FOTD -- April 14, 2004 (Rating 7) Fractal visionaries and enthusiasts: Fractals are said to be things with a fractional dimension. This concept is as hard to visualize as things with four dimensions, but I think I have a vague idea of fractional dimensions. The way I visualize an object or a space with, say, 2-1/2 dimensions is to picture something that extends indefinitely in two dimensions but has limited freedom to extend in the third dimension -- kind of like a lumpy plane. Of course, fractional dimensions are not supposed to be real things. Like the many interpretations of quantum mechanics, they are mathematical concepts which happen to work rather well. There is no uncertainty of the number of dimensions of today's image however. It most certainly has two dimensions. If it did not, it could not fill the monitor screen, and could not be printed on the surface of a sheet of paper. The scene is located in the fractal that results when 4.5 negative parts of Z^3 are combined with 3.375 negative parts of Z^4 and 1/C is added. This parent fractal consists of a main Mandeloid surrounded by numerous large holes, which act as the terminals of filaments. Today's image is located very near the point where a filament of a sub-bud of the main bud of the parent Mandeloid terminates in a hole. A good part of the image consists of empty holes, which have been brought to life by the 'bof61' inside fill. All this dimensional stuff inspired the name "Inter-Dimensional". I originally had rated the image at a 6, but then I happened to view it from across the room, and noticed that it looks as good at a distance as it does close-up. I raised the rating to a 7, which, when the render time of 7-1/2 minutes is considered, gives an overall value of 93. The most efficient way of viewing the image is to download it from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The clouds hung tough all day Tuesday here at Fractal Central, while the rain fell in sudden short showers. Combined with a temperature of 48F 9C, these conditions proved too rigorous for the dynamic duo, who spent the afternoon on their shelf by the window, watching the birds and taking turns washing each other. In the evening, a generous treat of mackerel helped improve their moods. Today is starting like Tuesday did -- with clouds and light rain. I expect similar things from the duo. For me, it's work until it's finished. That should take around 5 hours, then it will be time for the daily trip to Fractaltown. In 24 hours, I'll report what I find there. Until then, take care, and who could possibly solve the mystery of fractals? Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Inter-Dimensional { ; time=0:07:33.19--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.31630130595552000/+0.075484039727471\ 52/9.709767e+009/1/-17.5/-0.00200669961294230176 params=-4.5/3/-3.375/4/0/0 float=y maxiter=2000 inside=bof61 logmap=114 periodicity=10 colors=0000N_0PZ0RX0TV0VT0XR2_P4bN6eL8hJAkGEoAGs6J\ u0Nw0Pz0T60T60ZR0`M0eG0iPUmZ0shcvqmzqmzh0ziczA0zbU\ z60z6Kz60u60u80qG0oM0kT0g`0eh2bo4`u4Xd0zm0R80zz00z\ 00z00z06z0Ey0No0Vf0dX0kN0RXCRdPRj`PfdNdeNbgLZkJXmJ\ VoHRsGPuGNvEKzCIzCGzACz8Az88zGAzLCuRCmXEebEXgGPmGH\ sIAxI2qXGkkTeye`zsVzz0zm0zo4zoCuoHkoPdoXVobNoZKkVI\ iRGgNEeJAdG8bC6`86Z46V06T06R06P06N06L06J06H06T0Ad0\ Mo0Xz6hzuz0sy4swAssGsqLsoRqkXqjbqfeqdkqbqoZvoXzoTz\ oRzoPzgMz`KzVIzNGzHEzAAx48u06q06o06k06i06g0Cg0Ge0M\ e0Rd0Vd4`b6dbAjbEo`Hs`LyZPzZTzXXzXZzXPzeGzo6zx0zz2\ zz8zzEzzJuzPozVhz``zeTzkMzqGzv8zz6zz6zz6zz6zz6zz6z\ z6zz6zv6zu6zs6zo6zm6zk6zg6ze6zd6ze6zg6ziAziGzkMzmR\ zmVzo`xqfxqkxsqvuwvuzvszuqzsozqmzqkzokzmizmgzkezid\ zidzgbze`zeZzdXzbXzbbwZekXkZVoNTsCRuIJuNEvT6vZ0dh0\ Nq04z00z00z00z80yL0uX0qg0mu0jz0fz6bzGZzNXxXTseRmmN\ gvMbzIXzGRVjZLZgCPq2Gz06z } 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==================================