FOTD -- August 30, 2003 (Rating 5) Fractal visionaries and enthusiasts: When I opened my e-mail box this morning, I noticed a message with some real fractal substance in it from Osher Doctorow on the Fractint list. The message speculates that perhaps the proper application of fractal geometry could clarify some of the seemingly insoluable puzzles of modern physics. I can't quite grasp how fractals could clarify things such as quantum theory, but I have long watched and wondered how such a revolutionary discovery as fractals could find so little practical application and have so little impact on our under- standing of things. It will be interesting to see where, if anywhere, Osher's ideas go. I am still browsing that old physics text book of mine, which was published in the 1880's. At the time, there were many puzzles which have since been explained. To begin, we were seen living on a world hundreds of millions of years old, illuminated by a sun that could have been burning for no more than ten- thousand years. Then there was the problem of the Ether, which everyone knew existed because waves need a medium in which to propagate, but which was impossible to detect and needed to possess some impossible qualities. Finally, there was a very puzzling situation with thermal radiation, which according to classical physics should have been in the form of extreme ultra- violet radiation. These problems were not solved until we went beyond classical physics. The discovery of nuclear energy solved the puzzle of the generation of the sun's heat. The theory of relativity made the Luminiferous Ether unnecessary, and quantum theory explained why hot coals glow orange-red instead of emitting gamma rays. There are puzzles equally as perplexing in the world of physics today. Could fractals point the direction to the solution of these puzzles? Will fractals solve the puzzles, or better yet, make them irrelevant? And 120 years from now, will the idea of quarks and superstrings be considered as quaint as the idea of Luminiferous Ether seems today? Today's fractal is another scene in the Z^3+C Mandeloid. It is located deep in the West Valley, which is a mirror of the East Valley. For a change, today's image was rendered with the out- side set to the 'fmod' option. I named the image "The Tiny Crowd" because it is filled with many cubic midgets. The rating is an average 5. The 19-minute render time is slow, but speed may be found by downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday here at Fractal Central was very warm and muggy, with a temperature of 90F 32C and a dew point of 77F 25C. A brief shower in the afternoon cut short the cats' day in the yard almost as soon as it started, leaving them sulky and making a consolation treat of tuna and turkey necessary. They ended the day in resignation. Today is starting warm and muggy again, but there is more sun than yesterday at this time. Whether this bodes good or evil will not be determined until the day has ended. In any case, I shall return in 24 hours with another fractal, this one not in the cubic M-set. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ The_Tiny_Crowd { ; time=0:19:32.77--SF5 on a P200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotCube passes=1 center-mag=-0.\ 3875828936411013/-0.00020565676691499/4.793506e+009 params=0/0/0/0 float=y maxiter=7200 inside=0 proximity=0.015 outside=fmod periodicity=10 colors=0I0zzzzzzzzyzzyzzyzzwzzwzzwyzwyzuwzuwzuuzsu\ zsszsszsqzqqzqoyqoyomwomuoksoksmiqmiomfokflkdjkdhk\ bhibei`di`difefkhdojbsl`woZzqXzsVzuSzwQzzOzzQzyQzw\ SzuSzsVyqVuqXqoXmlZijZbhZZe`Vd`QdbMabE_dAXd4Vf0Tf0\ Tf0Vd0Xd2Xb4_b4_b7a`Ad`CdZCeZEeZHhXKhXKjXMlVOlVQoS\ SoSSqSVqQXsQZuOZuO`wObwMdyMbwHdyMdzOdzQfzVfzXfzZiz\ `izdizfkzikzkkzomzqmzsmzuozyozzozzqzzqzzqzzszzszzs\ zzuzzuzzuzzwzzwzzwzzwzzyzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzwzzuzzqzzozzkzzizzdzzbzzZzzXzzSzzQzzMzzKzz\ EzzCzy7zw4zu0zs0zq0zo0zl0zo0zl0zl0zl0zj0zj0zj0zh0z\ h2zh4ze7yeAueCqdEmdHkeEidKfaMd_Od_QbXS`VV`VXZTZXQ`\ VNdVNfSLiQIkQImOIoMIqKIsKIuHIyEIzEIzCIzAIz7Iz7Iz4I\ z2Iz2Iz7IzAIzEIzHIzKIzOIzQIzVIzXIzZIzbLzdNziQzkTzm\ VzqXzs_zwazydzzezzhyzjyzlwzowztzztzzrwzqsznqzjmzei\ zcfzabzXZzXXyTSwROuPKuIHsICqI7oI4mI0kI0kI0mI0oI0qI\ 0sL0uQ0wT0yX0za0ze0zj0zo0 } frm:MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================