; Date: Mon, 03 Oct 2011 20:46:25 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 03-10-11 (Royal Scepter [No Rating]) ; Id: <1.5.4.16.20111003204631.1457ae3c@pop.earthlink.net> ; --------- ; ; FOTD -- October 03, 2011 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; With today's FOTD we find ourselves roaming once again in four- ; dimensional hyperspace, as we will be all the month of October. ; Every image this month will be created with the Mandelbrot ; expression, Z^2+C, but none of the images will resemble the ; usual Mandelbrot or Julia scenes. ; ; Today's image is a view of Scepter Valley, which is the valley ; at -1.25 on the negative X-axis of the Mandelbrot set. This is ; the inspiration for the name "Royal Scepter", though the image ; looks nothing at all like the Mandelbrot or Julia aspects of ; Scepter Valley. ; ; The scene is sliced at an odd angle oriented 75 degrees from the ; Rectangular direction toward the Julia direction of the ; Julibrot figure. The brilliant pink vertical stripe in the ; center of the image is part of the open space between the two ; branches of the valley, viewed from the side. ; ; Though the mathematical interest rates higher than usual in ; today's image, I could find nothing of artistic value in it that ; might raise the rating above that of an average 7. I did spend ; some extra time on the coloring however. ; ; In 4-D space, such as the space in which the Julibrot figure ; lies, there are six perpendicular planes through every point. ; Every plane is perpendicular in the normal 3-D manner ; (intersecting in a line) to four other planes, and absolutely ; perpendicular (intersecting in only a single point) to one other ; plane. In the Julibrot the absolutely perpendicular pairs of ; planes are Mandelbrot-Julia, Rectangular-Parabolic, and ; Oblate-Elliptic. All other pairs of planes lie in the same ; 3-space and are perpendicular in the normal 3-D manner. ; ; Today's image is oriented between the Rectangular and Julia ; directions, which implies that the rotation is of the normal 3-D ; kind. In this case, the axis of rotation is the imag(z) line ; that intersects the M-set at -1.25 of the X-axis. ; ; In today's image, the rotation may be seen in progress by ; varying the real(p2) parameter between zero and 90, which takes ; us on a trip from the Rectangular to the Julia directions. But ; be warned, the calculation time increases dramatically as the ; value of real(p2) gets close to 90. ; ; The higher dimensions have always been a mystery, but over the ; years I have come to see 3-D space as a construct of the mind, ; and also as an indicator of our level of consciousness. We can ; not imagine spaces of four or more dimensions because we have ; not yet reached a level of consciousness where it is possible. ; ; Will the human race eventually evolve to a level where higher ; spatial dimensions are within our grasp? Will we then find ; ourselves in a world with four or more spatial dimensions? ; Physicists tell us that the higher dimensions (11 at the latest ; count) are there, but we cannot percieve them. If this is so, ; who knows what mysteries the universe yet holds. ; ; These questions will not be answered in today's image, but the ; image does calculate in only one brief minute. The image will ; make the questions just a bit more significant however. ; ; The inconvenience of calculating a parameter file may be avoided ; by viewing the completed image on the official FOTD web site at: ; ; ; ; The image may be enjoyed in high-definition at: ; ; ; ; The original FOTD web site may be perused at: ; ; ; ; Heavy clouds continued here at Fractal Central today, with a ; very autumnal temperature of 54F 12C. The fractal cats, solidly ; in cold weather mode, spent the day doing warm things such as ; curling up on the blankets. FL and I, the local humans, spent ; the day keeping things running, which is not always as simple as ; it first appears. ; ; The next FOTD will be posted in 24 hours. Who knows where in ; the Z^2+C Julibrot figure we might find ourselves tomorrow, or ; what we might find there. Until then, take care, and is three- ; dimensional physical reality really real? ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= Royal_Scepter { ; time=0:01:01.24-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=0/0.0169994/\ 2.456186/1.1123 params=90/0/75/90/-1.25/0/0/0 float=y maxiter=50000 inside=255 logmap=3 symmetry=yaxis periodicity=0 colors=000agobgocgodgoegnfgmggmhfmgfmgemfdmdcmbaj`\ _gZYcVW_RTWOPSLMOIJLFGHCDE9AA67734334635936C38F3AK\ 3CO3ES3GW3I_4Lc4Nf4Qi4Sl4Xo4Zr4au4bx4dz9dzDdzIczMb\ zR_zQYzPWzOUxNRvMOtMOqNOoNOnNOmOOlOOkPOjPNiPNhQMgQ\ LfRLeRLdSKcSKbSKaTJ`TJ_UJ_UIZUIZVIYVIYWJXWIXXIXXJW\ XJWYJVYKVZKUZKUZLU_LT_LT_MT`MS`MS`MRaMRaLRbLQbLQcK\ PcKPcKOdKOdKOeKNeKNeKMfKMfKLgKLgKKhKKhKKhKJiJJiJIj\ IIjIHjHHkHHkGGlGGlFFlFFmFEmFEnGEnIDoKDoMCoOCpPBpQB\ qRBqSAqTArU9rW9sY8s_8sa3sb4sZ4oU4kP4iK4iF4iA4i85i8\ 5i95i95iA5iA5iA5iB6iB6iC6nC6nD6nD6nD6nE7nE7nF7nF7n\ G7nG7nG7nH8nH8nI8nI8nJ8nJAr9FsAKsAPsAUsAZsAcsAhsBm\ sBrsBvsBzsBzsBzsCzsCzsCzsCzsCzsCzsDzsDzsDzsDzsDzsD\ zsEzsEzsEzsEzsEzsEzsFzsFzsFzsFzsFzsFzsGzsGzsGzsLzs\ LzsLzsMzsMzsMzsMzsMzsMzsNzsNztUzuUzvUzwUzxUzyUzzUz\ zUzzZzzZzzZzzZzzZzzZzzZzzZzzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczxbx } 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 ;