FOTD -- February 11, 2003 (Rating 6) Fractal visionaries and enthusiasts: The exponent of Z in today's image -- 1.5596104695 -- is a slightly more accurate refinement of the exponent that created yesterday's lowly image. This number, when raised to the power of itself, comes as close to exactly equaling 2 as is possible to calculate on my 10-digit pocket calculator. The difference in the resulting parent fractal is insignificant. The improvement in image quality is a result of my better fractal luck, plus a bit of skill. Today's scene could just as easily have been found in yesterday's parent fractal, if I had searched for it in today's area. The numbers create the fractal universe; the fractalist must find the goodies in the universe. I named the image "The Key". I have no idea what the key is supposed to unlock. It could be the door to enlightenment, the door to wonder, the door to mystery, or my favorite door -- the door to reality. Unfortunately, even though I now have the key, I have yet to find the door, so the mystery will remain unanswered. The parent of today's image resembles a mis-shapen M-set, with its nose pointed southwest. Today's scene is located in the 'East Valley' of this M-set, which is located off-center on the north-northeast shore of the main bay. The little midget at the center, shining golden in its isolation, was discovered entirely by luck. I found it by toggling into and out of color-cycling mode and searching for points on the screen that blinked. I often use this trick when searching for midgets, but in order for it to work, the inside must be set to the number zero, which in turn must be set to a very dark shade. In fractals of this exponent range, there are very few clues to the location of midgets. Sometimes a convergence of discontinu- ities points to the midgets, sometimes not. Sometimes I simply get a feeling that a certain feature holds a midget, and some- times I am right. The rating of an above average 6 shows that midgets which exist in fractals with exponents of Z in the range between 1 and 2 need not be the nearly hopeless jumble of disorganized bits and pieces that spoiled yesterday's image. The render time of 8 minutes is a bit excessive for an image which, even though it rates 3 points above the image of the day before, is still only slightly above average. The good news is that the wait to see the image can be largely eliminated by downloading the pre-rendered GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> As I mentioned in yesterday's discussion, when I became familiar with the consequences of relativity, I was forced to give up the comfortable and intuitive world image that I, along with most everyone else, had developed in the formative years. No longer could I consider time and space to be two separate things. I now needed to see them as two different ways of seeing the same thing -- spacetime. No longer could I assume that the present moment of time exists throughout the universe. There could be no universal moment of time any more than there could be a uni- versal point of space. Distance and time no longer had absolute- ly fixed measurements. Mass turned out to be a different form of energy, and mass also was no longer fixed. And most impor- tantly, at least to me, was the realization that the universe is actually four-dimensional. But when I discovered relativity, the world, as strange and counter-intuitive as it had become, was still out there, real and almost solid. It seemed counter-intuitive only because in our day-to-day lives we experience such an infinitesimally small range of its vast extent. Then I became interested in quantum mechanics, and my philosophi- cal problems grew far greater but far more interesting. If all goes well, I'll discuss this tomorrow. At this point I will say only that anything based on the assumption of the existence of an independent, objectively real world is opened to cross-exami- nation by the implications of Q.M. The occasional light snow continued most of the day Monday here at F.C. It never amounted to much, but with the temperature at freezing, was just enough to keep the dynamic ones confined to quarters, wishing for better things. The better things eventual- ly appeared in the form of a tuna treat. Today is starting sunny but very cold, with deep snow on the ground. It remains to be seen how the duo will react. I see it's past time for me to get busy, so until tomorrow, take care, and wonder about what to wonder about. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ The_Key { ; time=0:08:14.28--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.47182282050367800/+0.633258130587982\ 10/3329459/1/-67.4999999978284535/-7.9310562145495\ 922e-009 params=1.5596104695/0/-80/0 float=y maxiter=3600 inside=0 logmap=197 periodicity=10 colors=000maIkaJhaKfaLcaM`bNYbOWbPTbQQbRNbSKbTBWWD\ QYFK_IEaK8cM2eP5bS7_VAYYCV_FTbHQeKOhMLjPJmRGpUEsWB\ uY9rWAoUBlSCiQDfOEcMF`KGYIHVGISEJPCKMALJ8MG6ND4OA2\ OE1QH1RK1SN1UQ1VT1WW1YZ1Za1_d1ag1bj1ch2af3_d3Yb4X`\ 4VZ5TX5SV6QT6OS7NQ7LO8JM8IK9GI9EGADEABCB9BB8EFCGIF\ JLILOLORPQUSTXVV_YYca_fdbigdljgonirqlutnxwftx_pyTm\ yMizFfzCeqAdh8c_6bR4aI2`A1dN1hZ1lj1pv4ms7kqAioDgmG\ ekIbiL`gOZeRXcUVaWT_VUZUU_TU`SVaRVbQVcPWdOWeNWfNXg\ MWfLVeKWdJVcIVbHVaGV`FV_FVZGWYGWXGWWGWVGWUGVTGUSGU\ RHUQHUPHUOHUNHUMHUMHUMHUMHUMIUOIUPIUQJSRJRSJQTKPVK\ PWKOXLKYLIZLI_MJaMKbMLcNMdNNeNOfLPgKQhIRiHSjFTkEUl\ CVmBWnAXn9Ym9Zl8_l8`k7aj7bj6ci6ei5gh5ig4kg4mf4ofCq\ bJs_RtXYuTevQlwNjxLhyKfzJdzIczGazF_zE_zDbzCezAhz9k\ z8nz7qz6tz4wz3zz2zz1zz0zz1zz1zz2zz2zz3zz3zz4zz4zz4\ zz5zz5zz6zz6zz7zz7zz7zz9zzBzzCzzEzzGzzHzzJzzLzzMzz\ OzzQzzRzzTzzDzzEzzFzzGzzH } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================