This time a number of good articles have had to be held over, but I would still be grateful for some contributions for the next issue, preferably before the end of June. From now on, I am putting the editorial and disk articles first, so that the page numbers can be incorporated automatically.

Because of the popularity of Fractint, many readers would benefit from a regular column of articles on using Fractint, especially the Formula function. The first appears this time, and I look forward to receiving suitable material for publication in future issues.

I would also be interested in material concerning the use of the Roland LAPC-1 PC sound card to generate fractal music, preferably using a compiled BASIC, and one of our readers is entering into correspondence on this, which may result in future articles on the subject. I have been sent some ideas, but at the time of writing haven't had any success. (Not that I have had much time to "play" with it.)

Once again I would urge all readers to try and persuade friends to take out subscriptions.

A letter from Dr Michael W. Ecker, editor of REC appears elsewhere in this issue. In it he is critical of some of the statements made in articles. Of course it is not that practical to edit the camera ready material submitted to Fractal Report so to a certain extent the authors are really sub-editors. I suppose that I could have an editorial board, but it would make a lot more work both for myself, the authors, and those who serve on the board and the return for that work would be out of all proportion to the time used up. Personally I like to get value for effort, whether my own or that of those that have been kind enough to support Fractal Report with articles. On the other hand, mistakes of the kind mentioned by Dr Ecker do possibly make it less easy for beginners to understand the articles, so I would ask authors/sub-editors to be vigilant with material sent to Fractal Report.

Readers may recall that last year we announced that Karen Griffin was leaving. I am now pleased to announce that I have a new companion in the form of Chrissie Loveday who is also enthusiastic about Fractals. As she comes from an educational background, she is likely to be just as efficient a proof-reader of my own material as Karen. She also has many ideas for fractal products that will be appearing in the following months. I am sure that all readers will join me in wishing Karen and Trevor the best of luck in their new life, and of course they will still be lending a helping hand whenever possible.

The change over has lead to one of my time difficulties, and so some people who sent lengthy letters probably had a long wait for replies. I ardently hope that all were answered by the time this issue appears in print, although anything quick to answer was dealt with as usual. Also, those who ordered Fractal Creations had to wait longer than anticipated, due to the publishers losing our order. However this was eventually cleared up and the books were mailed in April.

Fractal Shopper did not receive enough advertisers to proceed, but plans are in progress to issue it in a reduced form during the summer in a combined mailing with a publishers' catalogue. Maybe there will be more support for an autumn issue.

I have now got a 3�" 740K/1.4M disk drive, so can accept material on this medium in future, provided it is recorded to MSDOS standard.

Announcements

Reader's Hall of Fame

No entry again for magazine articles, I am afraid. I wish someone could get an article in New Scientist mentioning Fractal Report! However Dr Gabriel Landini mentioned us on a bulletin board called Monochrome, which is accessible through JANet.

REC begins Seventh Year of Publication

REC, the journal of computer mathematical recreation, released its Jan, Feb, Mar 1992 issues in one in April, calling it nos 45 and 46. REC's advancing letter contest was won by a contestant who mailed his reply to arrive only five days after REC had been published. Apparently in my synopsis last time I hadn't made the point clear that the letters could be advanced by more than 1. For example, JOLLY₊₁₉=CHEER. Also, advancement could be looped, ie z₊₁=A. The winning entry was NOWHERE and ABJURER.

I am offering a free set of Art Matrix post cards for the longest word with more than 8 letters that fulfils these rules that is received here from a Fractal Report subscriber by the last day of June. Let's see if we can beat the REC subscribers!

This issue contained a lot of short and interesting articles on number puzzles and tricks and numerical phenomena. In a review section, mention was made of a really weird program Timewave Zero (Dolphin Software 48, Shattuck Square Suite 147 Berkley CA94704 USA). It uses fractal "waves" generated by infinite series to predict global events. As it predicts global termination on 21 December 2012, it should not be taken too seriously.

Dr Ecker also exposed further rip-offs: Premium rate telephone lines for software support, and a $350 per year newsletter for those seeking student grants. (The logic of the latter escapes me too!)

There are a number of interesting reader reviews, including Michael F. Barnsley's Desktop Fractal Design System, UBASIC (a BASIC that has numbers with 524 "words" of eight digits and runs quickly for what it is. A 40 digit number was factored in five seconds on a 16 MHz 386SX. Available from REC for only $5 plus postage) and IFS Explorer for the Macintosh.

There was also a nice little mention of Fractal Report 20 along the lines of my coverage of REC.

