FOTD -- September 02, 2006 (Rating 6) Fractal visionaries and enthusiasts: Today we come face to face with the monster that has been lurking in the background of nearly every fractal image I have posted -- the abstract but strangely real four-dimensional fractal object known as the Julibrot. The Julibrot must be four-dimensional. It is created by reiterating two complex numbers, and complex numbers have two parts. 2+2=4. But what is the fourth dimension? In the theory of relativity, time is the fourth dimension, but in the Julibrot a fourth spatial dimension exists, meaning that for the Julibrot, time is the fifth dimension. So what is the fourth spatial dimension? In sci-fi stories we sometimes hear of creatures visiting earth from the fourth or fifth or whatever dimension. These fantasy higher dimensions are not true higher dimensions. They are merely alternate parallel universes of three dimensions, like our own universe. The true fourth spatial dimension is a line simultaneously perpendicular to every line we could draw in our 3-space. Such a direction is absolutely unimaginable, almost like there were some kind of impenetrable mental wall blocking our visualizing ability. Yet we can explore 4-space with mathematics as easily as we explore the familiar three-dimensional space of everyday experience. I will have much to say in the next month about the wonders and seemingly impossible features of 4-D objects and 4-D space. But for now it's time to get to today's image. Today's image is an Oblate view of that warhorse of all fractal objects -- Seahorse Valley of the Mandelbrot set. Yes, I realize that the image has no resemblance to Seahorse Valley or its Julia sets, but the thing in the image, which somewhat resembles a party mask, truly is Seahorse Valley, and a lot more of it than we normally see, at that. I will show another totally new view of Seahorse Valley in tomorrow's FOTD, and explain how the images were produced. I rated today's image at a 6, which is slightly above average. The scene has appeared before, but the coloring of today's version is about as good as I have ever seen, justifying the rating. The image renders in 14 seconds, one of the all-time fastest, and fast enough for the most impatient. Those with Fractint deprived computers may see the image by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cloudy and unseasonably chilly morning here at Fractal Central on Friday gave way to a rainy afternoon. The fractal cats were not bothered by the bad weather. They spent the day indoors, by the window, watching the wet birds and squirrels outside, and wishing they could go out to get wet. My day was average, whatever that means. I expect tomorrow to be another average day. Hopefully, the FOTD, which will appear in 24 hours, will be above average. Until then, take care, and don't doubt the new fractal cats. I have a good picture of them sitting on their window sill, and I will soon send it to be posted on the FOTD web site. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= New_View_Seahorse { ; time=0:00:14.66--SF5 on a P200 reset=2004 type=formula formulafile=oldslice.frm formulaname=OldOblate center-mag=-2.22045e-016/4.4\ 4089e-016/0.85918 params=0/-0.75 float=y maxiter=50000 inside=255 logmap=yes symmetry=xyaxis periodicity=10 colors=000E2UC2WA2X82Y62Z40_50`60a70b70c80d90eA0fA\ 0eB0cC0aD0_D0XE0UF0RF5OCAKAEH7HL5KQ2LV0MZ4PZ8SZCUZ\ GXZJ_ZNaZRdZVgZYiZSeaNbcHZeCWgEYhG_hH`iJbiLdiMejOg\ jPhjNbeMYaLTYKOTJJPIELH9HYje`nacrYfvUizQeoNbdK_VHX\ KEUABQNNM_ZIljExuGwpIwkKwfLwaNvXPvSRvNSvJVtKXsKZrK\ `qKcoLenLgmLilLkkLihPheTgbXf_`eYcdVgcSkbPoaNrN6qLC\ oJInHOmFUlD_kBej9ki7qh6vgEkkMaoTSr`Ivg8yiAxjCwkDwm\ FvnGvoIupKurLtsNttOsuQswSrxTryVqzWqwVouUnrUmpTlmTk\ kSihShfRgcRfaQe_QdZUeYYfXagWehViiUmjhdYvXLrVKoTKkR\ KhPKeOJaMJZKJWIJSGJPFIMDIIBIF9IC8IJBJPEKVHL`JMdFKh\ CJk9IeJF_TDUbAOk8NoNMraLupLpqLkrLfrLasLXsMatNeuOiu\ RepTalWZhYVd_S`bOXdLTgHPiELkAHn7Dp39r05X_3WX5VV6UT\ 8TR9SPARNCRLDQJEPHGOFHNDIMBKL9LL7MN9KOBJQDIRFGTHFU\ IEUJFUKFULFUMFUNGUOGUPGUQGTSHTTHTUHTVHTWITXITYITZI\ T_JT`JTaJTbJTcJSdKSdLRdMReNReOQePQeQPfQPfRPfSOfTOg\ UNgVNgWNgWMhXMhYLhZLi_ji_ } frm:OldOblate {; Jim Muth real(z),imag(c) z=real(pixel)+flip(real(p1)), c=flip(imag(pixel))+imag(p1): z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================