FOTD -- August 05, 2003 (Rating 5) Fractal visionaries and enthusiasts: Sometimes I like to ponder questions that would never be considered by a sensible person. Of course, this is no handicap, because I have never claimed to be, nor do I make an effort to be, a completely sensible person. (I find such individuals a bit boring.) And even if I tried my best to be sensible, we would need total agreement on what constitutes sensible thought. (For example, is it sensible to believe in precognition when one has personally and unambiguously experienced it?) My current ponderings are somewhat more sensible than experiencing the future before it happens. I am pondering the Mandelbrot set. Is the set an objective thing, a subjective thing, or something in between, as ghosts are supposed to be? Would the Mandelbrot set exist if the universe were empty of intelligent life? And as far as that goes, did it exist before the 20th century? The answers, if such things as answers exist, depend on abstractions such as the much-debated nature of reality. We could state that the M-set (or at least the potential for the M-set) always existed, but the set itself was not discovered (or was it created?) until the latter part of the 20th century. We can also debate whether today's image is a real fractal, since it has no dividing line that separates trapped points from points that tend to infinity. In fact, it has no escaping points. The points, which are all trapped, are colored by the bof61 inside fill according to which iteration comes closest to the origin. The result is curious, but too chaotic to hold long-term interest. Today's image will be the last in the present series of Mystic2 images. Like the previous images in this series, it is filled with many potential proto-themes, but none of them are sufficiently developed, giving an effect of untamed Fractal Wilderness, which in fact is what I named it. Studying the image, I see many spots that promise interesting zooms. Some of these spots may indeed hold images worthy of being declared FOTD's. Others likely lead to fractal dead ends. This tendency is probably why the formula never became a favorite of mine, as the MandelbrotMix4 formula did. As a result of the disorganization in today's image, I can rate it no higher than a 5 -- an average effort. But the render time of 4 minutes is fast enough to make seeing the average scene reasonably convenient. And as always, the pre-rendered image is available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The on and off showers continued into the afternoon Monday here at Fractal Central, spoiling the cats' day. The sun appeared by 3pm and raised the temperature to 84F 29C, but by then the duo were already sulking. Luckily, the tuna treat made things right. Today is again starting showery, so I had best have more tuna ready. The day's work load is average. But the next FOTD, which will appear in 24 hours, will be far from average. Until then, take care, and go ahead and be silly. Fractals are fun, and is the world not little more than a cosmic joke? Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Wilderness { ; time=0:04:23.48--SF5 on a p200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=cotan passes=1 center-mag=-0.06074811025606387/-0.993573573575838\ 00/1425.244/1/-25/1.08651629360245749e-011 params=3.4/6/-9/3.8/6.1/-2.4 float=y maxiter=95 inside=bof61 logmap=yes periodicity=0 colors=000mfWqqQrpZsogtnpumxmkueirYgpQemIcjAbhJU`S\ QT`QLRHDcI5cTBobHnlNnvTiwYewaawefwbkq_piXuaUyVRj8w\ iAuiBtiCriDqiEoiFncOiZWeUdaPlYKtULuSMvRNvQOwOPwNQw\ LRwKSwJTwHUwGVwEWwDXwCYwAZw9_w7`w6aw5dwAfwFhvKkrPm\ oUolZrhctehvbmx_qvZptYprXpqWpoVpmUpkTpjSphRpfQpeQp\ PJpcPpaOp_NpZMpXLpVKpTJpSIpQHpOGpAahB_iCYjDXjEVkFU\ kGSlHRlIPmJNnKMnLKoMJoNHpwhltfmrdmobmm`njZnhXneVnc\ To`RoZPoWNoULpRJpPHpxwNruSmnWgg_b`dXUhSNlDPWFN`HLd\ JJhLHlBKoEJpGIpJHpLGpHw_It`IraIobJmcJjdJheKefKcgKa\ hLZiLXjLUkMSlMPmMNnNKoNIpwCOuDQsDRrDSpDToDVmDWlEXj\ EYiEZgE`fEadEbbFcaFd_FfZFgXFhWFiUGjTGlRGmQGnOGo8hg\ 9fhAehBciBbiCajD_jDZjEXkFWkGVlGTlHSmIRmIPmJOnKMnLL\ oLKoMIpNHpD`8FWHHSQJOZLKg7pE9lIBhMCdQEaUFYYHUaJReK\ NiMJmGwWHuXHsYHqZIo_Im`IkaJibJgcJedKceKafK_gLYhLWi\ LUjMSkMQlMOmNMnNKoNIp8JCAIGBIKDIOEHRFHVHHZIHbJGeLG\ iMGmtqprnpplpnjplhpjfphdp } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================