; Date: Sun, 14 Feb 2010 12:38:48 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 14-02-10 (A Crazy Angle [6]) ; Id: <1.5.4.16.20100214123951.2b9f6894@pop.mindspring.com> ; --------- ; ; FOTD -- February 14, 2010 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Not surprisingly, the antiquing bug did bite on Saturday, which ; explains why this FOTD is late. ; ; The name "A Crazy Angle" refers to the orientation of the image ; slice through the 4-D (Z^2+C) Julibrot. In the background of ; the image we see a grossly magnified version of the normally ; insignificant period-30 bud on the south shore of East Valley ; of the Mandelbrot set. ; ; The ridiculous enlargement is due to the angle at which the ; image cuts the actual 4-dimensional bud-complex. The closer the ; orientation lies to the true Julia direction, the greater the ; enlargement, and since today's image is cut 0.015,0.015 degrees ; from the actual Julia, the enlargement is spectacular indeed. ; (At the actual Julia orientation, the enlargement is infinite, ; and the same point of the bud is reflected in the entire scene.) ; ; Do not try to visualize how an object may be magnified in two ; dimensions by simply varying the direction in which it is ; sliced. It's another of those 4-D mysteries, like exiting a ; completely closed room by stepping around the wall, that make no ; sense in 3-D space. ; ; I rated the image at a 6, mostly because of the mathematical ; interest. The calculation time of 4-1/4 minutes is slower than ; I would have preferred, but with the image maxiter at 120,000 it ; is quite reasonable. ; ; And of course, the finished image, for all it is or is not ; worth, is posted for immediate satisfaction on the FOTD web site ; at: ; ; ; ; Partly cloudy skies, a high temperature of 30F -1C and a few ; flakes of snow made for a typical midwinter day here at Fractal ; Central on Saturday. The fractal cats passed the day sleeping. ; ; The next FOTD will be posted in 24 hours. Until then, take ; care, and free your mind from the bonds of convention. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= A_Crazy_Angle { ; time=0:04:14.06-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0\ /1.182144/1/90/0 params=89.985/0/89.985/20/0.26065\ /-0.0022/0/0/2/0 float=y maxiter=120000 inside=0 logmap=yes periodicity=6 colors=000PHZSGYVFXYDW`CVcBUf9Ui8Tl7So5Rr4Qu4Px4Pv\ AQuGRsMSrRSqVToZUnbUlgVkjWjkWljXmhXnfXocXp`XqYXrWX\ sTXtQXuNXvKXwHXxEXyCXpHOhLG_Q8SU0NPBIKLDFV8Bd9Ab9A\ `A9ZA9XB8VB8TC7RC7QD6OD6ME5KE5IF4GF4EF4DJAIMFNQKRT\ PWXU___dcdhfimjnqmsvpxzrruslqtglvahwWcxR_uTarVcpXd\ mZfj`hhaieckbem`gnYipWjqabgfVZkNQpFHu78rCFpGLmLRkP\ XhUbfYhcbnaft_jzZhrYfkXdcXbXW`QVZIUXBUV4VX5WY6XZ6Y\ `7Za8_b8_d9`e9afAbhBciBdjCdkCfjCgiChhCjgCkfCSiQShM\ ThIThLThPSfUReZQdcPchObmNarM`wL_wKZwJYwIXwHWwGWwFX\ wEYwDZwC_wB`wAaw9br3cm8dhCecGfZKgUPhPTiKXjF`kGUlIN\ mLCnOGoNJpNNqNQrNUsNXtN`uNcvNgwNjxNcxNcxNcxNcvMcuL\ ctKcsJcqIcpIcoHcnGQmzQmzRmzSmzSmzTmzUmzVmzVmzWmzXm\ zYmzYmzZmz_mzXmz_mzbmzemzgmzjmzmmzomzrmzumzxmzwmzw\ pzvwzvwzvwzuwzuwzuwztwztwztwzswzswzuwzswzrwzpwzowz\ mwzlwzjwziwzgwzfwzdwzcwzawz`zz_zzVzzQzzIzzLzzNzzPz\ zRzzTzzVzzXzzZzz`zzbzzdzz } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint