Dr Ecker chided the makers of a graphic adventure game designer for the poor English of their manual, but recommended the $40 product as being good value if you are interested in that sort of thing. It creates graphics and art and also sound and music for the games.

John A. Colls sent in some comments on Interset, which REC reprinted from Fractal Report 28 (with permission). He investigates the differing results produced using different compilers, and attributes this to the handling of the colour palette. He also notes how long the program takes to run with different BASICs. PowerBasic came out best, Q-BASIC taking so long he never bothered to let it finish! (PowerBasic is an upgrade of Borland TurboBasic. I never upgraded because the company that bought the rights from Borland asked for quite a lot more money after I sent in the price quoted in a magazine.)

Host update

Peter James informs me that the paperback version of his novel Host about computers and cryonics will be published by Penguin under ISBN 014 088376. For more information contact Penguin on 071-416-3000.

Even if you have no interest in cryonics, the computer side of this story will make it enthralling reading and it contains masses of interesting ideas presented in fictional form.

An article in Electronics World and Wireless World dated September 1994 (p713) outlined the reality behind much of the fiction of Host. Mike Lamming and his team at the Rank Xerox Cambridge EuroParc are reported to be working on a project to design a human memory prosthesis. The group are studying how various different research projects could be linked to create a system that records every place we go, everyone we speak to, what we say and what we do.

This is not for people suffering from memory deficiency diseases, or for political manipulation. The purpose is to ease the problem of finding files, papers and notes, recalling names of people and places, procedures and lists and remembering to perform tasks in the office environment.

The equipment will prompt users when they enter particular locations or encounter particular people. It will help him recall events that he didn't even know he needed to remember.

However the article concluded that there could be strong political opposition to the use of such a system, because although the user may be quite happy with it, people all around him would also be recorded without their knowledge or consent.

I have the following comment: If an individual has an excellent memory and access algorithm, then he naturally records all the aforesaid information around him and can recall it when required. Such people are usually the most successful in our civilisation, and amass great wealth and power.

Human progress would certainly benefit if more of us could be like this. However taken as a class, those who already have this gift would have to share their wealth and power more widely if their number becomes larger. Indeed, if everyone has this gift, then those exceptional people would not longer be exceptional, and other talents that still could not be augmented by "prostheses" would become the tickets to success.

Therefore those people who already have this gift, who are already in positions of power, are likely to use every means at their disposal to suppress its introduction. Civil liberties windgeing about privacy is likely to be their main weapon. They will probably introduce licensing, and try and cripple introduction of the prostheses by license fees and taxes. Government agencies will be formed which have powers vastly in excess of the normal police to enforce these license conditions and payment of fees.

In the long run such methods probably will not work. After all, logarithms, slide rules, mechanical and electronic calculators had to run a similar gauntlet, yet are now commonly accepted. These devices aided arithmetic, a branch of mathematics which is easier for people with disciplined memories (for holding carry sums). At present databases and PCs are running this gauntlet, and no doubt other products that allow people to increase their productivity and hence earning capacity will follow.

New Media Magic Catalogue

I have just received the 1994 Media Magic Catalogue. Once again there are many excellent items, far too many to detail.

One I particularly liked the sound of was a program that uses evolutionary theory to produce a picture that the viewer likes best. (Darwinian Art, p85 $30. Maths Co Pro or 486 DX required.)

On a more serious note, Nanotechnology Playhouse ($24) claims to simulate building machines using molecules as working parts. An enormous claim for so cheap a product, I should have thought.

Neural networks were more expensive, three examples each cost $185. Movie making and morphing programs cost less, but there is a price to be paid in hard disk space.

There is a substantial drop in the price of Images Incorporated, from $225 to $145. This enables you to fractally compress graphics and to expand them beyond the original size without becoming fuzzy as a result. Great for printing video graphics! This product should be much more marketable at this price.

There were many other fractal programs, pages of them in fact, together with books, prints, objects and videos as well.

Catalogue free from Media Magic PO Box 598 Nicaso CA 94946 USA

Stereolithography

Readers who have been taking Fractal Report from the start will be aware that I have been interested in the idea of producing three dimensional fractal objects by computer.

A recent article in Computing and Control Engineering Journal, an IEE publication, of August 1994 page 200 describes equipment that could be used for this purpose. Unfortunately it will be some while before this gets into the hands of the home user. Cost of apparatus ranges for $75,000 to $490,000.

In a subheading entitled getting started it was said that a bureau owning such a machine would charge a few hundred dollars for a small object to thousands of dollars for large and complex objects. If the user were to create files that could be read by the machine directly, the charges would be much less than if the bureau had to do processing work. The article said that substantial savings could be made if the user had his own Computer Aided Design (CAD) facility and CAD to rapid phototyping mechanism interface software.

Once you have a model, of course, it can be replicated by conventional moulding techniques, provided it is topologically possible.

The writer of this article was Dr Chua Chee Kai School of Mechanical and Production Engineering Nanyang Technological University Nanyang Avenue Singapore 2263.

If any Fractal Report reader is able to follow this up and produce 3D fractal objects of artistic merit we would be happy to include an announcement so that they could be offered for sale to other readers.

Physics programs

I have just received the new catalogue from Physics Academic Software. Although aimed at school and college lecturers and students, some of these programs will interest Fractal Report readers. There is a large chaos section, and also many other programs on such matters as space travel, relativity, orbit plotting etc. These are not games, but serious simulations designed to generate an understanding and feel for the physical principles behind phenomena without the student being bogged down with mathematics.

The some problem exists with mathematics as with computers and calculators - garbage in, garbage out. If however the operator has an instinctive feel for the subject, he will know at once whether the result of a mathematical calculation is within reason, whether it be performed on paper or with a machine. Physics Academic Software programs are designed to provide that instinctive feel for subjects. The catalogue if free for the asking from then at North Carolina State University Department of Physics Box 8202 Raleigh NC27695-8208 USA. The price of a typical program is of the order of $60.

Chaos Theory at

Terra Libra Conference

Mr Butler Shaffer is to present a lecture on Chaos Theory and Human Liberty at the second Terra Libra conference, to be held at the Irvine Marriott Hotel, near the John Wayne Airport, California on October 8-10, 1994. Cassettes of all the lectures will be available, regrettably for $199 for the set. If you are particularly interested in just the Shaffer lecture, then you could always ask.

As regular readers may know, I am fond of the idea that Chaos Theory shows that massive state control is scientifically impossible and that it was realisation of this that lead to the fall of Communism.

[Terra Libra, 2430 E Roosevelt apt 998SE2 Phoenix AZ85008 USA] Letters

From Dr Mark Stuckey

Associate Professor of Physics, Elizabethtown College, Pennsylvania

I have some comments/questions concerning the article Ordering Time Ideas by Yvan Bozzonetti (Fractal Report 6, # 34).

I am not a high energy physicist, but I don't believe cosmic strings are the same thing as superstrings, as alluded to on page 9. I understand topological defects, such as cosmic strings, to be regions of trapped false vacuum. According to Inflationary Cosmology, a rapid cooling of the early universe may have created "pockets" of vacuum which did not undergo the electronuclear phase transition at the appropriate temperature. Such a pocket is called a false vacuum and contributes negative energy density to the stress-energy tensor. This negative energy density drives an increasing expansion rate with time (inflation). Degeneracies in the true vacuum state allow for regions of trapped false vacuum, upon its transition. These topological defects may be 0-dimensional (monopoles), 1-dimensional (cosmic strings), 2-dimensional (domain walls), or 3-dimensional (texture). Cosmic strings can be millions of light-years long and may, like texture, account for large scale structure in the universe. Superstrings on the other hand are the fundamental elements of superstring theory and are only l0^-33cm long (Planck length). I've never heard speculation on their composition, just that their vibrational spectra and world-sheet topologies may account for the properties of the fundamental particles.

Also, I don't understand how a differential geometric model of space-time can be "a mist made up from very many small droplets without link between them" (page 11). At the foundation of differential geometry is the differential manifold. A prominent characteristic of the differential manifold is its smoothness on the smallest scales. This results from the requirement than an N-dimensional manifold be locally homeomorphic to R^N. I've not heard of a tensor defined in the zero-dimensional tangent space of a discrete manifold. In what sense can one have a differential geometry on zero-dimensional manifolds?

Comment

I am pleased to see Yvan's article have created an interest. Here is his answer:

First about strings in their context: When the smallest object in a space is a point, we can construct in this space a field theory. Particles are simply points of defect in this space. This is the level of the physics well known Standard Model. An extension is the supersymetry world where spins can be converted in half unit steps from 0 (the much sought after Higgs' boson) to 1/2 objects such electrons, protons... to spin 1 particles illustrated by photons, gluons, Z,W... and then to 3/2 elements and finally spin 2 entities such gravitons. There is no consistent field theories with intrinsic spins larger than 2. Beyond that value we enter the world of superstrings: Supersymetric spaces where the smallest defect is no more a point, but a line. This is the domain of quantum superstrings as seen from Euclidean space.

Cosmic strings, on the other hand, are indeed "defects" in space-time linked to false vacuum (= Higgs' field in particle field theories = cosmological constant in General Relativity). They have nothing to do with quantum superstrings for an Euclidean observer. That observer can look at three horizons: The Planck 's length, the black hole and the cosmological one. Near each of them, not only the Euclidean laws break down, but the space with smallest objects represented by points too. The first thing after that are strings in the three cases. It has recently been suggested than near a black hole horizon, superstrings expand to an infinite length, enshrouding the horizon behind a string little ball. There, superstrings (Planck's length strings) turn into cosmic-like strings, so there may be, it seems a link between Planck and cosmic strings. (I have not the exact reference at hand, but the information comes from a recent issue of Nature).

About string composition, a first suggestion was made by J. A. Wheeler in the 1976 Solvay Conference. He looked at string-like objects as the source of electrical charge at a more fundamental level than the U(1) symmetry of Quantum Electrodynamics.

About differential geometry now: All of the differential geometry is built on continuous spaces with locally "flat" properties. Counter examples are fractal spaces with no flat, that is, no Rn small domain and discontinuous spaces. To define a differential geometry, we need two basic components: A metric g to produce locally a kind of scalar product and a parallel transport operator G (capital gamma) to define how g is affected by a displacement from a point A to another point B. Now, G can have a finite range as seen from another operator G '.

A simple two dimensional example is given by the space of constant negative curvature first studied by C. G. Gauss, J. Bolay and Lobachewski. That space is infinite as seen from inside, but reduces at a finite radius "a" for an Euclidean observer. There may be a differential geometry built on G in the negatively curved space, but that is no more than a droplet of radius "a" in a mist of similar objects as seen from the Euclidean G ' (G ' is particularly simple in this case: G ' = 0).

A tangent space is defined at a point in the original space, if there was a tangent space at every point of the original space, this one would be endowed with a tangent field. By its very definition, a tangent space, tensor-like or not, is always defined at a point in the starting space. To get back at the above example of a mist of negatively curved spaces in an Euclidean one, a tangent space anchored in a mist drop will looks different from another fixed in an Euclidean domain with no such element. If the radius "a" of the negatively curved domain is very small (say some Planck's lengths) in the Euclidean space, then we can think of it as zero dimensional for most practical applications.

My feeling about the next physics extension is even stranger than you could think from my Fractal Report writing: I bet on the exploration of classical physics in chaotic and sub-chaotic situations. I am looking at a good book or course on Jacobi and Poisson's bracket representations of classical situations. If you know of such an information source, I am interested to get it.

(second letter) as received by email

I apologize for that long delay to answer your letter and messages. I was far away from Paris and computers for two weeks.

If I don't make a big error, it seems to me that the covariant derivative is the ordinary one with, in supplement, a connection operator, known as the Christoffel symbol: Gabg = xa/xi . 2x/xbxg. Because it is cumbersome to write it with my word processor, I have abridged it into capital gamma only in my first letter. The x's are curvilinear coordinate systems and the x an Euclidean one. The parallel transport operator is indeed the full covariant derivative. Following Gordon KANE in Modern Elementary Particle Physics (Addison Wesley, 1987) I think of a gauge as an operator using a Christoffel symbol derivative (a covariant derivative). If a space has more than one gauge symmetries, it contains too more than one parallel transport, this is why I have used that idea. About space of constant negative curvature, I assume it is the one built on the R field, what is the T field? I know about reals, complexes and hypercomplexes such Hamilton's quaternions and some less used ones.

The local properties studied by differential geometry do not preclude to draw conclusions on a larger scale. For example a two dimensional dweller on a curved surface can drawn a triangle and add up its angles. If the sum is larger than 180, he know its space has a local positive curvature. Using a parallel transport "machine" he can do the same at different points. If all give the same answer, he can deduce the complete geometry of its space: he is on the surface of a sphere. If the angles sum is always less than 180, the space is negatively curved, with a curvature constant K = 1/a. That space is infinite for the dweller but finite with a radius a for an Euclidean observer in the three dimensional "superspace". This is best explained in the historical introduction of Steven Weinberg's book: Gravitation and Cosmology (Wiley, 1972). (The idea of reducing a Relativity curved space at a metric gij and a covariant derivative comes from the same book).

The EPR paradox and Bell's inequalities are too much for me. I find hard to understand the mathematics behind string theories, so going further away is beyond my current scope. About deterministic chaos and quantum mechanics, I have no information. My current idea on the subject can be summarized as follow ( I have some difficulties to understand how deterministic chaos, a non linear phenomena, can subtend the linear quantum mechanics. I have seen somewhere than the non linearities can account for only one part in 10-27 , well beyond any significant contribution. The work was done some years ago by S. Weinberg. If I would invent an instant new science, I could interpret the things as follow:

If we define chaos as the limit where the doubling of allowed stable states get to infinity, then it seems to me we can see each doubling step as a dimension in a function space. Each such dimension would contains two times more states than the preceding one. The p-th dimension would map to the first half of the p+1 th one. The second half of the p+1 dimension would be something as the complex part of this dimension... In an infinite set, for any p there is always a p-1 dimension. So, the full set is a complex function space, it could be turned into a Hilbert's space with few more steps (an inner product for example). If that chaos is built on a vector space E with dim E = n, (n finite) then functions are 0-forms on E and the Hodge * operator turns them into n-forms or volume element V with length d = V-n. Reversing the Planck's length formula gives the unit of action associated with d: h' = d2c3/G with: c = celerity of light in empty space and G the Newtonian gravitational constant. In this way, a chaotic system can be seen as a quantum system. ( if the function space is turned into a Hilbert's one).

