June 2002 - Fractint - mailman.xmission.com

Re: [Fractint] JuhYhgtFFe2
by Andrew Coppin 25 Jun '02

25 Jun '02

Ah, Mr. Lee, concise as ever! Andrew. "I read a lot of math litriture, but don't know much about it!" >From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >Subject: Re: [Fractint] JuhYhgtFFe2 >Date: Mon, 24 Jun 2002 04:39:03 -0500 > >corollary (kôr´e-lèr-ê, kòr´-) noun > plural corollaries > Abbr. corol. > 1. A proposition that follows with little or no proof > required from one already proven. > 2. A deduction or an inference. > 3. A natural consequence or effect; a result. > >lemma (lèm´e) noun > plural lemmas or lemmata (lèm´e-te) > 1. A subsidiary proposition assumed to be valid and used to > demonstrate a principal proposition. > 2. A theme, an argument, or a subject indicated in a title. > 3. A word or phrase treated in a glossary or similar listing. _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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FOTD 24-06-02 (Green Scene [6])
by Jim Muth 24 Jun '02

24 Jun '02

FOTD -- June 24, 2002 (Rating 6) Fractal visionaries and enthusiasts: When I checked my e-mail box a few minutes ago, I found among the 22 junk letters four letters that told me I had 'opted in' to something or other, two letters that were a 'reply to my inquiry', and two letters that had bounced back because I had sent them to a bad address. Curiously enough, I have no memory of 'opting in' to anything or 'making an inquiry' about anything or sending any letters to any invalid addresses. All of these letters had a line saying something like 'if this letter has reached you in error'. The puzzle of the day is why such a line needs to be included in letters that I supposedly have asked to receive. Does the sender have reason to suspect that he actually *is* sending the letter in error? If so, then the letter with the misleading subject is not an error but a deliberate effort to sell something to me. Most of these letters have no chance to succeed, particularly with me, since I have no desire to get a bogus diploma or consolidate my debts or increase my size, (I'm already a bit overweight). In addition, many of the letters are in <html> format and I have my e-mail reader set to display <html> coding as text, which makes the over-designed letters virtually impossible to read and destined for immediate consignment to the trash bin. Now that I've got that off my chest, I see that we have a fractal to at least acknowledge. The image is that of another Mandelbrot midget. This one is just different enough to make it worth the position of honor as FOTD for June 24. The parent fractal was created when I iterated the unusually simple even for me formula (Z^3)+0.357(Z^4)+C. I named the image "Green Scene". The name is purely descriptive, and based on the strong green coloring which appears in the image. The rating of 6 has become normal since the FOTD slipped to its temporary every-three-days schedule. The render time of 10 minutes can be cut by 3/4 by downloading the GIF image from Paul's web site: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Sunday here at Fractal Central featured a bit too much of a good thing. The sun was a bit too hot, the air a bit too still, the humidity a bit too high, the ground a bit too dry, and the temperature of 91F 33C a bit too warm for cat comfort. The cats in question, after a few minutes outdoors, chose to spend the day in the indoor air conditioning. Which is where I'll spend most of today while I tend to the things that need to be done. Until next time, on the 27th, take care, and always try to separate truth from fiction. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Green_Scene { ; time=0:10:28.40--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.50637533704881520/+0.000758454262473\ 48/8.225209e+010/1/80.0208434512356774/-0.02262412\ 96535609898 params=1/3/0.357/4/0/0 float=y maxiter=1600 inside=0 logmap=218 periodicity=10 colors=000AFKGJREWfCgvWAsYDq_FoaImbKkdMifPhhRfiTdk\ WbmY`o`_pbYrdWtgUviSwkRjRSiLTfBUdCScCQbCPaDN_DMZDK\ YEIXEHVEFUGETICSKBQMAPOAOQAMS9LU9KW9IY8H_8Ga8Gc7Ge\ 7Gg7Gi7Gk6Gl6Gn6Gp6Gr5Gt5Gu5Gt5BrYDpXEnXGlWHjWJhWK\ gVMeVNcVOaUQ_URZTTXTUVTWTSXRSYQSZRQ_RP`SNaSMdTLgTJ\ jUImUGoVFqVEoTEmRElQEjOEhNEgLEeJEcIEbGE_FEYDEWBETA\ EQ8EQ7EUBDXEC`ICbLBdPBfSAgWAhZ9jb9ke8lh8mi7nj6oj6o\ k5pk5ql4rl4rm3sm3tn2un2uo1vo1wp0wp0cgJKZa1Rt8NoEKk\ KHgQEbWBZa8V`7W`7X_7Y_7Z_7_Z7_Z7`Z7aY7bY7cX7cX7dX7\ eW7fW7gW7gR8hM9iIAjDBk8Cl4CmAHmGMmLRmRWmW_madmfiml\ nmqrmmjZibKeW5``BWdHRhNMlTHpYGoWGoUFnTFnREmQEmODlM\ DlLCkJCkIBjGBjFAhG9gG8fG8dH7cH6bH5aH5_I4ZI3YI3XI4Y\ K5ZM6_O7`P7`R8aT9bVAcWBdYBd_CeaDfbEgdFhfFhgHffJgfL\ ifNkePmeRoeTqeVsdXudZwd`xdbycdzcfzchzcUzSFzHIzILzJ\ NzKQzLSzMVzNXzN_zOazPdzQfzRizSkzSnzRqzQtzPwzOyzOoz\ QfzRYzTOzUFzW6zXGzRGzRGzR } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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JuhYhgtFFe2
by Andrew Coppin 24 Jun '02

24 Jun '02

Question: It's nothing to do with fractals, but what does the word "corollary" actaully mean? And while we're on the subject, what's a "lemma"? >From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com, <fractint(a)mailman.xmission.com> >Subject: Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6]) >Date: Mon, 24 Jun 2002 13:09:47 +1200 > >At 06:21 24/06/2002, Multiple Bogeys wrote: >> > "Any sufficiently advanced technology is indistinguistable from magic?" >> >> > (If anyone knows whom wrote that, I'd be interested to know...) >> >>Arthur C. Clarke...I thought everyone knew that :) > >Corollary: Any technology distinguishable from magic is insufficiently >advanced. > >Morgan L. Owens >"Your mail seems awfully slow these days..." > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp.

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Re: [Fractint] FOTD 21-06-02 (A Nebular Minibrot [6])
by Jim Muth 24 Jun '02

24 Jun '02

I wrote: >>...What has happened is that the earth has reached the >>point in its orbit where the north end of its axis is >>tilted directly toward the sun,... Morgan clarified: >So the Sun's directly over the North pole? Don't you >mean that the Earth's Northern axis is intersecting a >line drawn through the sun perpendicular to the plane of >the Earth's orbit about the sun (since the Sun's own >rotational axis is irrelevant, even if it's the same)? Yes, this is what I meant. I simplified the wording. But on the planet Uranus, the sun does appear almost directly over the north pole once every Uranian year. Jim M.

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Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6])
by Multiple Bogeys 24 Jun '02

24 Jun '02

> "Any sufficiently advanced technology is indistinguistable from magic?" > (If anyone knows whom wrote that, I'd be interested to know...) Arthur C. Clarke...I thought everyone knew that :)Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com

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Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6])
by Jim Muth 19 Jun '02

19 Jun '02

A reply to Morgan's reply is posted to the philofractal list under the subject 'Theory of Everything'. Jim M.

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FOTD 18-06-02 (Squaring the Circle [6])
by Jim Muth 19 Jun '02

