; Date: Thu, 27 Mar 2008 19:12:37 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 28-03-08 (In a Soiled M-brot [8.5]) ; Id: <1.5.4.16.20080327181455.0da7d0ee@pop.mindspring.com> ; --------- ; ; FOTD -- March 28, 2008 (Rating 8.5) ; ; Fractal visionaries and enthusiasts: ; ; One of the reasons I am fascinated with fractals is because they ; are four-dimensional things, and I waste no end of time futilely ; trying to visualize a four-dimensional anything. Many phenomena ; in 4-D hyperspace have similar things in our familiar 3-D space, ; which help us to understand hyperspace. But there is at least ; one thing in 4-D space (I am sure many others exist.) that is ; totally unlike anything in our 3-D space. That thing is the ; motion called double rotation. ; ; In 3-D space an object rotates about a line as its axis, and due ; to the gyroscopic effect, that line will retain its orientation. ; But in 4-D space a 4-D object rotates about a plane as its axis, ; which makes the situation more complex. In a simple 3-D type of ; rotation, the points of a 4-D object describe a circle, while an ; entire plane of the object remains fixed in place as its points ; turn on themselves. And just as in 3-D space, the gyroscopic ; effect will keep the object rotating in the same direction. ; ; But what of that axis plane, where the points remain stationary, ; while turning in place? This is the weird thing. Since the ; axis-points are not moving, they are not subject to the gyrosco- ; pic effect, and the entire axis-plane can turn on itself around ; its center point, carrying the entire 4-D object with it, while ; the entire object continues to rotate in the first direction. ; The object is now in a state of double rotation, a motion ; totally alien to our familiar 3-D objects. ; ; While fantasizing a walk on a 4-D hyperplanet recently, and ; trying to imagine the apparent motion of the heavenly bodies, I ; realized that I was perilously close to visualizing double ; rotation, (as projected into 3-D space of course.) What I ; imagined is extremely difficult to put into words, but I'll give ; it a try in a near-future FOTD discussion. ; ; As for today's image, it lies in the parent fractal that results ; when 0.01 part of Z^(-2) is subtracted from the classic ; Mandelbrot set. This fractal is a distorted M-set, filled with ; debris. Today's image is located in the East Valley area of the ; remains of the large minibrot on the negative X-axis of the ; M-set. ; ; I named the image "In a Soiled M-brot", which the parent fractal ; most certainly is. I rated it at an 8-1/2 -- 8 points for the ; underlying fractal, 1/2 point for my coloring work. ; ; The calculation time of only 49 seconds means that no one will ; be disappointed with the result. Some may prefer to avoid the ; calculation however, so for convenience, the finished image is ; or soon will be posted on the FOTD web site at: ; ; ; ; Good weather in early spring never lasts long in Central ; Pennsylvania, so we were not too disappointed here at Fractal ; Central when Thursday turned out cloudy, chilly and drizzly. ; The temperature of 45F 7C kept people well wrapped, while the ; drizzly mist kept the rain gear handy. The fractal cats kept ; cozy near the heat. ; ; My day was on the busy side, though not too busy to affect the ; fractal. The next FOTD will appear in 24 hours. Until then, ; take care, and there is more to empty space than meets the eye. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= In_a_Soiled_M-brot { ; time=0:00:49.43-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-1.230634995848692/-0.488602834129332/\ 1.201185e+011/1/140/0 params=1/2/-0.01/-2/0/0/0/0 maxiter=1500 inside=0 symmetry=none periodicity=10 colors=000WJLVIJUHITFGSEFRDDQtCPrAMp9Mn7MlkMjhMheM\ fbMd_MaYMZVMWSMSPMPMMMKMJHMGEMDBMA8aEKZDIXCGVBESAC\ Q9AO88dhkjGbgF_eEXcDU`CRZBOXBLVAIS9FQ8CO799aiAZeoo\ rmiskcsjYthStfMueHucPsbWracq`jp_roZynHWXJYVL_UNaTP\ cRQdQSfPUhNWjMXkLZmJ`oIbqHcrGanF`kEM87_hEZeDYbCWZC\ VWBUTATQASN9QJ8PG8OD7NA6nsA`dh_aeZ_cYY`XWZWUWVSUUQ\ RTOPSLNRJKQHIPFFODDNBAM98qrcoo`mlZkiXifVgcTe`RcYPa\ VN_SKYPIWMGUJESGCQDAOA8NKTMIQMHOMGMMEJMDHMCFMACM9A\ M88f3mb4e_5Z4c`4c`4aZ4_X6YV7WT8URASPBQNCOLDMJFJHGH\ FHFDJDBKB9L97zzzwwwsssooohfhc`aZXYXUUVSSTQQQOOOMMM\ KKKDCKA9z6gw7cs7`o7Yk7Vg7Td7Rb7P`7NZ7KX7IV7GT7ER7C\ M7AJ78zUKrOAgI9XC7sTHnQFjNEfKCbIBYFAUC8Q97Lr_MnYMk\ WMhUMeSMbQMZOMWMMTKMQIMNGMJEMGCMDAMA8bmz`hzZdzX`zW\ WzUSzSOzRJzPFHNBBDxNErLFlJGfHH`FIVDJPBKJ9LD7zyKwwK\ rrVmhYhcUbYQ_TMWNITIEPCAzqHmaD_M9TVESTDRRCRPCQNBQL\ APJAPI9OG9OE8NC7NA7M86YLN } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } ; END PARAMETER FILE========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint