; Date: Sat, 30 Sep 2006 23:02:05 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 01-10-06 (Rectangle Apparition [7]) ; Id: <1.5.4.16.20060930230320.2b2790a4@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ;