September 2003 - Fractint - mailman.xmission.com

A Few Comments on the Number 666
by mdoctorow＠comcast.net 03 Oct '03

03 Oct '03

>From Osher Doctorow Ph.D. I am glad to notice the heavy volume of replies to my Feigenbaum Constant and Weak Force posting, although it is amusing to notice that they mostly concern my comment that I'd forgotten what 666 means. I hadn't been reading the replies because I'd been watching the California Recall Election for Governor here in California, which may explain why I had trouble recalling what 666 means (?). Actually, I looked up 666 as internet keywords ("The number 666") after seeing the replies and apparently in Revelation verse 18 Chapter 13 the Number of the Beast 666 is mentioned, which is taken to mean the Devil. Also there are some hysterically funny jokes at geocities.com about 666, including extremely high precision 666.0000... and so on. Is there anything that one can learn about fractals or chaos from 666 aside from Jerry Iuliano's and my and your interesting comments? Well, this got me to thinking after reading the comments and looking up the sites mentioned: what exactly was 666 doing in the Gospel or New Testament? According to one site, 6 + 6 + 6 = 18, which is the verse in which it appears, and chapter 13 is supposed to represent death because of the 13 traitors, etc. Well, what if 666 was put into chapter 13 verse 18 by whoever wrote that verse knowing that 6 + 6 + 6 = 18? What would be the purpose of this? Let's put on our Fractal Thinking Caps (FTCs, which also stands for Federal Trade Commission incidentally), and think about this. Whoever wrote that wanted to point out that Armageddon was coming. I suppose that a visitor from Outer Space looking at the ensuing history of humanity would tend to agree, although not quite in the literal sense. But what better way for the writer of ch. 13 verse 18 to emphasize the importance of his/her verse and chapter than by a mystical emotional number which succeeding generations would remember more than the usual warnings of future doom? This moves us into the rather non-mainstream (if not dubious) field of historical reconstruction, but wait! There's more. What would give a scholar whose main literary interests had been the Old Testament an interest in 666? According to one of the sites, this was related to the worth of the gifts received by King Solomon from Egypt (I think via Queen Sheba). So it started in the Old Testament. According to this interpretation, it was simply appropriated into the New Testament. This isn't the first such case where Old Testament ideas were used in the New Testament. But what does King Solomon have to do with anything in Armaggedon? Well, Queen Sheba was so to speak his downfall (well, in a sense - I suppose that Bill Clinton would have other comments on that). His people had been slaves in Egypt. Also, King Solomon was the smartest King of Israel. To my recollection, he was into numerology in addition and was stated to have "spoken with animals". This would appeal to New Testament writers and scholars probably. Ladies and Gentlemen, what we may have here is a number 666 that represents not the Devil but Number Theory - the birth of Number Theory which led to fractals and chaos and to where we are today (give or take some problems off the internet). As for the member of Fractint who has the social security number with 666 in it, the person is not the Devil but a prospective assistant Moderator of Fracint! I've forgotten his/her name, but I'll look it up as soon as there is another pause in the California gubernatorial race. Osher Doctorow

7 8

Re: [Fractint] Video drivers
by Russell Walsmith 01 Oct '03

01 Oct '03

I have XP pro on a laptop and XP Home on my current desktop and I've yet to see any difference in perfomance in regards to display. My 'default' display mode is shift/F7 (i.e., 1024x768 with 256 colors); what happens, Marty, when you try that? Russ -- --------- Original Message --------- DATE: Tue, 30 Sep 2003 00:39:54 From: Alex Dukay <alexdukay(a)rogers.com> To: Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com> Cc: >Marty, >I'm running Widows XP Home on a Dell laptop (Inspiron 8200) with an Nvidia >card. And to my amazement Fractint runs in high resolution mode...I'm no >expert but I would bet it could be XP pro - try the home version. Perhaps >others have other solutions. >Alex > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

