; Date: Fri, 01 Sep 2006 23:23:45 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 02-09-06 (New View of Seahorse Valley [6]) ; Id: <1.5.4.16.20060901232437.2b477b1e@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ;