; Date: Fri, 05 Jun 2009 16:26:40 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 06-06-09 (Seahorse Valley-06 [7]) ; Id: <1.5.4.16.20090605162758.2bcf3e8a@pop.mindspring.com> ; --------- ; ; FOTD -- June 06, 2009 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; Fractals are filled with bottomless spirals. They are probably ; the most common features in the world of fractals. But how ; often have we seen a set of concentric fractal rings with a very ; definite bottom? After viewing today's Seahorse Valley scene, ; we have seen such a set at least once. ; ; But are these rings truly what they appear to be. And for that ; matter, are the everyday fractal spirals truly what they appear ; to be. The Mandelbrot set does not exist in isolation. It is a ; particular slice down the center of a four-dimensional monstros- ; ity known as the Z^2+C Julibrot. The elements in the Julibrot ; are 4-D objects that twist and turn in four-dimensions. Those ; very attractive spirals are actually 2-D slices of 4-D things ; that cannot be visualized but most likely approximate nested ; hyperspheres. Today's image is simply a slice in a different ; direction through one of these nested hyperspheres. ; ; The disk at the center of today's image is the next inner shell ; of the nested hyperspheres, which has not been cut entirely ; through. A bit of parameter tweaking will punch a hole in the ; center of the flat central disk, which will then become another ; ring. I have not yet tried tweaking the parameters, though it ; should not be very hard to find the right ones. ; ; I added a bit of extra life to the scene by rendering it with ; the outside set to 'summ'. The rating of a 7 is the lowest ; rating that brings satisfaction for a fractal well done. ; ; The calculation time of 8-2/3 minutes is slightly slow. A more ; efficient way of viewing the sliced nested hyperspheres is to ; surf out to the FOTD web site at: ; ; ; ; and view it at leisure there. ; ; Solid clouds, steady light rain and a temperature of 61F 16C ; kept a strict damper on things here at Fractal Central on Fri- ; day. The fractal cats spent the day catching up on their sleep, ; though they did have a brief moment of excitement when a bedrag- ; gled stray cat passed by their window. ; ; My day was about average, as are most days. Hopefully, tomorrow ; will be the same. Unless we get involved in some kind of expedi- ; tion on Saturday, the next FOTD will be posted in 24 hours. ; Until next time, take care, and we know that an electron is a ; unit of energy, but is it a particle, a wave, a wave packet, or ; none of the above? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Seahorse_Valley-06 { ; time=0:08:42.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 maxiter=2820 center-mag=+1.074127267031372/-0.1217313849462725/\ 6907.325/0.03441/-45.7342470354590063/-52.78617\ 25848204202 params=90.1/46.3/90.9/91.4/-0.75/0/0/\ 0/2/0 float=y inside=0 outside=summ periodicity=10 colors=000bhgchecibdj`ejZekXflUflSgmQhnOhnMioJipHj\ pFkqDkrAlr8ls6mt4nw0mt2lq3ko5kl6ji8ig9idBhbCg_DgXF\ fVGeSIePJdNLcKMbIMcINdIOeIPfIQfIQgIRhISiITiIUjIUkI\ VlIWlIXmIYnIYoIZoI_pI`qIarIarIbJ_GJZGJYGJYHIXHIWHI\ WHIVHHUHHUIHTIHSIGSIGRIGQIGQJFPJFOJFOJFNJFNJHMIJMI\ KMIMLHNLHPLHQKGSKGTKGVJFWJFYJFZIE`IEaIEcHDdHDfHDgG\ CiGCnF9jGCfHFbIHZJKVKNRLPNMSJNVFOXBP_8QaBSaEUaHVaJ\ XaMYaP_aS`aUbaXca_eabexafaagD`fF_fGZeHYeJXdKWdLVcM\ UcOTbPSbQRaSQaTP`UO`VN_XM_YLZZKZ_JYaIYbHXcGXeFWfEW\ gDVhCVjBUkAUlAUmCTlDTlETlFTlGTlHTlITlJTlKTlLTlMTkN\ TkOTkPTkQTkRTkTSkUSkVSkWSkXSkYSjZSj_Sj`SjaSjbSjcSj\ dSjeSjfSjgSjfUkeVkdWkcXkbYkaZk`_l_`lZalYblXdlWelVf\ lUgmThmSimRjmQkmPlmOmmNlnNlnMkoMkoMkoLjpLjpKipKiqK\ iqJhqJhrIgrIgrIgsHfsHfsGetGetGetFduFduDbtFduGfuHhu\ IiuKkuLmuMnvNpvPrvQsvRuvSwvTxvUuwVrwVoxWmxXjxXgyYd\ yYbyZcv_dt_dr`ep`fmafkbgi } 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========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint