FOTD -- June 08, 2004 (Rating 5) Fractal visionaries and enthusiasts: This morning I was up early with my telescope and sun filter set up in the east-facing attic window of F.C., ready to see the final stages of the transit of Venus across the sun. Unfortunately, fog was in the air at the time the sun rose, obscuring the horizon. As a result, I saw nothing. When the sun appeared 2-1/2 hours later, the event had long since ended. Hopefully the luck will be better in 8 years, when the next transit occurs. If not, it's a wait of 122 years. I guess I shouldn't be too disappointed. Those farther west saw nothing at all. Today's fractal was created by iterating the expression Z^(2+0.1i) and examining a spurious valley of the resulting chaotic fractal. The scene is located near a larger midget in the valley. I named the image "Iterative Complexity" because I could find so little order in it. In the classic Mandelbrot set, the features are arranged around the midgets in the series 2,4,8,16... In the cubic Mandeloid the features follow the series 3,9,27,81... In Mandeloids of fractional powers, the series follows the same rule. Thus we have 2.5, 6.25, 15.625, 39.0625... But what series will a Mandeloid with an imaginary component in its exponent follow? Complex numbers are not counting numbers. As today's image shows, the result is total chaos. There is no order at all in the features surrounding the central midget. In a way this makes things more interesting. I rather enjoy an 'anything can happen' fractal. I didn't really know what kind of a rating to give to today's image. When in doubt, I always do the most likely thing, so I ended up giving the image a rating of an average 5. The render time of close to an hour holds the overall value to a modest 9, but this value can be drastically increased by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the image there. But before going to the web site, give Paul a chance to render and post the image. Monday was sunny and warm here at F.C., with a high temperature of 81F 27C. It was a perfect day to keep cats happy. They spent several hours in the yard, ignoring the cicadas, which are again singing. When evening arrived, they came indoors with no complaint. Today looks to be a repeat. I expect a repeat in the cats' mood also. The work is moderate, which means about 4 hours effort will put it behind me. Then it's on to the world of fractals. If I'm lucky, tomorrow's fractal will be better than today's. If not, it will still be interesting. Until next time, take care, and hope for clear skies in 8 years. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ IterativeComplexty { ; time=0:55:48.13--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.62142028795967830/-0.363045619197981\ 00/4.570629e+010/1/-7.5/-5.02629616519895128e-005 params=2/0.1/0/0 float=y maxiter=18000 inside=0 logmap=1430 periodicity=10 colors=000bMsaNqaNp`On_OmZPlYQjXQiWRgWRfVReUScTSbS\ T`RT_QTZQUXPUWOVUNVTMVSLWQKWPKXNJXMIXLHYJGYIFZGEZF\ DYDEZEEZFFZGFZGFZHGZIGZIHZJHZKHZKIZLIZMJZMJZNJZOKZ\ OKZPLZQLZQLZRMZSMZSMZTN_UN_UO_VO_WO_WP_XP_YQ_YQ_ZQ\ __R__R_`S_aS_aS_bT_cT_cU_dU_eU_eV_fV_gV_gV_gTbiRdj\ PfkNilLkmJmoHppFrqDtrCvsCuqCtpCsnCrmCqkCpjCohCnfCm\ eClcCkbCj`Cj_CiYChWCgVCfTCeSCdQCcPCbNCaLC`KC_ICZHC\ YFCYEHZIMZMRZQW_T`_Xe_`j`co`gt`ky`nx_nwZnvYnuXntWn\ sVnsUnrTnqSnpRnoQnnPnnOnmNnlMnkLnjKniJniInhHngGnfF\ neEndDndCncBnbAna9n`8n_7n_7nV8gR8aN8WJ8QE9JA9D6972\ 914A16B17C19C1BD1CE1EF1FF1HG1JH1KH1MI1OJ1PK1RK1SL1\ UM1WM1XN1ZO1`P1aP1cQ1dR1fR1hS1iT1kU1mU1nV1pW1qW1pY\ 2pZFp_Io`LoaOobRncUndXne_mfbmgemihmjklknllqlmtknwk\ ozkpzjqzjrzjszjtziszhszhszgszgszfrzfrzerzerzdrzcqz\ crzbszbtzauzbvzcwzcxzcyzczzczzczzczzczzczzczzczzcz\ zczzczzczzczzczzczzczzczz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(p/(2*PI)) r=real(p2)-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|<a } END 20.0 PAR-FORMULA FILE==================================