FOTD -- November 02, 2002 (Rating 4) Fractal visionaries and enthusiasts: Many years ago, when I was just discovering science, I became fascinated with the atomic world. My fascination was caused by a story I read about a man who begins shrinking. I forget the name of the story, (it might be "One Who Shrank"), but in it the man is placed on a block of very dense metal and shrinks until the atoms of the metal appear as large to him as stars and planets. He eventually lands on an inhabited planet, where they tell him that they have seen him coming in the sky for many years. As he continues to shrink, he finds that the atoms of this sub-atomic-sized world are also planets of still smaller worlds, ad infinitum. When I read it, the idea seemed sensible enough, so I promptly went to the local library to read about these miniature inhabited worlds that might exist within the everyday objects around us. But instead of alien civilizations, I found the world of quantum mechanics, where, unless one is a mathematical genius, (which I was not), nothing makes sense. I found that electrons, for example, are not objects in the everyday sense, but clouds of probability, where some indefinable non-thing has a certain chance of existing for an indefinable moment of time. I found that, for electrons, and all atomic particles for that matter, the very concepts of object and location are fuzzy at the best. But my small disappointment was far offset by my fascination with the discovery that the atomic world beneath the physical world is not as I had supposed it might appear to my senses. Today's image could be interpreted as a fractal atom, in which the electron cloud surrounds the nucleus, which in this case is a Mandelbrot midget. In fact, I actually did interpret it this way, and named it "Electron Cloud". The generating expression subtracts some Z^(0.9) from some Z^(-0.9) then adds (1/C). The parent fractal created by this expression is what I call unstable, that is it 'evaporates' when the bailout radius is increased. Since the bailout of today's image has been raised to 10^100, the entire scene has long since evaporated and left behind a totally black screen of trapped 'inside' points. Blank screens can sometimes be saved however, and I salvaged today's blank screen by applying the < bof61 > inside fill to it. The result is not great. Indeed, with its rating of 4, it is a bit below average. But it is worth a look. The slow render time of 1-1/2 hours makes rendering the image from the attached parameter file an option only the most devoted fractalists would choose. Fortunately, Paul and Scott are devoted fractalists, and as soon as they can render the image, it will be available on their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday was chilly and blustery, with a temperature of 54F 12C and heavy clouds that dropped sporadic showers of rain. Needless to say, the duo of dynamic fractal cats disliked the conditions, and showed their displeasure with intermittent shouts of frustration. A treat of tuna eased their distress. My distress, which is not all that great to begin, will be eased even further when I finish the tiny amount of work that still lies before me. The best news of all is that I shall return in 24 hours with the next FOTD, one that will rate at least a 6. Until that moment arrives, take care, and walk with your head in the clouds. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Electron_Cloud { ; time=1:35:40.12--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.00606704621369720/+0.088414130616388\ 71/2223917 params=2/-0.9/-2/0.9/-0.31/1e+100 float=y maxiter=8400 inside=bof61 periodicity=10 colors=000rdzrdzrdzrdzrezrezrezrezrfzrfzrfzrgzrgzr\ gzrgzrhyrhxrhwrhvriuritrisrirrjqrjprjorjnrkmrklrkk\ rljrlirlhrlgrmfrmermdrmcrnbrnarn`rn_roZroYroXroWrp\ VrpUrpTrpSrqRrqQrqPrrOrrNrrMrrLrsKzsJrsIrsHrtGrtFr\ tDrtDruDruCruCruCrvBrvBrvBrvBqwCpwCowDowDnwDmwElwE\ lwFkwFjwFiwGiwGhwHgwHfwHfwIewIdwIdwJcwJbwKawKawK`w\ L_wLZwMZwMYwMXwNWwNWwOVwOUwOUwPTwPSwPRwQRwQQwRPwRO\ wROwSNwSMwTLwTLwTKwUJwUKxWJwVJwUIwTIvSIvRHvQHuPHuP\ GuOGuNFtMFtLFtKEsJEsJEsIDrHDrGDrFCrECqDBqCBqCBpBAp\ AAp9Ao89o79o68n59o69o69o7Ao7Ao7Ao8Bo8Bo8Bo9Co9Co9C\ oADoADoADoBEoBEoBEoCFoCFoCFoDGoDGoDGoEHoEHoFHoFIoF\ IoGIoGJoGJoHJoHKoHKoIKoILoILoJLoJMoJMoKMoKNoKNoLNo\ LOoLOoMOoMOoMPpNPpNPpOQpOQpOQpPRpPRpPRpQSpQSpQOcz0\ FUNczMczMczLczLczKczKczJczJczIcz0FUHczHczHczIczJcz\ KczLczMczMczNczOczPczQczRczRczSczTczUczVczWczWczXs\ zYczZcz_cz`cz`czaczaczacz } 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==================================