FOTD -- October 01, 2006 (Rating 7) Fractal visionaries and enthusiasts: Nobody's prefect. Not even myself. I was surprised when someone actually caught the intentional mis-spelling in my recent note. Fractalists are sharp indeed. It's what happens to those who think about numbers too many times. Today is October 01, the day quadratic midgets are permitted to reappear. And I wasted no time. The image for the day shows a midget in the East Valley area of the large midget on the main- stem complex of the Z^(2.003)+C Mandeloid. This is the area of the Julibrot where the curious Julia rectangle is located. The train-tracks that criss-cross the area are obvious. And if you look carefully around the midget, you will find eight tiny copies of the great Julia rectangle itself. At first glance the Mandelbrot rectangles seem to be perfect copies of the Julia rectangles, but a bit of experimenting shows a significant dif- ference in their interior structure. The Julia rectangles stay almost fixed in position as the value of C is changed, while they fill in and their shape undergoes rapid transformation. The Mandelbrot rectangles zoom out of sight off the screen with the slightest change in the value of Z, but when they are finally found, it is seen that they are still open and their shape has remained largely unchanged. The reason for this lies in the peculiar four-dimensional geome- try of the rectangles. I will not try to describe this geometry until I can actually visualize an entire tesseract in a single moment of time. I do not expect to be able to do this for quite a while yet. The rating of a 7 for today's image seems about right. The name "Rectangle Apparition" has the slight hint of the mystical that is suggested by the entire world of fractals. The render time of 17-1/2 minutes borders on slowness, but the result is worth the wait, and no waiting at all will be needed if the finished image is viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cool cloudy drizzly day with a temperature of 55F 13C here at New Fractal Central on Saturday kept the fractal cats confined indoors. But since they never go out anyway, they were uncon- cerned. They had one moment of excitement however, when a mouse popped out and scurried down the hallway. The would be mouse- catchers fell over each other in pursuit. The mouse got away through a hole by a radiator pipe, having learned its lesson. The duo watched the hole for over an hour, but the mouse never re-appeared. When they finally lost interest, I praised them for their vigilance and gave them an extra treat. My day was reasonably pleasant. The work is up-to-date, nothing big is in sight, and the fractals are going well enough. What else could a fractalist want, other than the answer to the ques- tion of the meaning of existence? The next FOTD will appear in 24 hours. Until then, take care, and does meaninglessness reign supreme? If it does, what is the meaning of it. Or is the very concept of meaning a creation of human thought processes? I wonder. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= RectangleAparition { ; time=0:17:35.23--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=-0.000000312\ 87984841/-0.00000010697476267/5.35887e+011/1/20/\ 7.8241581935589721e-008 params=0/0/0/0/-1.7435/0/0\ /0/2.003/0 float=y maxiter=7600 inside=0 logmap=988 periodicity=10 mathtolerance=0.05/1 colors=000MBAODAQFASHAUJAWLAYNA_PAaRAcTAeVAgWAiXAk\ YAmZBm_AmaCmbEmdGmeInfKqhMtiOwkQznSzqUztWzwYzz_oYV\ mZXlZZkZ`jZbi_dh_fg_hf_je`ld`nc`pb`q`bnZclXdiWegUg\ eShbRi`PjZNlWzmUznRzoPzqNzrKzsIztGzsJzrMzqPzpSKoUM\ nXOm_PlbRkeSjgUijWhmXgpZfs_fuaetbetddtedtfdthctict\ kbtlbtmbtoatpatr`ts`tt`trdophkokgmoclr_jvWiySVXUO_\ WHbZAd`FeaJebNecRedVeeacigbmmaps`ty_wpbhhdU`fFdiLg\ lRjnXmqbpshsvnvxsoslioeck_YgTScMM_GLaBKb6Jc1NfLQid\ TkxXZ``NDZSCXWCV_CSYMPXWMVeJUo7lPFeUN_ZUUcXT`ZTZaT\ XcTUfTShTQjTO`0PxngfipPdxSUmUKcWAUU9RT9OS9LS9IV8FY\ 8C`89c51h86f0AzMAyAEqEIhFMdHQ_IUWJYSK`UJaWIbXHcZGd\ `FeaEfcDgk3ddDgYMiRVkKcmDlo3uy7uqAuiEubHuVLuOOuGRu\ 9_lGhcMqWSoUTmSUkQViOWgMXeKYnNagMWdOZbQa_SdYTfWUiT\ VlRWoDXrJYqPZqU_p_`peaojbopcnuenohjikgcncYq`StXMwU\ GzLHzOHzRIzdHzZHzUHzOBzLHzJNzITzHZzFdzEjzDpzCqz9qz\ 6qz4nz5kz6lzIlzLmzNmzQmzS } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), 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)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================