3 3

FOTD 30-09-03 (The Sun and Moon [7])
by Jim Muth 30 Sep '03

30 Sep '03

FOTD -- September 30, 2003 (Rating 7) Fractal visionaries and enthusiasts: Having found, or rather created, a spare moment, I used that time to find a very slow fractal, which I could let develop on my fractal machine while I accomplished other things on my other machines. The fractal took almost 3 hours to complete, and when it was finished, I named it "The Sun and Moon". I can give no reason for choosing such a name. Perhaps someone viewing the image can supply a reason. The parent fractal is an oversized something, too distorted to be called a Mandeloid, which consists of little more than two prominent valleys. Today's image is located rather deep in the larger valley. This valley must be of the 'Seahorse' variety, because the midget I found in it resembles 'Seahorse Valley' midgets more than 'Elephant Valley' midgets. When all was said and done, I rated the image at a 7. But even a 7-rated image is not worth a wait of almost 3 hours. So I recommend downloading the image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Things are coming along reasonably smoothly here at F.C. By working long days, I am getting the old work out a little faster than new work is coming in. And if the present trend continues, things will eventually get caught up. It is far too early to say when 'eventually' will arrive. Monday was a fine early Autumn day here at Fractal Central, with lots of sun and a crisp temperature of 66F 19C. The fractal cats enjoyed themselves in the yard for two hours in the afternoon, and settled for the evening without a treat of tuna. As for me, I still have enough work backed up to keep the 12-hour days going for another week or two. But the backlog will 'eventually' be cleared and the daily FOTD will resume. Until next new FOTD, whenever that is, take care, and keep checking those old classic FOTD images. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Sun_and_Moon { ; time=2:55:18.39--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-2.99293075927805800/+0.248764115526592\ 00/733067.4/1/-135/-8.75853476550725318e-009 params=1.3/0.9/-1.3/-0.9/0/0 float=y maxiter=42000 inside=0 logmap=3014 periodicity=10 colors=000i`Uj`Tl`Sm`Ro`Qp`QeVGWQ6XP7YP8ZO9_OA`NBa\ NCaMDbMEcLFdLGeLHfKIgKJgJKhJLiIMjINkHOlHPlHQeKMZMJ\ SOFMRCFT88V52X25Z58_8B`ADaDGcGJdILeLOfORhQTiTWjVZk\ Y`l`cnbfoehphkqjnsmptpsurvvuxwwvvtturruoptmntjmshk\ reircgq`eqZdpWboU`oRZnPXnMVmKUlHSlFQkCOkAMj7Lj5OiB\ RiHUiNWhTZhYahccgifgoigukgzmXhoNSqDBnFElHGjJIhLKeN\ McOOaQQ_SSYUUVWWTYYRZ`P`bMbdKdfIfhGhjEilBkn9mp7or5\ qt3rv3qs3qq3qo3qm3qk3pi3pg3pe3pc3pa3p_3oY3oW3oU3oS\ 3oQ3oO3nM3nK3nI3nG3nE3nC6kD8iEAgFCeFEbGG`HIZIKXIMU\ JOSKQQKTOLVMMXJNZHN`FObDPdAQf8Qh6Rj4Sl2Sm4Qm6Pm8Om\ ANmCMmELmGKmIJmKImMHmOFmQEmSDmUCmWBmYAm_9ma8mc7me6\ mg5ke4jd4hc4gb4fa4d_4cZ4aY4`X4_W4YV4XT3VS3UR5TQARP\ FQOKOMPNLUMKZKJcJIhIHmMFrQDwTBzSFzRKwQMmPOcOQVNRSM\ SPLTMKUKJWHIXEHYBG_9IaAKcALeBNgBPiCQkCSmDToDVqEXsE\ YuF_wFayGbzGdzHezHczJazL`zMZzOXzQWzRUzTSzVRzWPzYNz\ _Mz`KzbIzdHzebzXdzWezVgzV } 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==================================

1 0

The Feigenbaum Constant and the Weak Nuclear Force
by Bill Jemison 29 Sep '03

29 Sep '03

Lee, Lots of nice images in that gallery! I particularly liked "I'll Bite" and, if I remember correctly, "Bon Voyage" (or whatever the name of the one with the "ship" in it is). Great stuff! Bill