19 Jun '02

FOTD -- June 18, 2002 (Rating 6) Fractal visionaries and enthusiasts: I recently got hooked by one of those science book club offers. This club gives a joining gift of five popular science books at a bargain price in return for the obligation to purchase at least one not-so-popular science book at full price within a year. The books I received are mostly about the effort to apply Quantum Mechanics to the universe at large and find a Theory of Everything. (Via something like those trendy super-strings, I assume.) (I also noticed a recent letter from Osher Doctorow on the Fractint list about the topic.) Finding a T.O.E. is fine, but is the T.O.E. the books tell of really about *everything*? So far, I have had time only to skim the books, but in none of the indexes do I find an entry for mind or consciousness. It is as though the mind that is doing the searching does not exist, or if it does, is not included in the set of everything. Maybe self-awareness is simply too spooky for any respectable scientist to take a serious interest in. Maybe it is so mysterious that serious scientists would never tackle the problem for fear of being labelled soft on mysticism. I also find myself concerned that the theory of everything, when and if it comes and whether or not it includes the mind, will be in the form of mathematics so abstruse that only the initiated will be able to comprehend it. I do not want to settle for a watered-down version in a popularized (simplified) book, which will demand faith in the words I read. I want a theory that I can think about, understand, and connect to the 'real' world. I want to be able to say, 'yes, that explains everything', and observe the proof. (I realize that this will not happen.) A theory, the proof of which can be comprehended only by the high priests of science, would be of no satisfaction at all. In fact, IMO, it would border on mysticism. But then, considering how little of the world of science the common man can actually observe, science has been bordering on mysticism for the past 100 years. I'll have many more thoughts on this topic as I work my way through the five books. And by the way, there is a fractal for today -- another midget. This one is found in a prominent valley of the fractal that results when Z^(-1.54) is added to Z^(-15.4). I named today's picture "Squaring the Circle", and impossibility we learn in high school, and rated it a not-too-bad 6. The render time of 6 minutes is not bad either. For convenience, the completed GIF image is available for download on the W.W.Web at Paul's site: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday's weather here at Fractal Central was near perfect, making for contented cats and a pleased fractalist. The temperature of 82F 28C was made even more comfortable by the dry atmosphere, and best of all, at least 2 more similar days are forecast. The cats will be ecstatic. With a day's work before me, I'm not quite ecstatic, but ecstasy is within my grasp if only I play my cards right. While deciding which card to lead, I'll get a little real work finished. Until next time, which will arrive in about 72 hours, take care, and when the theory of everything appears, be sure it really explains everything, including why we need a theory of everything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ SquaringTheCircle { ; time=0:06:28.87--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.13533630348576/-0.000841184669495/28\ 39969/1/72.5/-2.86436934102130003e-008 params=1/-1\ .54/1/-15.4/0/525 float=y maxiter=1300 inside=0 logmap=110 colors=000HSEHVGHZIHbKHeMHiOHlQHpSHsUHw\ WHzXLvZPr`SobWkdZgfbdhe`jiYllUnjQhsNrwJtzGvrMsjRpb\ WnV`kNeiFjf8od7j`7fY7bV7YR7UO7QL7LHzzz7DBwmHonJmbK\ jSMhGNf5ObBP_GQWLRTQSPVTM_UIdVFiWBnX8sY5xZAsZEnZIi\ ZMdZQ_ZUVZYQZaLZeGZqGYpHXpHWpHWpHVpHUpHUpHTpHToHSo\ HRomRoHQoHPoHPoHOoHOlJRiKTfLWcMY`N`YPbVQeSRgPSiMTl\ JVnGWqDXsAYv7Zx4_z7Wv9TrCQnENjHKfJHcME_OBWR8ST5OV2\ LU8OTDQTITSNVSSXRX_RaaQfcQkfPphPujSogUidWcbYY__SXa\ MVcGSeAPg5Ni4Rj3Uk2Ym2`n1do0gp0jl6hhBgdGe`LdXQbTVa\ P__LdZHiXDnW9sU5xTEtWMqZVmabjdkfgscjudaweUyfMzgEqb\ IhYM_TQROUJKXLL_NMaPNdROfTPhUQkWRmYSo_TraUtbUvcXuc\ Zuc`tdbtdesdgseirekrenqfpqfrpftpfvpgkcgaRgSEdUJaVO\ _WSXXXVYaSZeQ_jN`oLasS_nZZie_dl`_saVpbWmcWjdWgeWdf\ WagWahWciWejWgkWilWkmWmnWooWqpWsqWurewsozukzwhzxez\ ybzzZzzWzzTzzQzzMzzJzzGzzDzz9zz6zz3zz0zz5zzAzzFzzK\ zzPzzUzzYzzXzzWzzVzzUzzTzzSzzRzzAzzC } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6])
by Andrew Coppin 19 Jun '02

19 Jun '02

>From: Jim Muth <jamth(a)mindspring.com> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >CC: philofractal(a)lists.fractalus.com >Subject: [Fractint] FOTD 18-06-02 (Squaring the Circle [6]) >Date: Tue, 18 Jun 2002 11:54:15 -0400 > >FOTD -- June 18, 2002 (Rating 6) > >Fractal visionaries and enthusiasts: > >I want a theory that I can think about, understand, and connect >to the 'real' world. I want to be able to say, 'yes, that >explains everything', and observe the proof. (I realize that >this will not happen.) A theory, the proof of which can be >comprehended only by the high priests of science, would be of no >satisfaction at all. In fact, IMO, it would border on >mysticism. But then, considering how little of the world of >science the common man can actually observe, science has been >bordering on mysticism for the past 100 years. "Any sufficiently advanced technology is indistinguistable from magic?" (If anyone knows whom wrote that, I'd be interested to know...) Thanks. Andrew. _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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Re: [Fractint] FOTD 18-06-02 (Squaring the Circle [6])
by Franktal Gallery 18 Jun '02

