FOTD -- January 28, 2003 (Rating 8) Fractal visionaries and enthusiasts: Questions, questions, questions . . . a fool can ask more ques- tions than a wise man can answer. I'm feeling a bit foolish this morning, so I shall ask a few questions that the wise men wisely brush aside. I expect no answers, because if questions such as these could be answered in an absolute manner, they would long since have ceased to be asked. Of course there is always the chance that the questions *have* been answered but those who still ask them have failed to recognize or will not accept the answers. Would fractals exist if there had been no intelligent beings in the universe to find them? Would the potential for fractals exist if there had been no intelligent beings to invent numbers? And what of numbers? Could they exist without having been inven- ted by a human type of intelligence? Things grow more complicated. Could intelligence exist without the universe? What if a few physical constants had a different value? Does the universe exist when it is not being observed? Does it exist when it *is* being observed, or is it some kind of consistent illusion. If the universe is an illusion, what is having the illusion? And if the universe is an illusion, is the same illusion common to all observers, or does each observer ob- serve his own private world. Are the observers also part of the illusion? Finally, the ultimate question: Why is there some- thing instead of nothing? No one can give absolute answers to such questions, though many hold opinions so strong that they confuse belief with knowledge and consider their opinions to be fact. And would we even want to answer such questions, when doing so would take so much of the fun and mystery out of life? Regardless of the answers or non-answers to the questions, one thing for certain is that we have another Fractal of the Day to discuss. It is another of my ghostly evaporated images, made visible by the <bof60> inside fill. In today's case, the evap- orated version proves to be better than the normal equal-itera- tion-band version. The parent fractal, which was created by subtracting quite a bit of minus pi from quite a lot of minus epsilon, is an oversized, double-lobed Mandeloid with X-axis symmetry. A meandering fila- ment extends from the northern bud, circles around to the east and joins the southern bud. Today's scene is located on a node of this filament, not far from where it joins the northern bud. I have rated the image at an 8. This rating might be a bit generous, but I'm feeling a bit contemplative this morning, and want to do something to cheer myself. I am unable to find a satisfactory name for the image for the second time in three days, so it enters the world as "UnNamed Fractal-II". Ghosts come and go quickly, and today's image lives up to its ghostly nature. It renders in less than 2 minutes, about the same time needed to download the completed GIF file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal temperature never made it to 20F -7C here at F.C. on Monday. Combined with biting winds, the outdoor conditions were far too rigorous for the whiskers of the dynamic ones, who passed the day thankful for a warm radiator to huddle close to. Today is starting cloudy and just as cold, with snow threaten- ing. We'll see how the dynamic ones take the harsh cold. Regardless of how the dynamic ones take the cold weather, I shall take it quite well, especially since I expect to be out in it only a few minutes. Until next time, take care, and know that fractals are mystical things that are normally invisible yet can be photographed. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ UnNamed_Fractal-II { ; time=0:01:44.52--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+13.1945886431/+21.1419337772/635.8224/\ 1/150/7.2211701895863456e-011 params=-23.3/-3.1415\ 9265358979/23.3/-2.71828182845905/0/1e+100 float=y maxiter=400 inside=bof61 logmap=20 periodicity=10 colors=000000000000000L9BDK85J64NA4QE3UUSXS3_YWcX2\ febiczz6hwHZtSPrb0m0hzzEnoMogVp_bpTKiL2bD8cIEcNKcS\ QcXWcaacffck``jWZjQWiLUiGSiLSmPSpTSsXSv`Sy`Ut`Wp00\ 0`_g`ac`c_PL8WBMb1_iMYeN`bOc_PfXQiUQlTRjSSiSTgRTfQ\ UeQVcPWbPWaOSbNPcMLdLIeKEfJBfPMbUW__fWdpTizQNw2Os9\ OoFPkLPgRPcXQ_bQWhQTnTUiWUeZVa`VYcWTfWPiXLkXHbVFUU\ DLSBCR94Q8hpZco__n`WnaSmbOmbSa`WQZ_EXb2VkKQt`MmdNg\ hOalPQgxSerUcmWagY_b_YXaWScUMeTHhWLjZPmaTocXrf`tid\ wlhynkdqLbhT`_`_Rh`U``XTa_LaaEQ6tszkpnfnbashXxnTfY\ 6dSFcMObGXdKSfONgRIiVEjY9000md0XVCHMO1DZRfJPbOOZTM\ WYLSbJPgILlHIqREr_Bsi7tr4up6pn8ll9gjBchDZfEVdGQcHM\ MtyMbBQeGUhKXjP`mTdpYgrakufnwjgnlaemWYnPPoJHpD8q70\ r69t6Hu5Pv5Yw4ex4myC64K86S98_BAgCCnDEcHCTKBINA7Q96\ RC5SE4TG4TJ3UL2VN2VPATMHRJPPGWNEcLBjJ8UcUyG3mD7bAB\ S7FH5JKGHNQFQ_DTiBVsAL9VOIVQQVSYVUeVRdXOcYLcZIb_Fa\ `Caa9`b7`c4__2ZWEUOPQH_LA } 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==================================