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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal, which illustrates a scene in the fractal created by the formula Z^(1.15)+C, reminds me of superstrings, those theoretical infinitesimal multi-dimensional abstractions that we hope will help us find the theory of (almost) everything. Thus, I named the image "Superstrings". The resemblance of the twisting filaments in the image to actual superstrings is a total fantasy on my part. Actual superstrings would be so far removed from the intuitive world of everyday experience that they would not have the attribute known as appearance. Nor would they have color or any of the other attributes that make the world we live in so familiar. The actual strings, if they exist, would twist and vibrate in a space of 10 or 26 dimensions. And of course, if the strings were ever actually found, and the super-math made to add up, the question of what the strings are composed of would immediately arise. Considering this last question, I suspect that a successful theory of (almost) everything is safely out of reach. Turning to the fractal image of the day, the midget at the center lies on a grossly enlongated, wildly twisting filament extending from the parent fractal. The abundance of filaments surrounding the midget is a result of the many branch-cuts and discontinuities. Calculated at such a low power of Z, the actual shape of the midget is oval, with only the slightest hint of buds -- a shape that mirrors the shape of the parent fractal. The borders of the midget consist of fragments of the most bizarre kind, but in this close-in area the calculation time becomes unacceptably long. If I find a few spare hours, I might do some exploring around the edges of the midget, but don't hold your breath waiting. Perhaps the most satisfactory aspect of today's image is its speedy render time. The image requires only 1-1/2 minutes to render in its full glory from the attached parameter file at SF5 resolution. SF6 resolution takes only 2-1/2 minutes, and the higher resolutions, proportionally longer. For those for whom rendering fractals is not a cup of tea, the image will soon be posted to the FOTD web sites of Paul and Scott. Paul's site is at: The fractal weather Tuesday here at fractal HQ was hazy, hot and humid, with not a hint of a breeze. After all, it is the hottest time of the year, so why shouldn't it be 100F 38C. The dynamic fractal duo passed the day in the coolest location they could find -- plopped on the tile of the bathroom floor. They stirred only to fill their empty stomachs. It's going to be hot again tomorrow, so the day will likely be a repeat of today. But at least the work will be lighter. Until next time, on Friday the 16th, take care, and work on those extra dimensions. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Superstrings { ; time=0:01:39.86--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=-10.13707406873212000/+17.3412503504878\
6000/6814.379 params=1.15/0/50.65/1500 float=y
maxiter=600 inside=0 logmap=44 periodicity=10
colors=000QOiGMc6LY0LT4JODJJMIDTI9aI4jG0sG0zG0z_0z\
rAzlDvgFscGo_JlTLgPMdLP`GQYCSVGTSJVPMXMPYJT_IX_F_`\
Caa9fc6id3lf1of4ld6jc7ia9gaAf`Cd_Dc_FaYI`XJ_XLYVMX\
TOVTPTSQSQSQQTPPVOOXMMYLL_JJ_IJ`GIaFGcDFdCDfACfAC`\
7FX6IS4LO3OI1QD0T90X40_00`00a00a03c04c06d09d0Af0Cf\
0Fg0Gg0Ii0Li0Mj0OjAVcJaYSiSapMjxGszArxGprMplQofXm`\
amVfMIu04zD7uV9gjAV0zoVjVzVCzY7z_4ya0uc0rf0og0g0z_\
0zS0zJ0zC1x33v04u04s69XC3YI0_M0`Q0VT6PXCJ_IDcO7fT1\
i_0ld0fc0aa4Y`CT_IOYOJXVFV`AVfS_Oga4xd0og0gj0_m0Sp\
0Ls4Cv74yC0zF6mQDa`MPlTDv`1z_9zYFzXLzVQzTYzSczQizQ\
ozXcz`SzdGzi4zm0zo3zoCzpMzpVzpczfozXyzMzzTvz_jzd_z\
lOzrCzx0zPTz0vz0lz0cz0Tz3Lz4Cz6Jz6Qz_Sz`PzaMzaJzcG\
zcDzdAzd9z`6zX4zS1zO0zJ0zF0zA0z60z43z4Dz4Oz4Yz4gz4\
pz3pz3rz1rz1rz1sz0sz0uz0uz0uz0vz0vz0vz0yz0xz0xz0yz\
0yz0yz0zz0zz0zz0zz0zz0zz0zz07z0Iz0Sz0`z0jz0uzzJzzL\
zzMzyOzvPzuPzsQzpSzoTzmVz }
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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