18 Jun '02

Usually attributed to SF author Arthur C. Clarke. >From: "Andrew Coppin" <orphi69(a)hotmail.com> > >"Any sufficiently advanced technology is indistinguistable from magic?" > >(If anyone knows whom wrote that, I'd be interested to know...) _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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A Fractal-Related Theory of Everything (TOE)
by Osher Doctorow 17 Jun '02

17 Jun '02

From: Osher Doctorow osher(a)ix.netcom.com, Mon. June 17, 2002 1:54PM Current physics fads explain the universe and its parts (toward a *Theory of Everything* or TOE) by discrete entities (quanta) and *fields* on the microscopic level and by bending of space on the macroscopic level, with the general opinion (for what it is worth) being that the quantum ultimately will explain everything. String/brane/duality/loop theories add string tension (sort of like how stiff a violin string is) to eliminate paradoxes, of which the standard quantum field theories are full, and to try to relate the microscopic and macroscopic in *quantum gravity*, which so far has not been achieved. Is there something wrong with this picture? I would say yes, but one must look at it quite a bit to come to that conclusion. One way to determine this is to ask what mathematical tools the physicists are using. It turns out that they are almost entirely using algebraic topology and algebraic geometry. Since Creative Genius tends to be most profound when it is across verbal and quantitative fields (like Leonardo Da Vinci), and since Creative Genius tends to be heavily interdisciplinary, the almost exclusive use of two mathematical techniques (which, by the way, provide extremely few intuitive explanatory concepts and are super-abstract) arouses some warning signals. There's actually a good candidate for an alternative TOE right amidst fractal- and chaos-related disciplines provided that we also use many interdisciplinary methods. It turns out that the most characteristic feature of the universe is its expansion (or theoretically expansion-contraction), which is growth, which is quite similar to the growth feature of life. But we know from botany that life solves the *packing with growth* problem of mathematics by putting seeds and buds and so on at an angle equal to the Golden Ratio (also known as the Golden Mean - not the ethical concept). The Golden Ratio in turn is related to the Harmonic and Geometric and Arithmetic Means, especially the Harmonic Mean. Is there an equation which we can PROVE MATHEMATICALLY that might give us some handle on a TOE? Yes. Here it is: 1) (x - y)/(xy) = (1/y) - (1/x) for real x, y, with y < = x. Recall that the harmonic mean h of x and y is given by: 2) h = 2/[(1/x) + (1/y)] I have introduced the *real conjugate* of u + v for u < = v, namely u - v (any real u, v), and I denote it by an asterisk: 3) (u + v)* = u - v for u < = v Now, the universe is divided into three types of events/process (events for short): Rare (R), Fairly Frequent (F), and Very Frequent (V). R corresponds to Lukaciewicz (L) fuzzy multivalued logical implication (x-->y)L = 1 + y - x, V to Godel fuzzy multivalued logical implication (x-->y)G = y, where L and G here are supposed to be subscripts on (x-->y). L, in turn, corresponds to Logic-Based-Probability-Statistics (LBP), G to Independent Probability-Statistics (IPS), and F to Bayesian Conditional Probability-Statistics (BCP). The correspondence continues across proximity-geometry-topology. So if we can rewrite (1) in terms of L and G and either the harmonic mean or the Golden Ratio, we will have related quite a few interdisciplinary fields. Here is the rewritten equivalent version: 4) [1 - (x-->y)L]/[(x-->y)G (y-->x)G] = -2HAR*(x, y) where HAR(x, y) = 1/h. Noting that the left side of (4) is the ratio of *extreme* events in the sense that L and G are rare vs very frequent events, while the third type of fuzzy multivalued logic Product-Goguen (PG) is *mean* or *intermediate* (fairly frequent events), we recall that Euclid defined the Golden Ratio as the solution of the extreme-mean ratio of line segment lengths: divide a line segment or string into two parts, one longer and one shorter, and the original segment is then the longest, the shorter cut segment is the shortest, and the other segment is the *mean* segment. The fraction or ratio of the shorter cut length divided by the longer cut length is now set equal to the ratio of the longer cut length to the uncut length. This yields an equation whose solution is the Golden Ratio. The similarity of extreme and mean lemgths and extreme and mean frequency events is remarkable. Osher Doctorow

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