Fractal of the Day (FotD) by Jim Muth

FOTD -- July 07, 2009 (Rating 7)

Fractal visionaries and enthusiasts:

In today's image we shift the direction of our gaze to the Rectangular orientation and see what goes on at the period-30 elephant complex when seen from this angle. Some fairly normal elephants are still there, such as those scrunched at the right edge of the image, but what caught my attention are the bits and pieces of elephants at the center.

I named the image "Elephantettes", an oxymoron if ever there was one. But the front halves of elephants, their trunks curling out left and right, actually do appear a bit delicate.

The double-half-elephant effect is due to the angle of the slice and the curved shape of the things being sliced. Elephants are actually four-dimensional shapes that curve and twist through four-dimensional space. It would take a five-dimensional viewer to actually see the entire 4-D elephant shapes, though a 4-D viewer could intuit the entire shapes.

The improved color palette makes the image worthy of a rating, and the rating I chose is a 7. The calculation time of five minutes is bearable for all but the most impatient. The most impatient may avoid calculation altogether by enjoying the finished image on the FOTD web site at:

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

A perfectly average early July day prevailed here at Fractal Central on Monday. The mostly sunny skies and temperature of 82F 28C were just what the fractal cats ordered. Their only complaint was that they never get to go outside like the old fractal cats used to do back at old fractal central. (Actually, the old and the new fractal cats never met.)

My day was comfortably busy. The next FOTD will be posted in 24 hours. Until then, take care, and I believe only what I see, and I'm not sure I believe most of that.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com

START PARAMETER FILE======================================= Elephantettes { ; time=0:05:18.62-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 float=y inside=0 passes=t center-mag=-0.0019407218694615/-0.4731591677497216/\ 2371/0.001754/90/0 periodicity=10 maxiter=27500 params=90/90/0/90/0.260821781/0/0/0/2/0 logmap=25 colors=000wzMxzLwzKuzKszJqzIozHlzHizGfzGczG`zFYzHW\ zKUzNSyQRxTQxWPxZPyaPycPyePxgPxjPxmPwpPwsPwvPwwPvw\ PvvPvsPuqPuoPumPtkPtiPtgPtePscPscPsaPr`Pr`Pr`Pq_Pq\ _Pq_Pq_Pp_PpZPpZPoZPoZPoYPnYPnYPnYPnYPnYPnYPnYPnYP\ lVPiSPfQPcNP`KPYHPVFPSCPP9PM7NM8MK8LJ9KH9IGAHEAGDB\ FBBF89EABEBCECDEDEEFFDGGDHHDIIDKJDLKCMLCNMCPNCQOCR\ PBSQBURBVSBWUBXVAZWA_XA`YAaZAc_9d`9ea9fb9hc9id8je8\ kf8mg8nh8oi8pj9oi9niAmiAliAkiBjiBiiBhiCgiCfjCekDdl\ DcmDbnEaoE`pE_qFZrFYsFXtGXuGXvHXwHXxH`yIYzI_zIazJg\ zJazJ`zKVzKUzKOzLNzLHzLGzMFzMEzMDzNCzNBuK5pM8pNApP\ CpNApOCuPDuQEuRFzRGzSHzTIzUJzULzVMzWNzXOzYPzYQzZRz\ _Sz`Uz`VzaWzbXzcYzdZzd_ze`zfbzgczgdzhezifzjgzkhzki\ zlkzmlznmznnzoozppzqqzrszquzqwzqwzpwzpwzpwzowzowzo\ wznwznwznwzmwzmwzmwzlwzlwzlwzkwzkwzkwzjwzjwzjwziwz\ iwziwzhwzhwzhwzgwzgwzgwzfwzfwzfwzewzewzewzdwzdwzdw\ zcwzcwzcwzbwzbwzbwzawzawz } 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=========================================