F.O.T.D., March 31, 1998 (Symphony in P-flat) Fractal visionaries: This first paragraph was written on October 18, 2003. I wonder whatever happened to Doctor J. in the 5-1/2 years since the rest of this discussion appeared. And things are looking good for the resumption of the ongoing FOTD by the end of the month. START MARCH 31, 1998 DISCUSSION=========================== I see that Dr. J is loose again on the internet. I heard his mad-scientist laughter the moment I signed on. I only hope he can keep himself firmly in three-space. We've been losing far too many good fractalists into the fourth dimension lately. As the doctor zipped past my place, he dropped off a fractal that looked like two M-sets, one on top of the other. To view the image properly, I needed my red and blue glasses. Luckily, I found them still tucked inside my "Fractal Creations" book. The glasses showed not two but three M-sets -- a red one that looks like a snowman and two overlapping blue sets. I had several questions to ask, but the doctor flashed away before I had a chance. Today I had planned, I had honestly planned on describing how I stumbled upon what I consider to be one of the most incredible of fractal objects -- the perfect rectangle at Z=0.00019,0.07388 in the Julia set of the Z^2.003+C figure with a starting point of C=-1.7435,0.0. I started out well enough on the article, and had it nearly half finished, when an unexpected rush job arrived that took longer than expected. Rather than rush the article to comple- tion, I decided to postpone it until tomorrow, when I will have time to get it right. But not to disappoint anyone, I have a fractal for today -- an admitted quickie. It looks rather like a Pollock painting, where streaks and splotches of paint are dripped and splashed around the canvas. But this one is a pure fractal. It is a scene in the (-Z)^(-0.95)+C figure, made more presentable by the epsiloncross inside fill, which adds the streaks to the splotches, which are part of the fractal. I named the picture "Symphony in P-flat" because it reminds me of a scene in an old Disney animated musical film. (I think it is the 'After You've Gone' segment of the film 'Make Mine Music'.) The image is sliced in the Parabolic direction. This particular image could really benefit from anti-aliasing to correct the fine lines which have broken into dashes. But even in its imperfect state, it is worth a look. The picture has been posted to: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow, I'll tell the tale of the vanishing rectangle -- I really will -- honest! Until then, take care and . . . Jim Muth jamth@mindspring.com jimmuth@aol.com START 19.6 PARAMETER-FORMULA FILE=========================== Symphony_in_P-flat { ; 38 seconds at 200mhz reset=1960 type=formula formulafile=slices.frm formulaname=ParabolicMiN passes=1 center-mag=0.0\ 860258/0.0841156/0.8239817/1/-57.5 params=-0.95/\ 0/0/-1/0/0.4 float=y maxiter=252 bailout=25 inside=epsiloncross logmap=yes symmetry=none periodicity=10 colors=000kBXP0mK_JnpEz0z000tzZJI\ bZCfd4J0v0HdGYNVpWmoJkHC5Y9Q3wNYpYfTcBT7VHRV9D\ <2>i6amV4nMInEWkMRmE`T7R<2>i6eRp5<2>hH_eSShKYkDc\ FcCRSObHZBBqP9na7kPzIK8xV7sd6n17E<2>b6a`7OCwjWXi\ 5iMLWU_Jac5d<2>l6hZThzwW<2>qJftjV<2>oGfpsC<2>nIa\ WG89Zi6JJ`N7<2>kA`EMQRGXbBcB2UNab<2>gEhrJ1jobl_e\ mLgXiabWdhJg`Cyafl<2>kFiFN3<2>eA_WOeeFghVdkIgU7L\ <2>i6cvb8B_mPQkaGjczOiYZrGfq`BpQNoGZC4WW5b4kL<2>\ cGcf4c<2>l6hrzPpY_fDfj9hRlyZYsfKnDLmQGkbBjRdgbNh\ 7GLhIqjEnlAk6vMLdU_NaXoZEnZR_bbLfNCb7F0<2>c8ZWdw\ `WseNpjEln7N<2>n6d7SjTHi5Wn<2>cCj0V9HMMYEYdY`hOc\ kFfwOZiH5<2>m8_lJemCgQpiZ`ifLisAyp8q`dG`y5efJjOX\ UcqdNmt4Ur5_p6dpli<2>nGi5ly<2>cGmnfSnUYnIclvu<2>\ nJlECnRAlb8jggjkPiqLLea2QcKBeaT8R<2>mM2<2>9up3i5\ TNHS_QSkZQhYPeXPSIPF3W4M<3>o11Uczn4OgGJiDQ } frm:ParabolicMiN {; Jim Muth b=p1, z=imag(pixel)+p2, c=real(pixel)+p3: z=(-z)^(b)+c, |z| <= 16 } END 19.6 PARAMETER-FORMULA FILE=============================