; Date: Fri, 06 May 2011 22:17:14 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 07-05-11 (Gate to the Abyss [8.5]) ; Id: <1.5.4.16.20110506221717.125781d2@pop.earthlink.net> ; --------- ; ; FOTD -- May 07, 2011 (Rating 8.5) ; ; Fractal visionaries and enthusiasts: ; ; Today we take a return trip to perhaps my favorite of all ; fractal objects -- the rectangle in the Julia set of the East ; Valley of the large split-apart minibrot on the infinitely ; divided main spike of the Z^(2.003) Mandeloid. ; ; This rectangle exists in its pure form only in the real(z) and ; imag(z) directions. In the real(c) direction it quickly shrinks ; to a dot and totally vanishes. In the imag(c) direction it ; falls apart at once, without bothering to shrink first. ; ; But in some strange manner, it manages to also appear, in an ; extremely squashed form, in the Rectangular and Oblate planes, ; where it must be considerably stretched to unsquash it. In ; today's image we see the rectangle at an orientation halfway ; between the Julia and the Rectangular, which makes the necessary ; stretching less extreme. To see other rotations, vary the ; real(p2) parameter from zero, which will give the Rectangular ; view, to 90, which will return to the original Julia rectangle. ; The stretching will need to be adjusted along the way. ; ; I named the image "Gate to the Abyss". At this new angle, the ; rectangle actually does resemble a doorway to a vast unknown. ; As to what that unknown might be, I leave it to the viewer to ; determine. To me, it is the fourth dimension. ; ; Since I did put extra effort into the coloring, I rewarded ; myself with a half point bonus for the coloring, bringing the ; image's rating to a very respectful 8-1/2. ; ; With a calculation time of 1-1/3 minutes, running the included ; parameter file will be a minor chore. ; ; The pre-calculated image is posted at: ; ; ; ; and in high definition at: ; ; ; ; The original FOTD web site may be accessed at: ; ; ; ; Friday began with lots of sun here at Fractal Central. A thin ; overcast arrived in the afternoon and filtered the sun, though ; it remained dry. The temperature reached a high of 70F 21C, ; which pleased the fractal watch cats. They manned their posts ; in the window, guarding against intruding strays. ; ; The day of the humans was reasonable enough. I spent the day ; scrounging up fractals, while FL passed the day recuperating ; from Thursday's garden work. The next FOTD is due to be posted ; in 24 hours. But sometimes Saturday brings a trip to a local ; antique emporium, so do not be concerned if the FOTD for May 08 ; is late. Until whenever, take care, and was it a fully rational ; scientist or a crackpot mystic who claimed that the world we ; observe around us is surrounded by other invisible worlds? ; ; ; Jim Muth ; jamth@mindspring.com ; ; ; START PARAMETER FILE======================================= Gate_to_the_Abyss { ; time=0:01:23.65-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/-0.0087045\ 7782794517/71.66298/43.054/180 params=90/0/45/90/\ -1.7435/0/0.00019/0.07388/2.003/0 float=y logmap=62 maxiter=60000 inside=0 symmetry=yaxis periodicity=6 colors=00040661982CA4FC6IE8LGAOICRKEUMGXOI_QKbSMeU\ OhWQkYSm_ToaUqcTseSugRuiRukQvmPvoOvqOvpStrWst_rvcq\ xhpzmozrpzvszzvzzzzzzzzzzzzzzvzzrzzmzzgzzdzyazxazw\ azw`zv`zu`zt_zt_zs_zr_zqZzqZzpZzoYznYznYzmYzlXzkXz\ kXzjWziWzhWzhWzcSzZOzUKzPGvKCrF8mB5hC8cDBZEEUFHPGK\ OGMRHPUISXJV_KYaK_dLbgMejNhmOkoOmmRkkTjiVhgXgfZed`\ dbbb`daZf_YhZgh_ph_dcTTZMHUF5P99SEDUJHXOLZTO`XN_YN\ ZYNYYNYYNXYNWZNWZNVZNUZNUZNTZMS_MS_MR_MQ_MQ_Q9HQ9G\ P9GP9GO9GOAFNAFNAFMAFMAELAELAEKADKADJADJADIBCIBCHB\ CHBCGBBGBBFBBFBBEBAEBADBADBACC9CC9BC9BC8AC8AC89C89\ C78C78C77C77D66D66D65D65D54D54D53D53D42D42D42D47U8\ CiCHyGGzFGzFGzFGzFGzFGzFFzFFzFFzEFzEFzEFzEFzEEzEEz\ EEzEEzDczDczDczDczDczDczDczDczCzzCzzCzzCzzCzzCzzCz\ zCzzBzzBzzBzzBzzBzzBzzBzzBzzBzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 ;