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

There's Gold in Them There Fractals

Mr Curnow kindly sent a newspaper cutting from The Daily Telegraph of 17 November, 1971 which described how Professor David Sanderson and his colleagues at Southampton University had managed to use fractal analysis to determine whether gold is present in mineral deposits. They count the number of veins above a given thickness in a rock sample to determine its fractal dimension. The lower the fractal dimension, the higher the chance of finding gold.

However Professor Sanderson says that it is no quick guide to riches. "At the end of the day", he is quoted in the paper "the only way to know if there is gold there is to dig it out."

Fractint Corner: SUSY M.

by Yvan Bozzonetti

Fractals are toy formulas to experiment with. Here, I use them to illustrate an idea in a very complex mathematical and physical field: The supersymetry theory, SUSY in brief. Here, I start with the problem in modern physics:

Electromagnetism is described by a very successful theory: Quantum electrodynamics. Unfortunately, that theory is plagued with infinite quantities rendering it unusable in its fundamental form. To exploit it, physicists need a mathematical tool named renormalization. Renormalized Quantum electrodynamics works well, unfortunately, nobody understands the physical basis of renormalization.

Recent work explains why: There is nothing to understand - renormalization is false! When applied at cosmological scale, it produces a picture of the universe very different of what we see. We are definitively not in a renormalized universe.

To discard infinities we need then a new, extended electromagnetism theory. The only one at hand is supersymetric quantum electrodynamics, SUSY QED for short. That theory expands in 11 dimensions, something very hard to understand... for most people. That is not a problem for you, in some minutes you 'll be busy exploring a SUSY world.

If for you QED is not a solution, think of it as an abstract formulas packet doing something on (or in) space. For our purpose, you may as well take another formula box, for example the Mandelbrot Set.

The RM formula is such a set. Try it, with real part of P1=1, all other parameters remain at 0. Really, there is nothing new. With P1 larger than one, you get a zoom-back effect. P1 works as a cursor moved on an axis. You have immersed your M-set in a one dimensional P1 space.

Now, assume you have 11 independent parameters to move the M-set in 11 different ways. You have there an 11 dim. space! To define a point in this space, you must project it on each of the eleven coordinates. The value on a particular coordinate is given by the P parameter attached at that coordinate.

Theoretically, there must be one formula with 11 parameters: P1, P2, P3,... Each one acting on a particular Mandelbrot move. Such a formula is too long for Fractint and too cumbersome to compute for a PC. So, I have broken it into 11 separate formulae. each contains the original P1 parameter and its own parameter P2. In the 11 dimensional space, only points lying in planes with a side given by the first dimension RM can be explored. Do not worry: There is plenty of room even in this limit.

Each formula given here distorts simply the original M-set. Even if it looks strange and unfamiliar, its content is the same as the original M-set. Similarly, QED will be reworked by SUSY by the mere effect of its 11 dimensional space. Something at small scale may turn big and a big thing may be packed in the quantum domain. Merlin was using it in some motion picture well before the fractal and SUSY era.

There are strange beasts in SUSY-M, for example that insect head (RMP with ctrl-enter zoom back.)

RMCH1 with P2 from 0.1 to 0.4 gives the Giotto comet. With P2 = 0.5 some badly inspired minds start to see something other. Happily, with P2 = 1 there is a preservative and a half way zoom back allows to see a more global picture.

Really, SUSY is a big mate theory.

Everything is there:comment = {*** IMPORTANT: These formulae do not work with P1 zero. ***}

RMP (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)/(.1+ABS(PIXEL))*P2, ABS(Z)<=4}

RMCH1 (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)/(cosh(ABS(C)))^P2, ABS(Z)<=4}

RMCH2 (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)/(COSH(C))^P2, ABS(Z)<=4}

RMSH1 (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)/(0.01+SINH(ABS(C)))^P2, ABS(Z)<=4}

RMSH2 (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)/(0.01+SINH(C))^P2, ABS(Z)<=4}

RMTH (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)*(1-(SINH(ABS(C))/COSH(ABS(C))))^P2,ABS(Z)<=4}

RME1 (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)/EXP(ABS(PIXEL)*P2), ABS(Z)<=4}

RME2 (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)/EXP(PIXEL*P2), ABS(Z)<=4}

RML1 (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)*(LOG(ABS(PIXEL)))^P2, ABS(Z)<=4}

RML2 (XAXIS) = {Z=C=PIXEL: Z= (ABS(P1)*SQR(Z)+C)*(LOG(PIXEL))^P2, ABS(Z)<=4}

RM (XAXIS) = {Z=P1: C=PIXEL: Z= ABS(P1)*SQR(Z)+C, ABS(Z)<=4}

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