FOTD -- May 26, 2008 (Rating Arbitrary) Fractal visionaries and enthusiasts: The unknown fascinates me, and what could be more unknowable than space of four dimensions? The problem is, while our math has no difficulty dealing with 4-D, and computers can be programmed to deal with it as logically as they do 3-D, we pathetic humans can do nothing more than twist our faces into a look of astonished puzzlement when asked to visualize something as simple as a 4-D tesseract. Today's image is a scene in Seahorse Valley of the Mandelbrot set, an object every tyro fractalist becomes familiar with the day after he discovers fractals. But the image bears little resemblance to either Seahorse Valley or its Julia set, yet what we are seeing is all part of the great Seahorse Valley complex. What has changed in the image is the angle at which we are viewing the valley. We are seeing it sliced at an angle very close to but not exactly in the Julia orientation. The Seahorse Valley Julia set (actually the -0.78,0 set) may be seen by changing the (p2) parameter to 0,0. The Mandelbrot aspect, which is Seahorse Valley itself, may be seen by changing the (p2) parameter to 1,0 and the (p4) parameter to -0.78,0. I can logically deduce what is going on in all these changing views of the same 4-D object, but I am no closer to visualizing the entire 4-D Seahorse Valley complex than I was that day 20 years or so ago, when I realized that the Julia sets and the perturbed Mandelbrot sets are differently oriented slices of a single 4-D object, the Julibrot figure. Perhaps what we call dimensions are simply another way of describing levels of consciousness, and mankind is now at the three-dimensional level of consciousness. This would imply that space appears three-dimensional because that is the only way we can perceive the abstract reality. If this is so, it is only to be expected that we would naturally develop a mathematics that would be compatible with and would confirm our perception. Enough philosophical rambling already. I named today's image "The Fourth Dimension" for obvious reasons. I gave it no rating, or rather left it to the individual viewer to decide its worth. The calculation time is but a few seconds, so have no fear when running the included parameter file. But if fear strikes, rush to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. BTW, tomorrow's image will be a zoom into today's. Absolute perfection wrapped in a package -- that describes the conditions here at Fractal Central on Sunday. How can cloudless skies, low humidity, light winds and a temperature of 77F 25C be improved upon? The fractal cats must have agreed, for they sat in their window for an hour, watching me finish the yard work, while FL supplied encouragement and occasional refreshment. And despite all this activity, I still found time for the FOTD. The next FOTD will appear in 24 hours or so. Until then, take care, and seek total fulfillment in your endeavor. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= TheFourthDimension { ; time=0:00:14.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=1 maxiter=1800 center-mag=0/-0.0486/0.86 params=2/0/0/0.15/-0.78\ /0/0/0 float=y inside=0 logmap=yes periodicity=10 colors=000IJJ97P7DU6IY5Nb4Sf3Yj2bo1gs0lw6muCnsHoqN\ ooSpmUmkWjiYgg_deaaccZaeW_gTYiQWkNUmKSoHQpEOpBMmCK\ kEIhGGeIEbKC`MAYOBVQCSSDQTEPUDPVDOWDOXDNYDNZDM_DM`\ DLaCLbCKcCKdCJeCJfCIgCIhCHiBHjBGkBGlBFmBFnBEoBEpBG\ qEHrHJsJKtMLuONrNPpNRmNTkMUiMWfMYdL_aL`_LbYKdVKfTK\ gRJiOJkMJmJInHIoFIpCHqAHr8HpAIpBJoCJoDKoEKnFLmHLlI\ MlJMmKNmLOnMOoNPpPPqQQqRQqSRqTRqUSqVSoWTmXUkYViZWg\ _Xe`YcaZab__c`YcaWcbUccScdQceOcfMcgKchIciHcjHckHcl\ HcmHcnHcoHcpHcqHcrHcsHctHcuHcvHcwHcxHcyHczHczHczHc\ zHczHczHczHczHczHczHczHczHczHczHczHczHczHczHczHczH\ czHczHczHczHczHczHdzHezHfzHgzHizHkzHzzHzzHzzHzzHzz\ HyzHxzHzzIvzJuzKtzPszUrzZqzcozhmzmzzrzzvzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } END PARAMETER FILE=========================================