FOTD -- June 26, 2007 (Rating 3) Fractal visionaries and enthusiasts: Today's image is a scene in the East Valley area of the Mandelbrot set. Or more accurately, it is a scene in the area of the four-dimensional Julibrot fractal that corresponds to East Valley. The Julibrot fractal is the 4-D object that would be formed if all the Julia sets were stacked into a single pile. Curiously, the same 4-D object would be formed if all the perturbed Mandelbrot sets were stacked into a single pile, though the object would be oriented in a totally perpendicular direction. Actually, the direction of today's slice is closer to the Julia orientation than the Mandelbrot orientation. It is rotated from the Julia direction in only two of the four possible directions, one rotation of 20 degrees and one of 60 degrees. The East Valley area of the Mandelbrot set is known as Elephant Valley for a good reason. It is filled with elephants -- an endless parade of them marching out of the valley, circling the main bay, and finally losing their identity completely as they near the large north and south period-3 buds. Curiously, the elephants are not to be found in the Julia sets of that area, but they do exist in most of the odd-direction slices between the Mandelbrot and Julia directions. In today's picture we see 4 proto-elephants. The third from the right is the best formed, but even this one leaves much to be desired. To the left of the best elephant is a tall skinny fragmentary one, and at the left edge of the frame is a bit of a trunk without an elephant attached. At the right edge of the frame is a hump that looks like the rump of a large elephant. Actually, this is only a hump. No head or trunk exists beyond the right edge of the screen. I named the image "Elephant Eruption", since the elephants kind of seem to be appearing out of nowhere. When it came time to rate the image, I could give it a rating no better than a miserable 3. It takes more than some twisted elephant parts to make a good fractal. Hey, I can't help it if I like elephants! The calculation time of 4-2/3 minutes is true on the fast P2000 machine. On the slow old P200 unit, the image would take around 23 minutes to finish. But calculation time will be no problem for those who visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed image there. Monday here at Fractal Central was a little too hazy, warm and humid for weather perfection, but the fractal cats enjoyed the temperature of 84F 29C anyway. And the commercial work was slow enough for me to enjoy the fractal elephants. The next FOTD will appear in all its glory in 24 hours. Until then, take care, and maybe fractals are real, while we are not. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Elephant_Eruption { ; time=0:05:41.59-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2a passes=1 center-mag=0.106307/0.591404/315.1321/0.01126/101.\ 178118038552896/76.1753564045048677 params=70/90/30/90/0.28/0/0/0/0/0 float=y maxiter=16000 inside=255 logmap=17 periodicity=10 colors=000bZz`bzZeyXhyVkyTnxRqwPtsNwsMxrMvoMsmMokM\ jhMdeM_aMVZMRWMOUMMSMKRMIRNHPNJOOLOOOQPSQPURPXSQ_T\ SaTXcVaeVffVkgUphTuiSpjRkkQflPdkPYkOSjNQiMQhLQhKQh\ JQhJWdHaaGfZFlVDrSCwPBvUBuYBtaBseBriBqmBqqBnnAB7Ck\ kAhhAeeAbbA__AXXAVUASRAPOAMLAJIAGFADCAA9Az9lw8em8_\ b8TT7NI7GFKbEI_DHXCGUCERBDOACLAAI99F88CszSnuQioOdi\ M_dKWZJRTHMOFHIDCCBbTE_RDYPDWODUMCRLCPJCNICLGBJEBG\ DBEBACAAA8Abrd_naYk_WhYUeWSbUQZSOWQMTOKQMINKGJIEGG\ CDEAACEzzDyzCstCmnBghBabAVX9PR9JL8DFzowxowtowpowlo\ wioweowaowYowVowRowNowJowFowBowXowVowTowSowQowPowN\ owMowKowIowHowFowEowCowBow9owzowzowrowjowbowVowNow\ FowFowEowDowCowBowBowAow9ow8owSowNowIowDowZowTowOo\ wIowDowGowFowEowDowDowCowBowAowAow9ow8owUowSowRowP\ owOowNowLowKowJowHowGowEowDowCowAow9owwoweowPowDow\ CowCowBowBowBowYowZowZowZowZowZowZowZowZowZowZowZo\ wZowZowZowZowZowZowZorVQS } frm:SliceJulibrot2a {; 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=sqr(z)+c |z|<=real(p5+9) } END PARAMETER FILE=========================================