FOTD -- October 30, 2002 (Rating 6) Fractal visionaries and enthusiasts: Since yesterday's FOTD I have been pondering, (I ponder a lot). I have been pondering the multiple-worlds interpretation of Q.M. If taken literally, this theory implies that there are a near infinity of myselves in a near infinity of alternate universes, living every possible life I might have lived. At the same time, experience shows that I can be in only one place at a time. Can I trust experience? If so, who then are these other versions of myself? And how can they be different versions of myself? If they merely look like me, they are not me, they are my identical twins. Are they unconscious auto- matons? If so, I might be justified in claiming that everyone in this world but myself is an automaton, an unconscious reflection of someone who is conscious only in some remote alternate universe. And when, if ever, does an alternate version of myself stop being me? In a world where I merely blink one extra time, the other version is clearly myself. But what of the worlds where I am born a woman in Mongolia in the year 1347? How can that person be said to be me if I am not aware of her? What of the worlds where I am born a Neanderthal woman? And the worlds where I am born an ape or a bacteria, or a mud-skimmer on a planet in the Virgo cluster? Taken to the extreme, it appears I might end up living through every possible experience every possible conscious living thing could possibly experience. There would even be a world where I am one of the fractal cats, and the cat is me! (But, unless fractals are conscious, there is no world where I am a fractal.) Or is there? Maybe if I properly understood certain esoteric things such as coherence-decoherence and consistent histories, paradoxes such as the above would vanish, or at least become less puzzling. Alas, I am not among the anointed high priests of science, the initiated few to whom these mysteries are revealed by means of arcane mathematics. Today's fractal might not be aware of itself, but I am certainly aware of it. And it is no puzzle at all. The generating expression takes a bit of (1/Z), adds a tiny bit of Z^8 to it, and finally adds (1/C). The resulting fractal is a bulging Mandeloid rotated 180 degrees, with the period-5 buds being the largest. Today's scene is located on a side branch near the tip of the tiny main stem that extends out from the tiny period-2 bud. Most of the worth of the image lies in the fiery coloring. The underlying shapes are nothing spectacular. After an exhaustive study, I decided to rate the picture at a 6. I named it "An In-Depth Look" because of the time expended on the exhaustive study. In most cases, the render time of under one minute will be faster than the download of the completed GIF image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The decision is left to the individual fractalist. The weather here at Fractal Central on Tuesday was truly abysmal. A cold steady rain mixed with ice pellets, a temperature of 37F 3C and a biting northeast wind kept the dynamic cats housebound the entire day. Even a tuna treat failed to pull them totally out of their funks. And today is once again starting out abysmally. It will make no difference for my work, but the cats will have another bad day. Until tomorrow and the next FOTD, take care, and take it one fractal at a time. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ An_In-Depth_Look { ; time=0:00:59.10--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip inside=0 center-mag=-0.74231185074844860/+0.000001268805934\ 57/1.319056e+012 params=100/-1/0.01/8/-0.951/0 float=y maxiter=1200 logmap=45 periodicity=10 colors=000O50hRCX50dC0lK0sR0zY0zb0zi2zpCztMzzUzm`z\ jTzRKQUA_O0hJ0gK2gMAfOKfPSdR_dSfdSlkXhq`fvdczh`zlY\ znWzi_ydasZdkVhdPkXJnQEpSR`T`KUi2XffYezvCzuPztazsl\ ysvx07kHSiUhhfxgqzghvk_fnQPqH5tMHlQSdT`YXiQ_qJcz9f\ z0lsAsbKxhPzlTzpXzzoyykuvhptdlqahn_WiUHePMb_QaiU`t\ YZz`YzgSznOntHazCPz7A9dpAXlAPiAHgQMicRloUnzYpz`qzf\ pqmogtnWznKzl7zk0zkEznUzohzpvzqzOzzVxz`uxetskqlqog\ vnazkXzilzczzYzyTzzNpzHczCQz5Az00z04z0Cz0Kz4Tz7_zA\ fzEAXPEVSHUUKSXNRYQP`TOcUMdYU_``WcfSglMisHlyCoz7pz\ HqvPstWtpaulivipxevybzzezzhyzixzlvzmuzptzqsxzShz0F\ zuMtvSlvWdv`VvfMviCvdJy_PzTXzNazHfzAlzSXpfEXt5AhE9\ XV7Mi57x40z40z70zA0zE0zH0yK0vN0tQ0qTCnMPmF_l9ik2ti\ 0haSYUqNKzKOzHRzFSzCVz9Yy7ZvCYsHXoMVkQUgUScYR_aPWd\ PTzFXxEXuEXsEXpCXnCXkCXhCXyfUzzTzuUpkUc`USPUCCU05U\ tSzsJ`sA0oK4lSFiZPfeYclg`soatqatsautauuavvavxavyQv\ pCvg0v_9mNzzazzpzzzzzltkW } 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==================================