2 1

Classic FOTD 31-12-97 (Galaxia)
by Jim Muth 29 Sep '03

29 Sep '03

Classic FOTD, December 31, 1997 (Galaxia) Fractal visionaries: (This discussion, as will be all Classic FOTD discussions, was written on the date in the subject line.) Today's fractal is the final one I'll post this year, so I wanted it to be a good one. But being very busy today, I had no time to find a new one. As a result, I went to my collection of fractals and pulled out one that had been lying dormant and unappreciated for several months. After a few quick minor changes to the color palette, I renamed it "Galaxia", and here it is. I think it's acceptable. The image is actually the Z^500 Mandeloid, turned inside-out, and with the number of arms reduced to two. The soft halo represents the combined glow of billions of stars, while the foreground could well be the ring of cosmic dust that exists in the galactic plane. The completed image has been posted to Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html I must run now, so that's it for today. But tomorrow, I'll be here again with another wonder-fractal. Until then, take care and Happy New Fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START FILE================================================== galaxia { ; 40 seconds on a P200 -- SF5 reset=1960 type=formula formulafile=jim.frm formulaname=JimsCompMand center-mag=-4.61853e-01\ 4/2.57017e-014/0.04201427/1/-37.5 params=500/0/-501/0/30000/0 float=y maxiter=1200 bailout=25 inside=bof60 logmap=yes periodicity=10 colors=00INFaICSKEULDYMDZND_ODaPEbQEcQEdREfSEgTEhU\ EiVEjWFlXFmYFnZFo_Fp`Fr`FsaFtbGucGwdGxeGyfGzgHzhHz\ iHzjHzkHzlHzmHznHzpEzoFznGzmIzlJzkKzjLziMzhOzgPzfQ\ zeRzdSzcTzbVzaWz`Xz_YzZZzY`zXazWbzVczUdzTfzSgzRhzQ\ izPjzOkzNmzMnzLozJqzKpzLpzLozMozMnzNnzNmzOmzOlzPlz\ eboeboeboebodbodbodbodbodbodbodbocbocbocbocbocbocb\ ocbocbobbobbobbobbobbobbobboaboaboaboaboaboaboabo`\ bo`bo`bo`bo`boaanabnabo`co`co`do`dp_ep_ep_fp_fq_gq\ ZgqZhqZhrZirYirYjsYjsYksYksXltXltXmtXmtWnuWnuWouWo\ uWpvVpvVqvVqwVrwUrwUswUsxUtxUtxTuxTuyTvyTvySwySwzS\ xzSyzRyzRzzRzzRzzTzzRzzQyzPxzOwzNvzMuzLtzKszJszIrz\ HqzGpzFozEnzDmzClzBkz9kzAjzAjzAizBizBhzBhzBgzBgzCf\ zCfzCezCezCdzCdzDczDczDbzDbzDazEazE`zE`zE_yE_yE_xF\ ZxFZwFYwFYvGXvGXuGWuGWtGVtGVsHUrHUrHTqHTqHSpHSpIRo\ IRnIQnIQmIPlIPkJOjJOiJNhJMgJLfJKeIJdHIcGHbFGaEF`DE\ _DDYCCWCBUCASB9QB8OA7MA6K } frm:JimsCompMand {; Jim Muth z=c=pixel: z=z^p1*(c^p2)+c, |z| <= p3+100 } END COMBINED FILE===========================================

1 0

Re: 666 Meaning
by JackOTradez 29 Sep '03

29 Sep '03

Although not wishing to continue the divergence from the normal subject, I wish to point out something here; I have always had a mystical interest in numbers, numerical ratios, numerology, etc. Some write this off as para-science nonsense, but I believe many of the keys to the Universe are hidden in numbers. As The Angel Gabriel told the children during a recent visit to Earth: "Study your math - it's the key to the Universe". The prevalance of numbers like the Golden Ratio and Feigenbaum constants has always fascinated me. I for one, believe the entire Universe is a Fractal, a Chaotic ("complex") System on an infinite scale that even it's very Creator can not predict with 100% accuracy; that then would be the whole point of existence - an experiment. Each of us are infinitesimal parts of an infinite chaotic system; what we do in our lives may be insignificant now, but may have ultimately major consequences in the far future. Sort of like very small changes affecting weather prediction over time (think Lorenz). The so-called "prophesies" are necessarily vague and not exactly predictive - they can't be. They are the equivalent of our weather predictions for next week - it may be close, but there is always uncertainty and intrinsic error. Consider this: Assign a number to every letter of the alphabet, 1 thru 26 multiplied by 6. Thus A=6, C=18, M=78, etc. all the way thru. Spell the word COMPUTER. Add it up. "Let he who hath wisdom understand ..." It is 666. "But that is only in English" you may argue. Well, have you seen technical papers in other languages? Certain words in English are ubiquitous in all languages, simply because they or what they mean were discovered, or are a product of, America, and there were or are no analogous words in that native language. It is strange to see a paper with Asian characters writing, and English words like "computer" peppered here and there! Computer=Antichrist? Could be. See Revelation 13:15-18. "And he had power to give life unto the image of the beast, that the image of the beast should speak ..." Artificial Intelligence? Robotics? Speach recognition, processing? Artificial speach? All these things exist today, if in rudimentary form, but how about a few years from now? A super-computer that is genuinely intelligent, (self-aware?) and can speak can not be too far off. "And he causeth all ... to receive a mark in their right hand or forehead ..." , "And that no man may buy or sell that he have that mark ... or the name or number of the beast ..." We have had credit cards for a long time, with the advent of chips in cards in recent years, the move to a cashless society has been predicted for some time - it may be very soon. We already implant microchips in pets to track them; some are seriously suggesting doing it to people. The technology is already here, all that stands in the way is politics (for now). First convicts and criminals, then the rest of us. It is also being seriously suggested that microdevices be implanted in people at birth, and upgraded ("flashed") over time in life to contain all info about that person, identification, life, medical, finances, occupation, everything. Also it would be used for commerce and financial transactions - eliminating both cash and credit cards! There was a chilling article on this in one of the cyber magazines recently (WIRED I think). You just wave your arm in front of the scanner ... Sounds good for convenience and security, but ... Thus a person without this chip ("mark of the beast") would not be able to function in society. Those who control the chips (computers and their operators in the central govt) would in effect totally control all of us and our lives. "And he causeth all ..." Something to panic about as a new week begins. But remember, as prophesies go, these are things that may come to pass, not necessarily will come to pass ... BTW, some of my new fractal animations are kick-A! Stay Amazed. JoTz

1 0

Please lets move the political commentary
by Tim Wegner 28 Sep '03

28 Sep '03

There are many other lists for politics. Tim

1 0

Re: The California Gubernatorial Campaign...
by Jim Muth 28 Sep '03

28 Sep '03

At 08:21 AM 9/28/03 +0000, Osher Doctorow wrote: <snipped> >2. Ethnic prejudice only works from majority to minority, not in the reverse >direction if we are to believe the current Recall speeches and actions. It gets worse than this. Here in Baltimore, a group that comprises 65 percent of the total population is called a minority group. And speaking of philosophical things, I heard people on the radio seriously talking about bringing a class-action law suit against God for sending the hurricane that caused the power outages and the inconvenience of no lights or TV for 5 days. As God's representatives, and because God would not be expected to appear in person, the churches would pay the awards. Too bad this is not connected to fractals and I have no time to continue. But sometimes I wonder whether 1+1 really does equal 2. Jim M.

2 1

[Fractint] A Controlled Growth Mandelbrot Riccati Equation of the Universe
by mdoctorow＠comcast.net 28 Sep '03

28 Sep '03

>From Osher Doctorow Ph.D. The renowned Professor Peebles of Princeton University in 1993 or 1994 devoted a few pages of his volume on Astrophysics to showing that a fractal model of the Universe appeared to disagree with various radiation results under the most common model. However, since the Universe now appears to be divided into Rare Event/Process, Fairly Frequent Event/Process, and Very Frequent Event/Process regimes or parts, which were not considered in Peebles' work, it's probably time to look at fractal and chaotic models of the Universe again. The Mandelbrot set in polar coordinates has cardioids of type: 1) r = a1(1 - cos(u)) where r can be intuitively thought of for our purposes as the distance from the origin or pole to a point on the cardioid and u is the angle which r regarded as a line segment makes with the positive x-axis or polar axis. I don't know how familiar the different members of Fractint are with calculus, so I'll assume that nobody knows calculus and just gives the result from calculus, letting v be the velocity or speed of u with respect to time at each instant of time and a be its acceleration with regard to time, and "speed of r" refers to its speed of change in time, etc.: 2) speed of r = a1vsin(u) 3) acceleration of r = a1asin(u) + a1(v)^2 cos(u) Here adjacent letters mean multiplication, so for example a1vsin(u) means a1 times v times sin(u), and ^2 means square so that (v)^2 is the speed squared. There is a space between (v)^2 and cos(u) to make reading easier, but they're actually multiplied. Equation (3) is a Riccati differential equation growth control type equation in v. Nowdays, most people learn sine and cosine functions in algebra courses already, so if anybody isn't familiar with them, just look up keywords like graphs of trigonometric functions on the internet. They're basically up and down wavy lines like hills followed by valleys followed by hills followed by valleys followed etc. I'm going to ignore the third dimension of space and concentrate on a two- dimensional model for simplicity, although a "round cardioid" in 3-dimensional space may be more applicable to the universe. The above equations tell us that the main results of astrophysics and cosmology such as the expanding universe and the recently (as geological time goes so to speak) accelerating universe can be modelled by the above equations provided that the velocities and accelerations of the angle u are properly chosen in certain parts or intervals of time. For much of the history of the Universe, there doesn't have to be much "control" of v or a, but periodically sine and cosine (abbreviated sin( ), cos( )) graphs become negative, and since two negatives multiplied make a positive, in those intervals of time v and/or a has to be made negative. This doesn't mean that the Universe slows down or decelerates, only that the angle u with which it traces out a cardioid in the Mandelbrot set decreases or decelerates in time. A slight problem concerns the interpretation of r as both the line segment from the pole to the cardioid and the interpretation of r as the "principal radius" of the Universe or for short the radius of the Universe. We could make r ultimately extremely large by choosing a1 in r = a1(1 - cos(u)) to be very large - far larger than we're likely to observe with current astronomical technology. Some people might argue that a1 should change in time, at least a little over long intervals, and in that case we get what might be called a time- generalized cardioid. So in a sense we can have our Chaos and eat it too. :>) Osher Doctorow

1 0

Classic FOTD 29-04-97 (Monster)
by Jim Muth 28 Sep '03

28 Sep '03

Fractal of the day, April 29, 1997 Fractal visionaries: Today's fractal is something a little different. It is a warped Mandelbrot created from the basic Mandel formula in Fractint, and colored using the ranges feature. There are only 10 colors in the entire picture, but those ten colors had to be carefully adjusted to create the three-dimensional effect of the foreground monster arms covering and enveloping the blue remains of the classic Mandelbrot set. I have always been fascinated by the way perturbed points, no matter where they start, if they don't escape first, eventually settle into the same orbits as points that start at 0,0, giving a ghostly background image in the high iteration range. The effect is almost one of independent but overlapping fractals, as this picture, which has been posted to ABPF, illustrates. Jim Muth jamth(a)mindspring.com START PAR FILE=================================================== monster { ; Draw time 2 minutes on a P200 reset=1950 type=mandel passes=1 center-mag=-0.25810954616588430/+0.6410480167014\ 6280/76.36852 params=0.777/-0.555 float=y maxiter=32500 bailout=100 inside=0 logmap=yes symmetry=none periodicity=25 ranges=0/-1/300/600/1000/1600/2400/3600/500\ 0/10000/32500 colors=000N9D`OKPTsPVz0cp0ew0iz0mz`\ kzYmwVpzSPRPSVMWYr0s`IiSzN<5>KbZyx2<2>TdT9Id<5>IX\ `oUH<5>RYWNZZHRH<2>JXWyiQ<4>Q__vzd<2>TeaUeZSc_Qb_\ gbY<2>ZNW<4>hL9dgS2Z7<2>f11<3>PbaXMNSRSNVXGhXHdZI\ a_IbR<5>J_ZJZ_LKL<6>JYZjUh<2>QYba6J<5>LVZdDw<5>MW\ cEFDHPPGeb<5>J_`ScG<6>KZZbRe<3>NYaYKp<6>KYb1`D7_L\ DZTjYN<3>OZZV3T<6>KV_MT9U`iyR_jU`XX`eQX<5>MY`vuC\ <5>OaYrVs<6>NZba69SLN4Lf9QdEVbC2X<3>IT`cYDLV1<5>\ JZWYum<6>K`a1I_<4>GX`pCW_OZZVD<5>LZYBT8<2>HYUez1\ UlJT57<6>KWYhrBWhOgOk<6>MYa } END PAR FILE====================================================

1 0