; Date: Mon, 25 Jun 2007 21:34:47 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 26-06-07 (Elephant Eruption [3]) ; Id: <1.5.4.16.20070625213951.2b5f5c82@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ;