; Date: Sat, 24 Nov 2007 23:20:03 -0500 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 25-11-07 (Imaginary Wilderness [5]) ; ; Id: <1.5.4.16.20071124232144.2ac76a2c@pop.mindspring.com> ; --------- ; ; FOTD -- November 25, 2007 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; Today's merely average fractal was found in the parent fractal ; that results when the formula Z^(2+0.01i)+C is iterated two ; levels up the logarithmic ladder. This parent at first appears ; to be a normal Mandelbrot set rotated so that its main spike ; faces southeast. But the surface appearance is deceiving. ; There is a split on the positive X-axis and the period-5 bud ; normally on the southwest shore of the main bay lies right on ; this split. ; ; It should come as no surprise that the features in the vicinity ; of the split are distorted. The minibrot in the center of ; today's image is a typical example. It appears to have gotten ; its north and south halves out of phase, with the two branches ; of Seahorse Valley no longer lining up. ; ; I named the image "Imaginary Wilderness" because fractals with ; complex and imaginary exponents are virtually unexplored -- at ; least by me. The rating of a 5 seems fair for a fractal done in ; such haste. The calculation time of just under 3 minutes may be ; avoided by going to the FOTD web site at: ; ; ; ; and viewing the finished image there. ; ; The sun was bright here at Fractal central at sunrise on ; Saturday morning, but the temperature of 21F -6C promised a cold ; day. The fractal cats slept until it warmed to above freezing. ; My day turned busier than expected when I let F.L. talk me into ; a trip to a local antique mall to see the stuff that someone ; else threw away. (Actually, I kind of enjoyed it.) When we ; returned around sunset however, the cats were sulky at having ; been left alone for most of the day. The next FOTD will be ; posted in 24 hours, for all it is worth. Until then, take care, ; and search for the secret. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= ImaginaryWildernes { ; time=0:02:54.25-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.8488258557/-0.0209973644/15601.18/\ 1/82.5/-3.5510218377e-010 params=2/0.01/2/0 float=y maxiter=5000 inside=0 logmap=203 periodicity=10 colors=0008FA9FCAGDAGEAHEAHFAIFBIGBJGBJHBKHBKICKJC\ LJCLKCMKCMLDNLDNMDOMDONDPNEPOEPPEQPEQQERQFRRFSRFSS\ FTSFTTFTTFTTLYWRbZYh`cmcirfowhlsgjpfhmefiddfcbcb``\ aZX`XU_VRZTOYRKXPHWNEVJATLBUNCVODWQEWRFXTGYVHZWIZY\ J_ZK``LaaMacNbeOcfPchQdiRekSflTfnUgpVhqWisXitYjvZk\ xYlwZkvZkuZktZjsZjsZjrZiqZipZioZhnZhnZhmZglZgk_gj_\ fj_fi_fh_eg_ef_ee_de_dd_dc_cb_ca_ca_ca_ca_ca_cb`ac\ a_dbYecWfdUgeSgfQggOfgMffKffIeeGedEddCdcAdc8cb6ca6\ ca6b`6b`5a_5a_5aZ5`Y4`Y4`X4_X3_W3ZV3ZV3ZU2YU2YT2_U\ 0YT2XS4VS5UR7TR8RQAQQCPPDNPFMOGKOIJNJIMLGMNFLOELQC\ KRBKT9JV8JW7IY5IZ4H`0Gb3Ha5Ia7J`9J`CK_EL_GMZIMZLNY\ NOYPPYRPXUQXWRWYSW_SVbTVdUUfVUiUUhVWgVYfV_eVadVccW\ ebWgbWiaWk`Wm_XoZXqYXsXXuWXwVYyWXzXWzXVzYVzYUzZTzZ\ Sz_Sz`Rz`QzaPzaPzbOzbNzcMzcNzdOzePzeQzfRzfSzgTzgUz\ hUziUziUzjUzjUzkUzkUzlUzmUzlUzmUzmUzmUzmUzmUzmUzmU\ zmUzmUzmUzmUzmUzmUzmUzmUz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|