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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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=========================================