; Date: Sun, 02 Oct 2011 08:32:07 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 01-10-11 (The Fourth Dimension [8.5]) ; Id: <1.5.4.16.20111002083210.13978ee2@pop.earthlink.net> ; --------- ; ; FOTD -- October 01, 2011 (Rating 8.5) ; ; Fractal visionaries and enthusiasts: ; ; I have decided to make the fourth dimension the FOTD theme of ; the month for October. 4-D hyperspace is not that much of a ; departure from the 3-D space we are so familiar with, since the ; Z^2+C Julibrot, (the composite of all the Julia and Mandelbrot ; sets), is a 4-D figure anyway. ; ; Today's image shows a small part of the shore line of the ; period-4 bud that lies on the northeast lobe of the main bay of ; the Mandelbrot set. Actually, the scene shows a section of the ; shore-line as it extends into hyperspace ; ; The entire scene has been stretched by a factor of over 57, ; (the tangent of 89 to be exact), in the direction of the ; Mandelbrot Y-axis. This stretching was necessary to keep the ; Mandelbrot ghost buds in their normal near circular shape as the ; view was rotated from the Mandelbrot orientation to within one ; degree of the Oblate orientation. ; ; The result of all this stretching and the additional skewing ; that resulted from rotating the image is a scene that vaguely ; resembles a scene on an alien planet with wispy cirrus-like ; clouds in the sky. ; ; I could have given the image a name such as 'Alien Cirrus' but I ; decided to name it simply "The Fourth Dimension", which quite ; nicely leads off a month that will be devoted to Julibrot scenes ; in 4-D hyperspace and hyper-objects such as the six regular 4-D ; polytopes. ; ; The extra half-point in the rating of 8-1/2 is due to the ; coloring. My modesty prevents me from granting myself any ; additional bonus points, even though they were deserved. ; ; The calculation time of 13-1/2 minutes is somewhat slow, leaving ; it to the individual fractalist to decide whether the 4-D scene ; is worth the wait. ; ; To avoid calculation altogether check the finished image on the ; official FOTD web site at: ; ; ; ; And check it in high definition at: ; ; ; ; The original, now classic, FOTD web site may be reached at: ; ; ; ; Today's weather left much to be desired here at Fractal Central. ; The fractal cats felt that the temperature of 52F 11C was too ; chilly for comfort, while FL and myself felt that the heavy ; clouds that blocked the sun and the occasional rain that fell ; through the day were too unpleasant for the first day of ; October, which is supposed to bring bright blue weather. ; ; The next FOTD will be posted in 24 hours. Until then, take ; care, and the formula for the hypervolume of a 4-dimensional ; hypersphere is 1/2(pi^2)*(r^4). How long will it be until ; someone other than a physicist actually needs this formula? ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= TheFourthDimension { ; time=0:13:38.22-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=t center-mag=-0.09254657031508136/+0.561631274103498\ 60/855.02/0.03822/-1.073/-87.9929489969829319 params=0/0/89/0/0.25/0/0/0 float=y maxiter=125000 inside=255 logmap=140 periodicity=6 colors=000UizUhzUgzUfzUezUdzUczUbzUazU`zU_zU`zUazU\ bzUczVdzWezVfzWgzVhzUizThzShzRgzRfzRezQdzQczPczPcz\ OczOczNczNczNczLczLdyJdxJdwHevIeuFetEfsEfrDfqDgpCg\ oCgoBhpBhqAirAisAit9ju9jv8jw8kx7ky7kz6lz6lz4kz5iz6\ gz6fz7ez8ez8dz9cz9czAdzBdyBdyCdxCdxDcxEbwEawFavF`v\ G_vHZuHYuIYtIXtJWsKVsKVsLUrLTrMSrNSsNRtOQuOPvPPyQO\ zQNzRTzRSzSSzSRzSPzSOzSNzSMzSLzSLySLxSLwSLvSLuSLsS\ LqSLqSLqSLqSLqSLqSLqSLqSLpSLoSLnSLmSLlTLkTLjTLiTLh\ TLgTLfTLeTLdTLcTLcTLbTLbTLbTLaTLaTLaTLaTLaULbVLcWL\ dXLeYLfZLg_Lh`LiaLjbLkcLldLmeLnfLogLphLqiKsiKtjKuj\ KvkKwkKxlKylKzmKzmKznKznKzoKzoKzpKzpKzqKzqKzqKzrKz\ rKzsKzsKztKztKzuKzuKzvKzvKzwKzwKzyKzyKzyKzyKzyKzyL\ zyMzyMzzNzzNzzOzzOzzPzzQzzQzzRzzRzzSzzSzzTzzUzzVzz\ WzzWzzXzzYzzYzzZzz_zzazzazzbzzbzzdzzdzzezzfzzfzzgz\ zgzzhzzizzjzzjzzkzzlzzlzzmzzmzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzznzznzzozzpzzpz00H } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;