Unfortunately, if n = 3 dimensions, h' is not equal to the Planck's constant h for any physical system with smallest chaotic volume V. It could be argued than chaos takes place in a kind of phase space for quantum properties and so, the true Planck-like constant would be h" = 1/h', but that would produce a quantum space with h going to near zero. If that work, we have a way to superimpose on any quantum space a chaotic quantum-like space with h = 0, this could be a way to "dequantify" at a given scale any phenomenon...

Another way to explore would be to look at prechaotic systems with a finite number of period doubling. May be the work of Cantor on the foundations of set theory would permit to turn this system into an infinite function space with characteristic unequal to 0. Any eddy would then qualify for a quantum-like space.

From Dr Stephen H. Meech

I note you mentioned that your article pile is low. I am still struggling with the Fractint formula compiler and I wonder if someone more expert might like to revisit some of the algorithms published in previous issues of Fractal Report and produce the appropriate Fractint formulae. The Basic programs printed will usually convert to Qbasic for example but Fractint is faster and does allow zooms without re-writing program lines to do the same.

In this vein I was very pleased to see the article on page 5 of Issue 34 - at least until I tried it!

By the way I don't know if you noticed that your TurboBasic program is not quite true to the Amiga listing. Your use of "e=e*e" affects line "y=2*e*f+b" where e should not be squared Correctly "e=e*e" should be omitted and the phrase two lines down should be "x=e*e-f*f+a" to compensate.

Anyway, having typed in the program Qbasic gave me, not the image you produced but, the top-left-hand two thirds of the image at the top of page 6. Not to be undaunted I tried the Fractint formula, adding the missing semi-colons on the line ends. Try as I might I could not get the same image. I thought this was because I wasn't sure how to enter the variables (3.99 & 0.99) but eventually worked out they are the real components of pi & p2 (think, all other entries for the imaginary components produced a different image to that obtained by inserting the constants directly into the formula). All the images I obtained were dumb-bell shaped with two poles, unlike the more interesting four way images you printed.

As some of the images had horizontal lines of black spots using guessing mode, and blocks of black using the two-pass mode I wondered if the result is more due to precision errors than the algorithm. Certainly running the formula with floating-point "on" results in no image at all which is highly suspicious. I am not sure where the problem occurs although the variable "f" tends to get pretty close to zero at times I think.

As you can see some help with the formula system would be much appreciated. I am not sure about the "zl =(O, 1) .... |z2|<=4" and why this should not simply be "x*x+y*x<=4". The use of "x=real(z); y=imag(z)" was helpful and other examples would greatly aid my understanding.

I have managed to subscribe to REC although the currency problem made it difficult and it's quite expensive anyway. I may make the effort to get some back issues.

Reply:

Yes, you are right about e*e. This goes to show why many people prefer not to speed up programs by such methods - they lead to mistakes. If you want to recreate the pictures as shown you have to continue the "mistake", which I put in quotes as this is how many fractal images are found!

All variables are complex as defined by the system, and putting Z1 equal to (0,1) makes it 0+j. |Z2|<=4 is the way the system requires us to state the limit. It is after all quicker than writing it all out. I will print your letter to see if anyone is interested in coming up with a formula system tutorial. I fully agree with your reasons for wanting one. It is some while since I wrote that formula and I do seem to remember having to spend some hours getting it to agree with the TurboBasic. To repeat the results, do be sure that every dot and comma is correct.

I agree with the currency problem. A lot of American publications take credit cards, which helps as they give a fair rate of exchange, unlike the banks. I can't remember whether REC does without looking it up.

Thanks again for writing. No doubt I would learn more myself about the formula system if I were to work though every possible combination and write it up. Regretfully I don't have the time for the foreseeable future.

From Mr Jon Horner

Herewith FRAC'Cetera 03.11

I expect that you have already discovered that On the Track of M Bacteria in Fractal Report 34 is a duplication of the same article in Fractal Report 24. Just one of the perils of an editor's life!

I wonder if you are undermining subscriber loyalty by including material such as Global 2000? It's just a disguised chain letter, and many people are very anti such mechanisms.

Also, I wish I understood Bagula's stuff!

Editorial Reply:

Actually you were the first to report the Bozzonetti duplication, and it was the first time this has happened. As you say, such a thing is inevitable eventually. I do not have enough time to be sufficiently methodical. Electronics World and Wireless World did a similar thing. They published a letter of mine Virtual Travel in two consecutive issues.

There was also a mistake in the Lichenstein article on page 5, "e=e*e" shouldn't have been there in the translation from Amiga BASIC. e*e should be in the following x= line instead. Only one person pointed this out. (Which is probably just as well really.) However these mistakes do generate new fractals! This also goes to show why perhaps it isn't a good idea to speed up programs this way.

As to Global 2000, I think people should learn tolerance. I fully appreciate these things are gambles and say so in the editorial. If successful, they could provide funding for specialist newsletters that cannot be economic any other way. I find it interesting that they seems to be more acceptable to intelligent people and rejected by down to earth types. This is possibly because most professions work on the chain principle, eg a solicitor always tells anyone they are writing a hostile letter to, to consult another solicitor. Lloyds insurance was funded by a chain of re-insurance that finally crashed. VAT is a chain system where only force is used to get people to join - there is no benefit. Doctors benefit by long training and poor work conditions for juniors. This keeps numbers down so most juniors get a chance to become well paid consultants.

On Penny Saving/collecting

As An Experimental Observation

By R. L. Bagula 18 May 1994 Copy Rights Reserved

I have a habit of putting all my pennies from change into a piggy bank. About ever six months I package them up in lots of fifty after sorting them for older coins. Since the change from copper to zinc, I think some of the older pennies might be worth something by the time I'm in my sixties. There is no way I'm going to get rich and retire on this scheme! That's not what this essay is about anyway. This last time when the piggy got full, I found two "wheaties" which I haven't seem any of in literally years. This made me wonder what the probability of finding an "Indian head" are? My piggy holds close to 500 pennies and gets full about every six months. In the last five years I've gotten only 3 "wheaties" with the two I got this time.

Now, the funny way my mind works : suppose one million people in 1994 each collect 500 pennies over six months? What is the probability of then finding one Indian head penny? What is the probability they will find a penny minted in 1997? Yeah, I just watched Terminator Two after watching the tamer part of "The Stand". By the way I got a bad cold about the time "The Stand" was on! Any way it has occurred to me that the efforts of using every means and source of information to "predict the future" is very much like getting information through a time machine. It's like the test for artificial intelligence: how can you distinguish a true prediction of the future from information gained from a time machine?

Since we seem to be seeing indications that fractal radiative fields can exceed the Einstein speed limit, why ,then, can information not be passed to the past using such fractal radiation fields? As long as more entropy is created by the process than is converted into the information transfer, I don't see why it shouldn't be possible. I used the "Wavelet" orthogonal fractal procedure of one of my articles to make an orthogonal iteration to the fuzzy logic iterative/Julia map; the resulting logic iteration was "noisy". In terms of kinds of logic one is like deductive logic and maybe the other is like inductive logic? Science is a form of philosophy in which inductive experimental observations are used to form laws from which deductive predications about future events can be made. (A particle continues in a straight (geodesic) line unless acted upon by an external force.) The formation of probability to predict uncertain events has been the result and from that came both quantum mechanics and fuzzy logic. That the current doctrine is that "time travel" is a forbidden process doesn't entirely rule it out in even Scientific terms, since many physical processes that are theoretically forbidden are observed every day: the model or theory is flawed.

Now, suppose a housewife in mid-America finds a 1997 penny in her change? What would the reaction of our "popes of science" be? Would they call it a weather balloon? This kind of Science by only "registered Scientists" attitude is a modern folly? Ordinary people can't be trusted to report events as they truly are because they aren't trained. If that is true, then our legal system is in real trouble as it uses such testimony every day. This essay is offered as a thought experiment in "What in if's?" You can't find any books on "alternative" theories of time in the ordinary press, but only in science fiction novels! Fuzzy logic was impossible to find in computer books until the Japanese began to actually use it!

The American tradition is to offer you a penny for your thoughts. This essay is a penny for yours.

Lorenz Butterfly Music

by Malcom Lichenstein

'MPU3.bas v3.i MIDI 1/0 IN UART MODE FOR MPU4Oi and Quick Basic
'By G. Landini e-mail: G. [email protected]
'Please let me know of any improvements you do to these 'subroutines!
'Instruments data and subroutine added 10.12.93 by John de Rivaz.

DEFINT A-Z
screen 12
sta = &H331    'status port default (may be different in your machine)
dat = &H330    'data port default (may be different in your machine)
drr = &H40     'data read register ready
drs = &H80     'data ready to send
ack = &HFE     'MPU acknowledge response
cmd = &H3F     'UART mode command
mpurset = &HFF 'Reset command
randomize timer
dim r(10)  ' for getrnd function

CLS
print "started"
call MPUrst    'reset MPU to intelligent mode
print "first stage completed"
call UARTmode  'put MPU in UART mode
PRINT "UART mode"
dim instruments$(127)
restore players
for n=1 to 127:read instruments$(n):next n

'PAYLOAD PROGRAM START
'---------------------
defdbl h,x,y,z
call instrument(2,108) 'shakuhachi
call instrument(3,113) 'tympani
call instrument(4,1)   'piano
call instrument(5,13)  'pipe organ

call volume (2,255)
call volume (3,255)
call volume (4,255)
call volume (5,255)

REM LORENTZ BUTTERFLY 'MUSIC'
REM by Malcom Lichenstein
REM (Thought to do this because track
REM of Lorentz butterfly is mooth flowing
REM and so might sound that way,too).

REM I thought the result was eerie,
REM but definitely more euphonious than cacophonous

REM Use Lorentz butterfly sequential
REM values as basis for tones
REM Four functions of the x,y dimensions
REM converted to SOUND sines and played as 4 note chords
REM for durations that are f(z dimension)

'LORENTZ BUTTERFLY 'MUSIC'
'initial butterfly conditions
h=.01: h2=8/3
x=.06:  y=.06:  z=.06
window (50,50)-(178,255)
cls
line (50,50)-(178,50),1
line -(178,178),1
line -(50,178),1
line -(50,50),1
locate 4,1: color 14:Print "Lorenz Music for Tympani, shakuhachi,
piano and pipe organ.":print
color 4: locate 8,1:PRINT "Any key to stop da music! ";
PRINT "(after unspecified time elapses)":color 15
WHILE not instat: ' turbo basic quick check to see if any key pressed
  'three Lorentz (digitized) equations
  xnew = x+10*h*(y-x)
  ynew = y+h*(28*x-y-x*z)
  znew = z+h*(x*y-z*h2)
  x=xnew: y=ynew: z=znew
  xs=x+50: ys=y+50: 'all positive

'below,4 separated functions of x,y
'played (pure sines) with duration z mod 8+2
'(durations from 2/18 sees to 9/18 second)

  frequency0 = (xs*xs+ys*ys)       mod 128 + 50
  frequency1 = (xs*ys)             mod 128 + 50
  frequency2 = (xs+ys)*8           mod 128 + 50
  frequency3 = SQR(frequency0)*10  mod 128 + 50
  locate 1,1: print frequency0,frequency1,frequency2,frequency3,
  duration=z MOD 8+2
  print duration
  volume=127:

 call note(2, frequency0, volume)
 call note(3, frequencyl, volume)
 call note(4, frequency2, volume)
 call note(5, frequency3, volume)

 pset (frequency0,frequency1), frequency2
 pset (frequency1,frequency2), frequency3
 pset (frequency2,frequency3), frequency4
 pset (frequency4,frequency0), frequency1

  for nwe=0 to duration*1000
    for mwe=1 to 100:next mwe
  next nwe

  call silence(2)
  call silence(3)
  call silence(4)
  call silence(5)
wend

'PAYLOAD PROGRAM ENDS
'--------------------
'some of the routines and data which follow are not specific
'to and are not required for the payload given above.

exitpoint:
for channel =1 to 9
call silence (channel)
next channel

call MPUrst    'reset MPU to intelligent mode
PRINT "Intelligent mode"
END

SUB GetMIDI (byte)
'-----------------
     shared sta, drs, dat
     rem WHILE (INP(sta) AND drs): WEND
     byte = INP(dat)
END SUB

SUB MPUrst
'---------
do : ' rem modified by G. Landini from previous version.
while (INP(&H331) AND &H40) <> 0 : wend
OUT (&H331), &HFF
LOOP UNTIL INP(&H330) = &HFE
END SUB

SUB SendMIDI (byte)
'------------------
DO
     IF NOT (INP(&H331) AND &H80) THEN k = INP(&H330)
LOOP WHILE (INP(&H331) AND &H40) <>0
OUT (&H330), byte     'or use K for MIDI INPUT
END SUB

SUB UARTmode
'-----------
WHILE (INP(&H331) AND &H40) <>0: WEND
OUT (&H331), &H3F
DO
     WHILE (INP(&H331) AND &H80) <>0: WEND
LOOP WHILE INP(&H330) <>&HFE
END SUB

sub note(channel,pitch,velocity)
'-------------------------------
call sendmidi (&H90+channel)
call sendmidi (pitch)
call sendmidi (velocity)
end sub

sub instrument(channel,program)
'------------------------------
call sendmidi (&HC0+channel)
call sendmidi (program)
end sub

sub silence(channel)
'--------------------
call sendmidi (&HB0+channel)
call sendmidi (&H7B) 'send "all notes off"
call sendmidi (0)
end sub

Sub modulation(channel,depth)
'----------------------------
Call sendmidi(&HB0+channel)
call sendmidi(1)
call sendmidi(depth)
end sub

Sub volume(channel,vol)
'----------------------
call sendmidi(&HB0+channel)
call sendmidi(7)
call sendmidi(vol)
end sub

Sub panpot(channel,position)
'---------------------------
call sendmidi(&HB0+channel)
call sendmidi(&H0A)
call sendmidi(position)
end sub

sub expression(channel,expr)
'---------------------------
call sendmidi(&HB0+channel)
call sendmidi(&H0B)
call sendmidi(expr)
end sub

Sub hold(channel,duration)
'-------------------------
call sendmidi(&HB0+channel)
call sendmidi(&H40)
call sendmidi(duration)
end sub

Sub rst(channel)
'---------------
call sendmidi(&HB0+channel)
call sendmidi(&H79)
call sendmidi(0)
end sub

Sub bend(channel,bender)
'-----------------------
local b1,b2
let b1=bender mod 128:b2=bender\128
call sendmidi(%HE0+channel)
call sendmidi(b1)
call sendmidi(b2)
end sub

'DATA FOR INSTRUMENT NAMES
'-------------------------

'not required for the program to sound, but may be used to
'associate instrument number with name.

players:
data "Acoustic Piano 1","Acoustic Piano 2","Acoustic Piano 3"
data "Electronic Piano 1","Electronic Piano 2","Electronic Piano 3",
"Electronic Piano 4"
data "Honky Tonk Piano","Electronic Organ 1","Electronic Organ
2","Electronic Organ 3","Electronic Organ 4"
data "Pipe Organ 1","Pipe Organ 2","Pipe Organ 3", "Accordion"
data "Harpsicord 1","Harpsicord 2","Harpsicord 3"
data "Clavicord 1","Clavicord 2","Clavicord 3","Celesta 1","Celesta 2"
data "Brass 1","Brass 2","Brass 3","Brass 4"
data "Synthetic Bass 1","Synthetic Bass 2","Synthetic Bass
3","Synthetic Bass 4"
data "Fantasy","Harmo
Pan","Chorale","Glasses","Soundtrack","Atmosphere"
data "Warm Bell","Funny Vox","Echo Bell","Ice Rain","Oboe 2001","Echo
Pan"
data "Doctor Solo","Schooldaze","Bellsinger","Square Wave"
data "String Section 1","String Section 2","String Section
3","Pizzicato"
data "Violin 1","Violin 2","Cello 1","Cello 2","Contrabass"
data "Harp 1","Harp 2","Guitar 1","Guitar 2","Electronic Guitar
1","Electronic Guitar 2"
data "Sitar","Acoustic Bass 1","Acoustic Bass 2","Electronic Bass
1","Electronic Bass 2"
data "Slap Bass 1","Slap Bass 2","Fretless 1","Fretless 2"
data "Flute 1","Flute 2","Piccolo 1","Piccolo 2","Recorder","Pan
Pipes"
data "Saxophone 1","Saxophone 2","Clarinet 1","Clarinet
2","Oboe","English Horn"
data "Bassoon","Harmonica","Trumpet 1","Trumpet 2","Trombone
1","Trombone 2"
data "French Horn 1","French Horn 2","Tuba","Brass Section 1","Brass
Section 2"
data "Vibrophone 1","Vibrophone 2","Synthetic
Mallet","Windbell","Glockenspeil"
data "Tubular Bell","Xylophone","Marimba","Koto","Shakuachi","Whistle
1","Whistle 2"
data "Bottleblow","Breathpipe","Timpani","Melodic Tom Tom","Deep Snare
Drum"
data "Electronic Percussion 1","Electronic Percussion
2","Taiko","Taiko Rim"
data "Cymbal","Castanets","Triangle","Orchestra","Telephone","Bird
Tweet"
data "One note jam","Water Bells","Jungle Tune","error 1","error 2"

Dr Landini has produced a slightly different version of this program
which I am sure he will email any reader wanting to try it.  He has
inserted the "volume/3"s which personally I didn't like, and it has a
different graphic display: Frequency(n) is plotted against old
frequency(n) in colours 1,2,3,4, reduced to a small square. Old(n)s
are defined = to current frequency(n)s after the "call silence"s.The
"+50s" in the "frequency(n) ="lines have been removed./

He uses a different BASIC compiler which is not totally compatible
with TurboBasic.

