FOTD -- January 13, 2003 (Rating 7) Fractal visionaries and enthusiasts: Unable to find a good opening for today's FOTD discussion, I shall simply place my mind in idle and let my thoughts ramble where they will. Now let me see . . . Every day for almost the entire life of the FOTD, I have opened the discussion with the line 'Fractal visionaries and enthu- siasts'. I do it without thought of the meaning, since the line is part of my pre-formatted FOTD template file, and is inserted into the text of the discussion automatically. The nature of the fractal enthusiast mentioned in the line is obvious, but what is a fractal visionary? My dictionary defines the word 'visionary' both as an adjective meaning 'existing only in the mind', and as a noun meaning 'a person who sees visions of hidden things'. So a fractal visionary is one who sees visions of the normally hidden things known as fractals, (which BTW are only partly unreal). Those who can see things, real or unreal, that others cannot see are also known as mystics. In times past, mystics were seen as wise people; in our present age of reason run amok, they are looked upon as a little weird, amusing but harmless -- that is unless they start claiming and convincing too many others that their visions are actual glimpses of other real worlds, in which case they must be shown to be deluded. In this age of reason, there is and can be only one real world, the physical world, with which we can be in touch. There is no possibility of interaction with other real worlds, which preferably do not exist. This status quo must be preserved at all costs. Well, I often see things that others cannot see with eyes alone, though I'm not sure if this makes me a mystic. The things I see are called fractals, and must be seen with the aid of a computer and monitor. With my real eyes, I can see fractals on my computer screen whenever I wish, and I sometimes see them in my dreams as real 3-D objects existing and evolving in 3-D space. Since others can at least see my fractal visions on their own computer screens, I guess this makes me a mystic of the second order. I could not be a mystic of the first order unless others could also see the fractals I sometimes dream of in my dreams. Today's image is a fractal of the third order. It is mystical in the sense that it cannot be seen without the aid of a computer and also that it is another of my 'evaporated' images, which consist entirely of the ghost of a fractal that once was there. (To see the fractal that once was there but has vanished, change the imag(p3) parameter from 10^100 to zero.) The parent of today's image consists of a multi-lobed string of bays extending north to south. A filament extends southwest from the southernmost bud, and terminates in a zig-zagging ring. Today's scene lies on this ring, not far from where the filament joins it. I named the image "Mysterious Energies" for no good reason, and rated it a 7 because in my opinion it is above FOTD average. The render time of 9 minutes is a bit beyond the range of reason for those with busy lives to lead. But the already completed GIF image is available for download on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather Sunday was sunny but cold here at Fractal Central, with a high temperature of 29F -1.5C. The cats endured their indoor confinement with patience, blaming me only twice for the chilly conditions beyond the door. Today has so far been uneventful. Hopefully, it will remain so, as there is a bit more than the average amount of work to be done. Until next time, take care, and is it reasonable to believe that fractals are real? Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ MysteriousEnergies { ; time=0:09:16.89--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.80567324593928600/-2.034640713112640\ 00/2.056237e+009/1/-62.5/2.93630749607157182e-005 params=-7.57/-1.5/-0.98/-6.5/0/1e+100 float=y maxiter=900 inside=bof61 periodicity=10 colors=000_QjXSl000STmVXgXYaY`Y_aS`dOcfIdiDfj7gm3i\ o0jp0fo0co4`oAYmFVmLSmQOlXLl`IlfFjlCjr9jvDdxI`xMVx\ QQyVLyYGyX`pXuiXzarz0mz0jz0gy0dv0as0_p0Xm0Tj0Pg0Md\ 0Ja0000DX0AT07Q04P0CV9J`GQdOYjVcoaczfczigzclm_o`Ts\ OPxAJz0Fv1Js4Mp7PmASjDVgGYcJ``McYPfVSiSVlPYoGMv9Cz\ 11z00z0Az0Tz0jzLVTfG0cM0aS0`X1Ya4Xg6Vl7SrA000PzDQz\ GSzITzLVzMXzOYzQ_zS`zTazXczYdz_fzagzcizdgxc000dpac\ m`ci`000`aY__YYVXYSX`VQaXLc_Fd`Agc4id0jg0li0gf0dc0\ ``0YY0TV0QS0MP0JM0FJ0CG07D04A00700410A10730N40F40P\ 60L60S70S70Y90_A0eA0dC0nC0lD0uD4iAGi9T_7dV4rP3zL1y\ Q6uV9r`CmdGiiJfoMasPYxTVzXQz_OzaPzcQzdSzfSzfTzgVzi\ XxiXvjYul_rl`pm`oo00ocjpdirdgrQfpCfo0fo3_f6T_0S_0S\ _0Ma6Gd_QT`Qa`QjgJ`mCQu4Gz07x4MvA_sGlrMypSzmXzl`zj\ dziiz90_DAPIQGMg6Px0Ts1Yo6aj9fgDjcGo_LsXOpTGmQAfMG\ _IMSDSM9YF4c70i10m41f66_7AT9FMAJGCO9DS37`01g0Ai0Ij\ 3Pl7XmCcoGjpLrrPyrTupQpoP } 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 20.0 PAR-FORMULA FILE==================================