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: <http://www.crosscanpuzzles.com/Archives.html> and in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> 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=========================================