FOTD -- July 09, 2006 (Rating 5) Fractal visionaries and enthusiasts: Due to a late night out, we're a bit late with today's image, but it's better late than never. Today's image rates a 5 and has been names "Surprised Cyclops". Well, it's what I saw when I studied the image. It is a view of a midget in East Valley of the Mandelbrot set. But it looks nothing like a Mandelbrot midget. Nor does it resemble a Julia set of East Valley. True, there is a vague feeling of East Valley-ness in the image, but the so-called midget is nothing more than a shapeless hole that might have been bitten out of the background by an alien zombie (or cyclops). The bifurcating 4-8-16 pattern of elements that surrounds every Mandelbrot Midget and Julia midget has been so distorted that it is barely recognizable. The stretched and twisted elements are a sure sign that we are viewing a remote oblique slice of the Julibrot, the four-dimensional object of which the Mandelbrot set and all Julia sets are but differently-oriented two-dimen- sional sections. Everyone with any interest at all in math wonders what the fourth dimension is. It is totally impossible to visualize, yet we can work with it quite well and know as much about it as we do about the third dimension. 4-D objects are in no way merely unusually-complex 3-D objects. They are entirely different animals, hypersolid monstrosities with outer surfaces that are fully three-dimensional. It is immediately apparent that we have no chance of seeing an entire 4-D object at a single moment of time with our physical eyes. Our retinas have two-dimensional surfaces and could never receive all the information in a 4-D cone of light. The most we could do would be to scan the 4-D object one 3-D slice at a time, making time the fourth dimension. We would see a 3-D object changing shape over time -- a feeble impression of 4-D space. But though we could never see a 4-D object with our physical eyes, could we visualize it with our inner eyes, which have a greater range than our physical eyes? Once again the answer is a resounding no. Some mysterious limit blocks even our imagination. I suspect that this limit is deeply involved with our stage of consciousness. We are at the 3-D stage of con- sciousness, and to visualize the fourth dimension, we would need to expand our consciousness. Can mystics, who expand their awareness, visualize the fourth dimension in their expanded imagination? If they could, how could we determine it? Even if they did, they could do nothing but relate to us the things they had experienced. But we already know about 4-D space and the things they would describe. Mystics might claim that they had actually visualized the fourth dimension, but they would have no way to prove it. As for today's tiny slice of a 4-D monstrosity, it renders in 4-1/2 minutes. Due to the lateness of this message, there might be a delay before the completed image is posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies, dry air, and a temperature of 81F 27C made things quite pleasant here at New Fractal Central on Saturday. But the new fractal cats were more interested in wrecking today's newspaper than in the weather. If they can find so much enjoyment in a small Saturday paper, they will really go bonkers over tomorrow's larger Sunday paper. The local fireworks display went off only four blocks away Saturday evening, making quite a bit of noise. Cassie ducked under the bed for a few minutes, but soon realized that there was no threat. Nico actually went to the window to see what all the excitement was about. For me, things are settling down here at N.F.C. We are not yet at the point where we can find any object almost without thinking of where it is stored, but we are making good progress toward that goal. The next FOTD will appear in 15 hours. Until then, take care, and keep your feet on the earth and your head in the clouds. 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