; Date: Thu, 10 Jan 2008 17:58:50 -0500 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 11-01-08 (Gateway to Infinity [No rating]) ; ; Id: <1.5.4.16.20080110174833.2be767ea@pop.mindspring.com> ; --------- ; ; FOTD -- January 11, 2008 (No Rating) ; ; Fractal visionaries and enthusiasts: ; ; Today's trip to Seahorse Valley reveals an entirely new aspect ; of the valley. The slice is centered at C=-0.75+0.095i Z=0,0 ; and is sliced in an orientation double rotated 15 degrees from ; the Julia direction toward the Parabolic direction. Double ; rotation is another of the seemingly absurd things that are ; simple in four-dimensional space. It has no analog in 3-D ; space. ; ; The closeness to the Julia orientation is evident in the open ; top half of the image, which bears an unmistakable relation to ; the well-known Julia sets of Seahorse Valley. But the lower ; half of the image is a different story. Here we are apparently ; skimming through the buds of the valley, which have been ; stretched to infinity in the horizontal direction and appear as ; mere slits. ; ; Don't try to figure out which buds we are skimming through. I ; tried to deduce it and ended up totally mentally congested. ; It's just not possible for we beings of limited visualizing ; ability to mentally picture four-dimensional things. ; ; One of the more interesting aspects of the image is the ghostly ; transparent yellowish rings that are projected on the venitian- ; blind background of the bud slits. But strangely enough, when ; stretched in the proper direction, these ghostly rings prove to ; be quite ordinary Seahorse Valley elements. ; ; I named the image "Gateway to Infinity". The open background ; inspired the name. I gave the image no rating, since it is ; almost solely of mathematical interest. The calculation time ; however is very reasonable. The 24 seconds required to complete ; the calculation should try the patience of no one. The finished ; image is available as always on the FOTD web site at: ; ; ; ; With variable clouds and a temperature of 48F 9C, Thursday ; proved to be an ordinary day here at Fractal Central. The ; fractal cats must have agreed. They became so bored that they ; got into an overheated tussle and mouthed some disgraceful cat ; words at each other. ; ; My day was moderately busy, which means the day's work was up to ; schedule by 3pm. The next FOTD will be posted in 24 hours. Who ; knows what havoc we will wreak on Seahorse Valley at that time. ; Until then, take care, and I assume the objective world must be ; real because every time I open my eyes, I experience in my mind ; consistent visual, auditory and tactile mental images of an inde- ; pendently existing outer world. But what would I experience if ; I could directly know the thing or things that are causing those ; mental images to be generated? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= GatewayTo_Infinity { ; time=0:00:24.61-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=t center-mag=0/0/0.862069/1/0/6.08852815419518389 params=75/75/90/90/-0.75/0.095/0/0 float=y maxiter=6000 inside=0 logmap=yes periodicity=10 colors=000HCUIDUJEUKFULGULHUMIUOJUPKUQLUSMUSNUTOUV\ PUWQUYRUZSUYTUXUUWVUVWUUXUSWURWUQWUPWUOWUNWTMWSKWS\ JWRIWQHXPGXOFXNEXMDYMEYOEZQE_RF`TFaUFcWGdXGeZGf_Gg\ aHicHjdHkfIlgImiIojJplJqmJroJspJrqJqqJpqJpqJorJnrJ\ nrJmrJlrJlsJksJjsJisJisJhtJgtJgtJftJeuJeuJduJcuJbu\ JbvKavL`vM`vN_vOZwPZwQYwRXwSVxTXwUZvV`vWbuXduYftZh\ t_js`ksamrborcqqdsqeupfwpgyohzoiynjymkxllxkmxjnwiq\ whtwgwvfzvezvdzuczubzubztazt`zt_zsZzsYzsXzrWzrVzrU\ zqTzqSzqRzpQzpQzpPzoOzoNzoMznLznKznJzmIzmHzmGzlFzl\ EzmCzlEvkFrjHmjIhiKchLZhMUgOPfPLfRNeSOdTPcVRa_S_cU\ YhVWmWUrYSwZQz_OzaMzbKzdMzeOzfQzhSziWzjYzj_zkazkcz\ kezlgzlizmkzmmzmoznqznszotzouzpvzpwzpxzqyzqzzrzzrz\ zszzrzzqzzqzzpzzpzzozznzznzzmzzlzzmzzmzzmzzmzznzzn\ zznzznzzozzozzozzozzpzzpzzpzzpzzqzzqzzqzzqzzrzzrzz\ rzzrzzszzszzszzszzszzrzzrzzrzzrzzrzzrzzrzzrzzrzzrz\ zrzzrzzrzzrzzrzzqzzqzzqzz } frm:SliceJulibrot2 {; 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|<=9 } ; END PARAMETER FILE========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint