FOTD -- October 09, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows Julia sets of a point on the west shore line of the large period-3 north bud of the Mandelbrot set. I say Julia *sets* because the image is filled with countless Julia sets. All the tiny orangish things spotting the deep blue background are smaller Julia sets. But don't bother checking them. They all appear the same as the large set filling the frame. The image is actually a scene in a 'perturbed' Mandelbrot set. The perturbed sets are slices through the Julibrot in the Mandelbrot orientation, but they have starting points other than 0,0. (For some reason, the type=mandel formula starts the points at the square root of the value assigned the parameters, but IMO, the formula is so fast that this is only a tiny, easily- worked-around flaw.) In this particular area of this particular perturbed set, the low-iteration stuff appears to be moth-eaten, filled with holes of varying size, while the high-iteration stuff remains mostly hidden beneath the low-iteration stuff, with only small patches showing through the moth-holes. The curious thing is that the moths who ate the holes were very well-educated, and ate holes in the shape of Julia sets. To see the true Julia set of this area, reset the parameters to 0,0 and, without waiting for the image to finish, strike the space bar twice. A skeletal Julia set will result. At this point, reset the logmap to 1 to see the surface Julia set or leave the logmap at minus-4375 and do an inzoom or two to reveal another version of the large Julia set that appears in today's FOTD lurking in the depths, just a bit too small to be visible at the surface. The name "Julia in Mandelbrot" accurately describes today's image. The rating of a 6 is a bit low to fully justify the 7-1/4 minutes required to run the parameter file. To avoid all this tedious calculation, check the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Or check the high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Morning fog and afternoon sun earned mixed reviews for the weather in the Fractal Central area today. The temperature of 79F 26C was about as perfect as it can get however. The fractal cats were apparently energized by the perfection, and spent a good part of the afternoon playing hide and seek games on the book shelves in the hallway. The humans, who always knew the location of one another, spent the day dreaming of things to come, such as the next glorious FOTD, which will be posted in under 24 hours. Until then, take care, and from what I read in a magazine recently, the Limerick: A crusty old codger named bright, Could travel must faster than light. He took off one day, In a relative way, And came back on the previous night. just might be true. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Julia_in_Mandlbrot { ; time=0:07:16.13-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.2176\ 546382061398/+0.7252284839096655/6.042805e+009/1/\ -145/0 params=-0.984435560167241/-0.220313119907224 float=y maxiter=2500000 bailout=9 inside=255 logmap=-4375 periodicity=0 colors=00055H55H56H45H46H45H36H35H36H36H26H26H25H1\ 5H14H14H14H45J76LA7NC8PF9RIATLBVNBWMCVLCVKDVJDVIEU\ IEUHFUGFUFGTEGTDHTDHTCISBISAJSbSDcRCdQCdPCePCeOBfN\ BgMBgMBhLAhKAiKAjJAjIAkH9kH9lG9mF9mE8nE8nD8oC8oC8p\ D9pD9pE9pE9pF9pF9pF9pG9pG9pH9pHApIApIApIApJApJApKA\ pKApKApLApLApMBpMBpNBpNBpNBpOBpOBpPBpPBpPBpQCpQCpR\ CpRCpSCpSCpSCpTCpTCpUCpUCpVDpVDpVDpWDpWDpXDpXDpXDp\ YDpYDpZEpZEp_Ep_Ep_Ep`Ep`EpaEpaEpaEpbEpbFpcFpcFpdF\ pdFpdFpeFpeFpfFpfFpgGpgGpgGphGphGpiGpiGpiGqjGrjGsk\ GtkHulHvlHwlHxmHymHznHznHznHzoHzoIzpIzpIzqIzqIzqKz\ rKzrIzsKzsKzsKztUzuUzvUzwUzxUzyUzzUzzczzczzczzczzc\ zzczzczzczzczzczzczzczzczzczzczzczzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzwzzwzzwzzwzzwzzwz\ zwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzw\ zzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzz\ wzzwzzwzzwzzwzzwzzwzzwzzw } END PARAMETER FILE=========================================