FOTD -- August 13, 2003 (Rating 8) Fractal visionaries and enthusiasts: While assembling the parameter section of today's FOTD, I noticed my humble MandelbrotN formula. I saw all four lines of it -- about as short and simple a formula that could produce a fractal. Then I brought up Albrecht's latest Multifractal formula -- a work of fractal-programming genius, a mini-program with hundreds of lines that took many days of labor to develop, and still may not be finished. The two formulas illustrate two different approaches to the art of fractaling. I find my fractals; Albrecht creates his. Which method is the better way of working with fractals? Asking such a question is like asking whether fractals are art. It is up to each individual to decide. In my long fractal career I have written thousands of short, simple formulas, most of which took less that 1/2 hour to complete and have long since been filed away and forgotten. I could never imagine myself working weeks or months on a single formula, even if I did have a clear idea of where I was going. But why should I need to, when nearly every fractal created by every formula contains infinite surprises? Today's image rates an 8. One point of this rating is due to the surprising nature of the image. Until I found it, I had assumed that the near-perfect rectangles such as I used to create yesterday's 'Space Station' image exist only in the Julia plane of the Z^2.003+C Mandeloid. I should have known better. Yesterday, while searching the area of the Julia rectangle in the Mandelbrot direction, I found many small figures like the larger Julia figure that holds the rectangle. I found no midgets, but most surprising, I found that the small figures hold near-perfect empty rectangles where the arms branch out. To see some empty rectangles in their natural surroundings, toggle today's image of one of these small figures in and out of color-cycling mode and watch for the areas that blink. Clearly, I have much more exploring to do in this area. To begin, I must find those elusive Mandelbrot midgets. And if the figures with their rectangles are present in both the Julia and Mandelbrot directions, they should be present in the odd and oblique Julibrot directions also. I gave little thought to the naming of the image. "Mandelbrot Object" was as good a name as I could come up with. But the name is a perfect description of the surprising nature of the scene. The render time of 15 minutes is starting to border on the excessive. Relief in the form of the completed GIF 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> Tuesday was actually a pleasant day here at Fractal Central. The temperature reached 86F 30C, the humidity was bearable, and the heavy rain storms that broke out in the afternoon stayed well west of us, leaving the F.C. area with a partly cloudy day and happy cats. If tomorrow's FOTD is as surprising as today's, I'll be happy. If it's not, I'll still be happy. Until next time, take care, and life is just a happy procession of fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Object { ; time=0:15:38.35--SF5 on a p200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=-1.74350425707497900/+0.000006977798978\ 60/4.029834e+008 params=2.003/0/0/0/0/0 float=y maxiter=7200 inside=0 logmap=644 periodicity=10 colors=000404601700900A00C00D00F00G00I00J01L01M01O\ 13P33Q33S44T44V64X76Y76_96`97aA7cC7dC9fD9dA6gD9iGC\ jJFlMImPJoSMpVPsYSu`TvcXxf_yiazlczofzrizulzxmzzpzz\ szzvzzxzzvxxvprvilvafuVauOXuGQu9Ls1Fs09s04s06o07j4\ 9gAAcFC_LDXQFSXGOYFP`GLcIIdJFgLAiM7lO4mO1jS7iXDf`J\ ddPaiV`m_YrdXvjTzpSzvPzzOzzLzzJzzGxzFrzCmzAiz7cz6_\ z3Vz1Pz0Lz0Gz0Az06z01z00z00z03z06z39z7CzAFyFIvILuM\ OsPQrTToXXm`_lcaigdgjgfojdrmavp`ys_zvXzyVzzTzzSzrV\ zgXzXYzM_z9azC`xF`uG`sJ`pL`mO`lP`iS`fV`cX`a_`_``Xc\ `YiXVd`SadQ_gOXlLSoJPsGMvDJzCGz9Cu77l63c40V30M10D3\ 0I40L61O74Q97TAAXCD_DGaFJdGMgIPjJSmLVpMYsMYtOXuPWr\ QXmQWiTWdYYaa_YddTikPmqLrvIuxDyz9zz4zz0zz0xz0ru0jp\ 3dl4`i7VdAPaCMgFJoIGvJFvMCvO9vQ7vT4vV1vY0v`0va0vd0\ vi0vf0vd0vc0va0v`0vY1gX1TV3FT41S63Q74O96MA6LC7JC9I\ D9GFADGCCICAJD9LF7LF6II7GL9FO9DQACTCAXC9_D7`D4cF3f\ G1iG0lI0oJ0rJ0uL0vL0uJ0sI } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================