; Date: Sat, 05 Oct 2002 09:36:05 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 05-10-02 (The Great Spirals [5]) ; Id: <1.5.4.16.20021005093729.29ef5a06@pop.mindspring.com> ; --------- ; FOTD -- October 05, 2002 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; Sometimes, while discussing fractals, I remark that the image on ; the screen is but a slice through an abstract four-dimensional ; object. When I say this, the question is often asked, 'where is ; the fourth dimension?' I then reply by stating that the fourth ; dimension is sideways to the inside of solid objects, and of ; course, the person I am talking with remarks that such a direc- ; tion does not and cannot exist because there is no space for it. ; ; The real difficulty with the fourth, and all higher dimensions, ; is that we cannot visualize them. Early in life, we learn to ; decipher and organize our sensory input so that it forms in our ; minds the image a three-dimensional exterior world. The image ; works quite well because all people, (with the possible excep- ; tion of the insane), have formed the same image. That world ; might or might not resemble our mental images of it, but what ; if, perhaps with the aid of virtual-reality computers, a child ; in his formative years were fed images of a four-dimensional ; world. Could that child then grow to visualize four-dimensional ; space and all the figures that might exist in it? ; ; Maybe he could, maybe not. We'll never know because the experi- ; ment will never be done. But I can't help but wonder whether a ; three-dimensional reality actually exists 'out there' or whether ; we learn early in live to organize our mental impressions into a ; world of three dimensions, and then go on to invent a math- ; ematics that works with that three-dimensional image. ; ; I mention the fourth dimension because it is one of my favorite ; topics of contemplation when I settle into my ponder chair, and ; also because in the upcoming FOTD's I will often be discussing ; the fourth dimension. ; ; Today's image is part of a critical Mandel-plane of the four- ; dimensional julibrot that results when 1 part of Z^2.2, 2.2 ; parts of Z, and C are added and iterated. The two prominent ; spirals are impressive, and inspired the name "The Great ; Spirals". But it takes more than two spirals to make a great ; fractal, so I could rate the image no more than an average 5. ; ; With a render time of 13 minutes, the parameter file is slow. ; The good news is that the completed GIF image will soon be ready ; for download on the two FOTD web sites at: ; ; ; ; and: ; ; ; ; The weather Friday here at Fractal Central started with low ; clouds and fog, which then gave way to hazy sun and an afternoon ; temperature of 81F 27C. Ignoring the high humidity, the cats ; approved of the conditions, and showed their approval by sitting ; on the porch, guarding the yard through most of the afternoon. ; ; I'm now going to try to take it easy for the rest of the day. ; If I'm lucky, no work will appear; if I'm unlucky, a few minor ; tasks might arise. Being a firm believer in Murphy's Law, I ; expect to be unlucky. In any case, the next FOTD will appear ; tomorrow around the same time at the same place. ; ; ; Jim Muth ; jamth@mindspring.com ; ; ; START PARAMETER FILE================================ The_Great_Spirals { ; time=0:13:10.00--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.17759792180486490/-0.451262352528888\ 60/107065.9/1/172.5/-5.05322658717055617e-011 params=1/2.2/2.2/1/0/0 float=y maxiter=2400 inside=0 logmap=134 periodicity=10 colors=000LNQJMRGLRELSCKT9JT7IU2JT5IU7IV9IVBIWDIXG\ IXIIYKIYMIZOI_RH_TH`VHaXHaZHbaHbcHceHdgHdiHekHejGc\ jGbjGajG`jF_jFYjFXjFWjEViEUiETiERiDQiDPiDOiDNiCLiC\ KhCJhCIhBHhBGhBEhBDhAChABhAAhA9dCD`EGXFJTHMPIPLKTH\ MWDNZ9Pa5Qd5Rc5Sc5Sc5Tb5Tb5Ub5Ua5Va5Va5Wa5W`5X`5X`\ 5Y_5Y_5Z_5Z_5_Z5_Z5`Z5`Y5aY5aY5bY5bX5cX5cX5dW5dW5e\ W4dU5eW6eX7eZ7f_8f`9fb9gcAgeBgf2hiBggKgeTgcagajg_q\ fVrgZrgbshfrlpshjsedsaZtZTtVNtSHuOBuL5uI0tOEtUSs_e\ serpfnmgkjghghedhbai_ZiWWjTTjQQkNNkKKlHHmDIlEIlEIl\ FJkFJkFJkGKjGKjGKjHLiHLiILiIMhIMhJMhJNgJNgKNgKOfLO\ fLOfLPeMPeMGfWPiMXmDdo4br3ap3`n3_l3Zj3Yh2Xf2Wd2Vb2\ U`2TZ1SX1RV1QT1PR1OP1QO2RN3TM4UM4VL5XK6YJ7ZJ7`I8aH\ 9cGAdGAeFBgEChDDiDDkCElBFmAGo9Gp8HqAIsCJtEJuGKwILx\ KMyMMzOLzQKzSJzUJzWIzYHz_HzaGzcFzeFzgEzhDziDzjCzkB\ zlBzmAzn9zo9zp8zq7zr7zs6zt5zuUzv5zw6zx6zy6zz6zz6zz\ 6zz6zz6zz6zz6zz6zz6zz9zzC } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } ; END PARAMETER FILE================================== ; ;