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