FOTD -- July 26, 2003 (Rating 5) Fractal visionaries and enthusiasts: In today's image we take another look at the rectangle that caught fire in yesterday's image. That rectangle, which is located in the Z^2.003+C Julia set with a C-value of -1.7435, at the Z-coordinates of 0.00019,0.07388 and at a magnitude of 100, is one of the most curious things I have yet discovered in the world of fractals. When viewed as a Julia set, it is as perfect a rectangle as one will find in any random fractal. But the slightest deviation from the Julia orientation has a devastating effect on it. A rotational deviation of as much as 1 degree totally destroys the perfection of the rectangular shape and produces a curvilinear quadrilateral such as we have in today's image. Changing the imaginary part of the C-value even the slightest distance from zero has an even more devastating effect. The entire rectangle rapidly falls apart into fractal debris and vanishes into the fractal ether. Since today's image is another sequel, I have named it "Blazing Rectangle-2". As an FOTD, it rates an average 5, but hey, the average FOTD is nothing to be sneezed at. And the render time of 5 minutes is fast enough to make the attached parameter file a near-joy to run. Those who prefer the acquisition of their fractals to be total ecstasy may download the completed GIF image file from one of the two FOTD web sites: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday, with its brilliant sun and temperature of 86F 30C, turned out to be one of those rare perfect summer days here at Fractal Central. The fractal cats were in one or their rare near-perfect moods as they passed the afternoon in the yard. My mood was a bit less than perfect as the work piled up faster than I could accomplish it. Today's weather is promising to be less than perfect, but still quite pleasant. If I can finish the modicum of work by noon, I'll have a pleasant enough day. And I'm certain to find an interesting fractal before the day ends. To see that interes- ting fractal, check back here in 24 hours. Until then, take care, and is truth a fractal? Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ BlazingRectangle-2 { ; time=0:04:59.97--SF5 on a P200 reset=2002 type=formula formulafile=julibrot.frm formulaname=SliceJB-new passes=1 center-mag=+0.004\ 99268009490636/-0.00325779513771971/76.89922 params=0.5076/0.5037/0.49256/0.49876/2.003/0/-1.74\ 35/0/0.00019/0.07388 float=y maxiter=1000 inside=bof61 logmap=51 periodicity=10 colors=000GADIAFJAHKAJMALNANPAPQARSBTTBVUBXWBZXC`Z\ Cb_Cd`CfbChcDjeDlfDngDpiErjEtlEvmExnEzoGzpIzpKzqMz\ qOzrQzrSzsUzsWztYzt_wubtueqvhnvklwnjwqhytgywhzwhzw\ hzmczjfzgizdczaYzZTzWNzTHzQCyN6xK1wJ5uI9sHDqGHoFLm\ FOkESiDWgC_eBccBfaAj_9nY8rW7vU7yS9wQAuOBsMCqKDoKEm\ MFkOGjQHhSIfTJdVKbXL`ZMZ`NYbOWcPUeQSgRQiSOkTMlULhS\ MdQM`OMXMMTKMPIMLGMHEMDCM9AM59MF8MO7MX6Me6Mc7La8L`\ 9KZAKXBKWCJUDJTEJRFIPGIOIHMKHKMHJOGHQGGSGEUFCWFBYE\ 9_E7aE6cD4eD3gD6iE8kFBmGDnHGnIImJLlKNkLPjMSiNUhOXg\ PZfQaeRcdSecTd`SdYRdWQdTPcQOcONcLMcILcGKbHNaIP`JSZ\ KVYLXXM_WMaUNdTOgSPiRQlPRoOSqNTtLSwMTvMTvMTvMTvNTv\ NTvNTvNTvNUvOUvOUvOUvOUvPUvPUvPUvPVuRVuQVuUVuQVuXV\ uRVu_VuRWubWuRWueWuSWuhWuSWukYvSXunWuTVtqVtUUttTsU\ SswSsVRrzQrWPrzPqXOqzOqYQpzSpZUozWo_Yoz_n_anzcn`em\ zgmaimzklbmlzopaqnzslcukzwiezhzzfgzdzzcizazz`kzZzz\ YlzWzzUnzTzzRpzQzzODzfzza } frm:SliceJB-new {; by John R. H. Goering, July 1999 pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+(p4), z=r+flip(s)+(p5): z=z^(p3)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================