; Date: Sun, 09 Jul 2006 09:17:17 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 09-07-06 (Surprised Cyclops [5]) ; Id: <1.5.4.16.20060709092155.2b27cdf0@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Surprised_Cyclops { ; time=0:04:29.18--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000037451060175/-0.000000006544927\ 92/5.378279e+007/0.01533/180/-89.1953663839249487 params=51.7/38/2/0/0.265084671264/0.002993829528/0\ .265084671264/0.002993829528 float=y maxiter=10000 inside=0 logmap=228 periodicity=10 colors=000DRJGVOJYUMaZPdcXcXdcRlcLtcFjXCaQASK7360J\ D5962UmEkpCdhAYa8RU7KM5DF3671KnoFabAPQ5CDKjkG`aCSS\ 8IJ499Bo95Q4qUQ_KHIA8B`B9U97O75I53C31618bY7YT6TP5O\ L4JH3EC298144v7ag5ST3JE196R64L43G32A2151L1WH0QE0LA\ 0G70A305G2kA1W50GpyoZdYHKHiTVYLNNEFB77ATI8NE6HA4B7\ 253jr0dk0Zd0TY0NR0HK0BD0560gW3ZP2QJ1HC1860vuamlWed\ RXXLPOGGGA885Zb0TW0NQ0HJ0BD05608Jg6EX49M24BGpXDhSB\ `N9UI6ME4F9274sH5iE4`B3S82I51920ut3ml2fe2_Z1TS1LL1\ EE0770RRjCVF6F7_VCUPAOK8IF6CA4652ql`jeWc_RXUNROIKI\ DDC9664sRbkNXcJRWFMOBGG7B835slwe_hSOUECFiPYbLTWHOQ\ EJJAED79634GBOD9KB7H96D64A436213s56l45e34Z33S23L12\ E11700M4vI3lE2bB2T71J309e23V12L11A00zsiVSNq5Ec3AR2\ 7D136Ox8Iz6Kz5Mz4Oz2Qz1SzuUzfWzTYzE_z8az4czzezVgzE\ izekzomzgoz`qzTtzMwzEzz7zzBzz8zz6zz4zz2zzIzzDzz9zz\ 4zzYzzTzzPzzLzzHzzCzz8zz4zzezzVzzLzzAzzrzz_zzIzziz\ zczzYzzSzzNzzHzzBzz5zzRzz } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } ; END PARAMETER FILE========================================= ; ;