; Date: Thu, 24 Jul 2003 09:47:00 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 24-07-03 (Four-Dimensional Scene [?]) ; Id: <1.5.4.16.20030724094707.2b3f01b2@pop.mindspring.com> ; --------- ; ; FOTD -- July 24, 2003 (Rating ?) ; ; Fractal visionaries and enthusiasts: ; ; How does one answer the question, "Where is the fourth spatial ; dimension?" This, in my opinion, is one of the most puzzling ; questions that has ever been asked. We know where it would be ; if it existed, but it cannot exist. There is no room for it. ; Three-dimensional space is all there is. Yet it does exist. ; Using numbers, we can take apart and examine 4-D hyperspace as ; rigorously as we examine three-dimensional space. I suspect ; that the inability to perceive 4-D space is a limitation of our ; awareness, and that the fourth dimension is there all around us, ; if only we had eyes to see. How to open our eyes and adjust our ; numbers is anyone's guess. ; ; Today's image is a scene in the Z^2.003+C Julibrot. Julibrots ; are four-dimensional things that, sliced in one direction give ; Julia sets and, sliced in another direction, give perturbed ; Mandelbrot sets. Of course, being hypersolid, the 4-D Julibrot ; can also be sliced in oblique directions between the Julia and ; Mandelbrot directions. ; ; Today's scene is sliced in a direction only one degree from the ; Julia direction, but that single degree makes a world of differ- ; ence. (To see the pure Julia set, change imag(p1) from 89 to ; 90.) The Z^2.003+C Mandeloid is shaped almost exactly like the ; classic Mandelbrot set, whose formula is Z^2+C, the major change ; being along the negative stem, which has split into an infinity ; of curving, infinitely-divided filaments. The large midget at ; -1.75 has also started to split, and today's scene is located in ; the East Valley of this midget, which has broadened into a much- ; divided wedge-shaped thing. ; ; I have given the image the name "Four-Dimensional Scene", which ; is a fair description. But I am undecided on the worth of the ; picture, which comprises all there is of the fractal. Sometimes ; I think it is worth an 8, then I view it again and see an image ; worth only a 4. The image will likely go unrated. ; ; The modest render time of X minutes can be avoided by download- ; ing the finished GIF image from: ; ; ; ; or from: ; ; ; ; Though it was quite humid, the temperature rose no higher than ; 84F 29C and no rain fell here at Fractal Central on Wednesday, ; giving the dynamic fractal cats a most pleasurable day. The ; good weather also helped conserve the stressed tuna population, ; since no treat was necessary. ; ; Today is promising to be a slightly less humid repeat. I expect ; a repeat from the fractal cats. More good news is that the work ; shelf is filling up. And the best news of all is that I shall ; return in 24 hours with another glorious fractal. Until then, ; take care, and when I started the FOTD on the Fractal-Art list ; in April of 1997, I expected to keep it going maybe a week or ; two. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ 4-DimensionalScene { ; time-0:06:55.34--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip center-mag=-0.0156752/-0.0738926/7.021696/1/-90/3.\ 88578058618804789e-016 params=90/89/2.003/0/0.0001\ 9/0.07388/-1.7435/0 float=y maxiter=8000 inside=0 passes=1 logmap=yes periodicity=10 colors=0000000000000000200400600830A60C90EC0GF0II4\ KL6MOAOREQUGSXJU_LWbPYeT_hVakZcnbeqdgtgiwhjzikzjmz\ kmzlmzmmznmzomzpmzqozrqzssztuvuvnvogugTkbEbV0XR0VP\ 0VN0TN0TL0RJ0RJ0PH0PG0PG0RL2RP8RVERZJRbPRgVRk`RqdU\ uicxomzurzzzzzvzzrzzmzzhzzfzoosbxiPz`CzT0ob4Rk82uC\ 0zE0zG0xH0vJ0sL0qN0oP0mR4iR6gTAeVEdXG`ZJZ`NXbbGRPV\ bCim0xv0zz0zz0zz0zz0oz0dz0Ru0Eq00m00i40g`6ez0mzEeq\ R`ddVPqNCzH0z00zC8zLJzXTzebzoezigxeigbkRZk2NmAVoH`\ qPesXkudqvkvxszzzzzzzxuzvqzukzsezqbzoXxoRvmNukHuiC\ sg8qe2od0md0md0qd8udGxdNzdVzdbz``zXZzTXxPXuLVqJToG\ RkCRg8Pe4Nb0Na2N`H40RE0`N6iXCseJzoPzxXdbzdbzdbzdbz\ dbzdbzdbzdczcczcczcczcczcczcczcczcczcczcczcczcczcc\ zcczcczhc0mc0rc0vc0zV0zT2zP8zLEzJHzGNcczz8Zz6dz2iz\ 0oz0s20z40z60z60z86zAAzAEzCJzENvERuGZsGdqHioHomJuk\ JziLzgLzeNzdNzbPz`Pz`NzdNzeNzgNziNzkNzoNzqNzsNzuNz\ vGsqAmm4gi0be0X`0RX0LT0GP } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } ; END PARAMETER FILE================================== ;