FOTD -- June 03, 2002 (Rating 6) Fractal visionaries and enthusiasts: Things are moving on schedule here at fractal headquarters, which means that the CD is entering the late mid-stage, the ongoing fractals are continuing to appear, the cats are sleeping, but I have yet to receive the 24-million dollars I was promised by that man who sent me the e-mail. :-) Today we take a trip to the cubic Mandelbrot set to see a cubic midget. The cubic set is basically an extension of the classic quadratic set M-set, with corresponding features in corresponding areas. The main difference is that there are 2 lobes in the buds, and instead of the 2,4,8... arrangement of elements around the midgets, the arrangement is 3,9,27... It also becomes meaningless in the cubic set to orient midgets in the 'normal' manner, as I do with quadratic midgets, since cubic midgets have 4-way symmetry. I have given today's midget a diagonal orientation, which is both dynamic and somewhat artistic. As is the case with most of the FOTD's, the coloring is done with the standard equal- iteration-band method, with the inside set to black. Feeling that the image has at least a modicum of worth, I rated it at a 6. The name "Cubic Mandelbrot" is a description of the image, with no pretense at cleverness. The 11-minute render time makes running the parameter file a drag. The wiser choice is to let Paul and Scott do the dragging, and download the completed image from their web sites. Paul's site can be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Sunday here at Fractal Central was near perfect, with total sunshine and reasonably happy cats. The slightly too-warm temperature of 88F 31C was offset by low humidity and a fresh breeze. The cats would rather have had no wind, because wind conceals the presence of intruders. But they took the breezes in stride and explored the yard peacefully. Being faced with a day of work, I must now end this latest chapter in the unending series of FOTD's, but I'll return on schedule on the next day evenly divisible by 3 -- June 6. Until then, take care, and search for the meaning in fractals. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Cubic_Mandelbrot { ; time=0:11:06.68--SF5 on a P200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotCube passes=1 center-mag=-0.00037280362079087/+1.091145090358868\ 00/1.05861e+010/1/-19.9998811849355604/-0.00012469\ 0785224791656 params=0/0/0/0 float=y maxiter=6000 inside=0 logmap=836 periodicity=10 colors=000Skz_mzhozspzqqzqrzqtzqtzqtzqszqrzqqzppzp\ ozpnzpmzplzpkzpjzpizphzngznhznhznhznizniznjznlznkz\ mlzmkzmkzmkzmizmizmhzmhzmhzhgzegzbgu_enXehUe`PcWMc\ OJcIGbCEb5Bb06`08b08b08b08b08b18b29b59c69c89cB9cC9\ cEBcFBcIBeJBeLBeOBePCeRCeUCeWCgXCgZCg`EgbEgcEggEgh\ EhiEhmFhnFhpFhqFhuFhvFiwGizGizGizGizGizGizGizZX0XW\ 0XW0WW0WW0WW0UW0UW0UW1SW4SW5RW6RW8RW9PWBPWCPWEOWGO\ WIMWJMWLMWMLWOLWPJUPLWRMWSMXUOXWOXXPZZPZ_RZ_S_`S_b\ U`cU`eW`gWbhXbi__hXbiWekUhmSimRmnOppMsqLuqJwsIzuFz\ vEzvCzwBzy9zyBzvCzsCzpEzmEyiFvgGscGp`InZIkWJhSLePL\ bMM`JMZGOWEPRBPO8RJ5RF2SB0S90W80X80Z90_90`91bB1c92\ e92gB4hB4iB5kC5mB6nB6pC8qC8sC8uC9vC9wBByBBzBCzBEzB\ GzBJz9Mz9Pz9Sz9Wz9Zz9`z9czGgzMizSmzZpzeszkvzqwzwyz\ uzzszzqzznzzmzykzwhzugzsezqczpczmczkcziczhczeczccz\ bcz`czZczXczWczPczUczXcz_czcczgczgczgczgczgczgczgc\ zgczgczgczgczgczgczgczgcz } 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==================================