'PAYLOAD PROGRAM START
'---------------------
defdbl a-Z
screen 12: cls
LET INSTRUM=13
call instrument (1,INSTRUM)
LOCATE 14,30:PRINT INSTRUMENTS$(INSTRUM)
x0 = .5  'initial condition for iteration
A = 3.98 'initial value of  "a"
LINE (0, 0)-(127 * 4, 127), 1, B
locate 1,70:Print "Variation"
LOCATE 12, 1: PRINT "x1=a*x0*(1-x0)"
LOCATE 13, 1: PRINT "a:     x1:"
locate 15,1: print "Cursor down to decrease a"
print "Cursor up   to increase a"
PRINT "I to increase instrument number, i to reduce it"
print "S to increase speed, s to reduce it"
print "ESC or RET to end"
DO
     k$ = INKEY$
     IF k$ = CHR$(27) OR k$ = CHR$(13) THEN 
            'press ESC or RET to end
      call sendmidi (&H91)
      call sendmidi (MIDI)
      call sendmidi (0)
      exit loop
     END IF
     while k$ = CHR$(0)+CHR$(&H50)  'decrease a
        A  = A - .01: IF A < 0 THEN A = 0
        x0 = .5
        k$="":k$=inkey$
        locate 14,1
        print using "#.##  ###";a;midi
        FOR I = 1 TO 200
          x1 = A * x0 * (1 - x0)
          x0 = x1
        NEXT 'settle down transients
     wend
     while k$="i" or k$="I"
       let instrum=instrum+k$="I"-k$="i"
       IF INSTRUM=>128 THEN INSTRUM=1
       IF INSTRUM<=0 THEN INSTRUM=127
       locate 14,30
       print instruments$(instrum);"       "
       k$="":k$=inkey$
       if k$="" then call instrument (1,instrum)
     wend
     while k$="S" or k$= "s"
       let speed=speed+k$="s"-k$="S"
       locate 15,30 :print "Speed ";speed
       k$="":k$=inkey$
     wend
     while k$ = CHR$(0)+CHR$(&H48)    'increase a
        A = A + .01: IF A > 3.99 THEN A = 3.99
        x0 =  .5
        k$="":k$=inkey$
        locate 14,1:print using "#.##  ###";a;midi
        FOR I = 1 TO 200
         x1 = A * x0 * (1 - x0)
         x0= x1
        NEXT 'settle down transients
     wend
     LOCATE 14, 1: PRINT USING "#.##  ###"; A;MIDI
     x1 = A * x0 * (1 - x0):        'iteration
     MIDI = INT(x1 * 127):   'scale 0..l to 0..127
     x0 = x1                 'send out the data
     call sendmidi  (&H91)  'MIDI channel 2           '(possible are
1-16: &H9O-&H9F)
     call sendmidi  (MIDI)   'send MIDI data
     call sendmidi  (100)    'send velocity
     xp=a*127:yp=127-midi
     colour=point (xp,yp)
     if colour=16 then colour=0
     PSET (A  * 127,    127 - MIDI), colour+1
     variation=colour*100
     locate 2,70:print variation;"       ";
     FOR I& = I TO 2000+speed-variation: NEXT
'note length, change according to your computer speed
     call sendmidi (&H91) 'note off
     call sendmidi (MIDI)
     call sendmidi (0)
LOOP
LOCATE 20,1
'PAYLOAD PROGRAM ENDS

'FISHTANK: A fun program in QuickBASIC.
'Fractals in animation.
'by Cecil J. Freeman.
	cls : SCREEN 9
	DIM a(1000), b(1000)
	DEFINT K, N
	FOR nx = 0 TO 48: FOR ny = 0 TO 29
	  cx =-1.3 + nx * .1125: cy = -2.1 + ny * .1448
	  u=0: v = 0
	  FOR k = 1 TO 50
	    IF ABS(u) > 10 OR ABS(v) > 10 THEN 115
	    uu = u * u - v * v + cx / (cx * cx + cy * cy)
	    r = 2 * u * v + cy / (cx * cx + cy * cy)
	    u = uu
115     IF (ABS(v) < 10 OR ABS(u) < 10) AND k < 50 THEN 140
	    IF ABS(u) > 10 THEN 150 ELSE 170
140   NEXT k
150   z = k MOD 15
	  PSET (20 + 9 * nx * .1125, 20 + 7 * ny * .1448), z + 7
	  PSET (140 - 9 * nx * .1125, 20 + 7 * ny * .1448), z + 7
170 NEXT ny: NEXT nx

	GET (20, 20)-(70, 90), a
	GET (90, 20)-(140, 90), b
	CLS
	LINE (18, 0)-(622, 302), 15, B
	LINE (20, 0)-(620, 300), 8, BF: '(? - ED)
1000 FOR p = 0 TO 160 STEP 40
	x = 500: y = 10 + p
	GOSUB puta
	GOSUB putb
	NEXT p

	FOR p = 0 TO 80 STEP 40
	  GOSUB puta
	  GOSUB putb
	NEXT p

GOTO 1000
END

puta:

DO
IF INSTAT THEN END
 ' FOR TURBOBASIC- ED
PUT (x, y), a
PUT (x + 30, y + 30), a
PUT (x + 60, y + 10), a
FOR z = 1 TO 2000: NEXT
PUT (x, y), a
PUT (x + 30, y + 30), a
PUT (x + 60, y + 10), a
x = x - 20
LOOP UNTIL x = 20
RETURN

putb:

DO
IF INSTAT THEN END
 'FOR TURBOBASIC - ED
PUT (x, y), b
PUT (x + 30, y + 30), b
PUT (x + 60, y + 10), b
FOR z = 1 TO 2000: NEXT
PUT (x, y), b
PUT (x + 30, y + 30), b
PUT (x + 60, y + 10), b
x = x + 20
LOOP UNTIL x = 440
RETURN

Rem  Bagula set 2 k monitor
Rem by R.L.Bagula 8 oct 1993