; Date: Tue, 13 Aug 2002 22:04:35 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 14-08-02 (Superstrings [6]) ; Id: <1.5.4.16.20020813220523.29cfaff4@pop.mindspring.com> ; --------- ; FOTD -- August 14, 2002 (Rating 6) ; ; 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) every- ; thing. 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 ex- ; perience that they would not have the attribute known as appear- ; ance. 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. Consider- ; ing 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: ; ; ; ; Scott'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 PARAMETER 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|