; Date: Tue, 24 Aug 2010 22:16:15 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 25-08-10 (Squarely Cubic [5.5]) ; Id: <1.5.4.16.20100824221614.11c7260c@pop.mindspring.com> ; --------- ; ; FOTD -- August 25, 2010 (Rating 5.5) ; ; Fractal visionaries and enthusiasts: ; ; The four-dimensional Julibrot is an abstraction, yet a two- ; dimensional slice through it becomes as real as today's image. ; In effect, we are getting something from nothing -- a big-bang ; on a microscopic scale. ; ; Today's image is a totally-real oblique slice through the Z^3+C ; Julibrot. The corresponding point in the Mandelbrot set lies on ; the southern shore line of the western branch of the northern ; seahorse-type valley of the parent Cubic M-set. ; ; I rated the image at a 5-1/2, with 1/2 point of that for the ; coloring. The image is mostly of mathematical interest and not ; all that attractive artistically. The most interesting feature ; in my opinion is the way the elements stretch out from the ; central minibrot in four different directions. In the quadratic ; Julibrot they stretch in three directions, so it is not surpris- ; ing that in the cubic Julibrot they stretch in four directions. ; ; The unlikely values are a sign that the parameters were picked ; at random by the 'evolver' feature of Fractint. This feature is ; of great help in finding the very stretchy orientations in the ; Julibrot, which tend to be quite critical. ; ; I have calculated a second version of today's image, in which ; the central minibrot has been un-skewed and un-stretched until ; it appears almost normal, but in this image the surrounding ; elements are stretched almost beyond recognition. ; ; The name "Squarely Cubic" refers to the square arrangement of ; the groups of nine elements surrounding the open area at the ; center of the image, whatever one might call such an open area. ; ; The calculation time of 3-2/3 minutes is brief enough to avoid ; excessive impatience yet long enough to allow time for anticipa- ; tion to build. Most of the emotion may be taken from rendering ; the image by viewing it in finished form on the FOTD web site at: ; ; ; ; The clouds here at Fractal Central on Tuesday were made more ; enjoyable by the temperature of 75F 24C. Only a few drops of ; rain fell, which were not even enough to dampen the sidewalk. ; The fractal cats were alert when a stray tomcat wandered into ; the yard, but after leaving his mark, the intruder moved on ; without incident. ; ; My day became more interesting when the line leading to the bath- ; room vanity sprang a leak. Leaping to the rescue, I repaired ; the leak before the water rose above the mop-up stage. All the ; while FL gave moral support. The next FOTD will be posted in 24 ; hours. Until then, take care, and what's the latest dope on the ; Theory of (almost) Everything? Are colliding eleven-dimensional ; super-membranes still in fashion? ; ; (The 'almost' refers to the presumably intelligent minds that ; are searching for the theory. The last I heard, physicists had ; neglected to include conscious minds in their everything theory.) ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Squarely_Cubic { ; time=0:03:42.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0\ /2.249922e+009/0.3167/-86.5401900691157948/86.7595\ 921127404353 params=-93.82766624958037/-144.395622\ 7301859/21.19229285561693/-59.73072481460005/-0.06\ 10232505039753/0.7672163526131864/-0.0610232505030\ 753/0.7672163526131864/3/0 float=y maxiter=10000 inside=0 logmap=505 periodicity=6 colors=000ULIULIVLFWKAZK6aKFeKOiIXmGeqEnrDwqCooChl\ D`jDUgEMdEFaF7_F0aG5cHAeFFgDKi8Pk4Um0Zo5cn9plEwiIz\ gNyeRveQwePucOtdNteMteMraOpZQlWUhTYdQaaMeYJiUGmQDp\ MArJDqMFpPHoRKmUMjWOhZRf`TccVaeY_i`YkbVndUofSrgQsf\ SmeUgcVabXW`YP__JY`DXb7Wc1U`1TY1SV1RS1QP1PM1NJ1MG1\ LD1KA1J71I41H11F32E53C74B949A58C66E65G73I82J86KA9K\ BDKCGKDKLFNLGRLHULLXMP`MUcMZgMcjOhnRmqWrt`vhfzYlzM\ lzBkz0ky1jx2iw3hv4gt5es6bm7Zg7Va6T_6Q_6OY6LX6JW5GW\ 5EV5CV5DU5EU4DT4ET4FS4GS4HR4HR7IQAJPDKOFLNIMMLNLOO\ KePJpQIWRHZSG`TFZUIXULVbzTNzSUUQUXPU_OUXcggKTQJTNH\ SKGSHESECRADOBERDFREGRGINHJRJKRKLRMNRNORPjURbU7`UC\ _UIYUNWUTVcYTczSdhQdmOesbazabz`c6cc7cd8ceAceBcfDcg\ EcgFchzciIciKcjLckMckOclPcmRcmSmnTmoVmoWmpYmqZmq_m\ ramsbmtdzu3zv4zw5zx6zy8zz9zzAzzBzzDzzEzzFzzGzzIzzJ\ zzKzzLzzMzzOzzPzzQzzRzzTzzUzzVzzWzzYzz6zzAzzFzzJzz\ NzzSzzWzz`zzdzzhzzmzzqzzv } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } ; END PARAMETER FILE========================================= ; ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;