FOTD -- April 09, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to the land of the mysterious Z^(2.003)+C Julia rectangles. But today we are not concerned with Julia rectangles. Today we are after bigger game. We investigate the Mandelbrot aspect of the area. In the Mandelbrot orientation, the Julia rectangle corresponds to a tiny peninsula jutting west into a tiny bay on the east shore line of the strait connecting the partially overlapping large minibrots on the infinitely divided main spike of the Z^(2.003)+C Mandeloid. When I first arrived in this Mandelbrot area, I almost gave up. Nothing even remotely resembling a rectangle or a minibrot was visible. But after a short search I stumbled upon a feature with the 2-way symmetry that often indicates the presence of a minibrot. Today's image shows the minibrot that I found. Since Mandelbrot sets are kind of catalogs of all the Julia sets created by a particular formula, today's image should be filled with open rectangles, and indeed they are there, most of them beyond resolution but some well within range. In tomorrow's FOTD a full-blown Mandelbrot rectangle will be featured. The name "A Hidden Peninsula" refers to the tiny peninsula that holds today's scene. The rating of a 7 is FOTD average. The calculation time of 6-1/2 minutes is on the slow side, so I recommend visiting the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> to see the finished image without the task of rendering it. The image is available in hi-def at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be found at: <http://www.Nahee.com/FOTD/> BTW, we are considering posting a picture gallery of the cat action here at FOTD. I have been writing of the fractal cats for many years. Now we feel it is about time to give them the exposure they deserve. Saturday brought clouds and rain showers to Fractal Central, while Sunday brought lots of sun and a temperature of 68F 20C, earning the approval of the fractal cats. On the human side of things, nothing went wrong, which makes for a satisfactory day. The next FOTD will be posted in 24 hours. Until then, take care, and before you put your faith in skepticism, think ration- ally about it. Jim Muth jamth@mindspring.com START PARAMETER FILE======================================= A_Hidden_Peninsula { ; time=0:06:32.48-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN center-mag=-1.743496834151\ 223/+0.00000003977466762/1.077858e+011/1/22.5/0 params=2.003/0/0/0/0/0 float=y maxiter=7500 passes=1 inside=0 logmap=854 periodicity=6 colors=00005U04P03K02F57FCB8JF6QJ4XN2bR0lOTvMtnQqf\ UoZYlRajJegBie3lcKraOnXRkSVgNYdIVcMScPQcSNcWLcZIca\ GcdLWnNYiP_dR`_SbVUdQWeLYgGZhCOQOSTTWWX_Z`cadgdhjg\ loUfsG`w3Vr7VnBVjFVfIVbMVZQVVTVhfRutOsrSqqWooZmnbk\ lfikigimfhpg`WhUCb_AXd9Ri8Ln7Fs6Ax5TtOjpfblbWi_PeX\ IbUBZR4WOARQFNSLJUQFWWBY`7_e3ag7_hBYjEXkIVmLUnPSoS\ Rc_XTgaHof6vkDwlKxlRymYzmczm0iW7jZDk`KlcQleXmhbnji\ omooonihncbnYXnTQnNKnHEnC8kG9iJAfMBdQCaTD_WDtTcfJQ\ TACLFDDJE6NFBKHFIIJGJODKSBLW9MTJQQTUOaXUeRZiMdmHiq\ Bou6ty1oo4jf6fY9aPBYGDWFFUFHSFJQELOENMEPLERJFRHGRA\ 0KPMOYSMgXJpbHygFwYPuPZsGhr7qjCscGtXKuQPwJTxCXy5`z\ CazIblPcfKPU`eTgfNmgGsgAlj8el7Zn5Tp4Mr2Fz1Uz0PcAcM\ Kr4TqOapgiozqnremkVmdKoeIpgHriFsjEulCvmBxo9yp8wqDv\ qHtqLsrPrrUprYosamselsjktnitrhtvgtzftyetydtxctxctx\ btwatw`tv_tv_tzYszWszUrzSrzczzczzczzmzzmzzmzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================