; Date: Tue, 11 Oct 2005 11:51:52 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 11-10-05 (Mandel Variation-1 [7]) ; Id: <1.5.4.16.20051011115310.38cf17c6@pop.mindspring.com> ; --------- ; ; FOTD -- October 11, 2005 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; The topic of politics just will not go away. While paying the ; phone bill yesterday, fractal lady wondered aloud whether she ; should check the box that would add a dollar to the bill to be ; used to help teach the children to read. I reminded her that ; three months ago when we paid the taxes, about one-thousand ; dollars of the total went to support the city schools that are ; supposed to teach children to read, and if one-thousand dollars ; from every tax-payer were not enough to eliminate illiteracy, I ; doubted that one more dollar from us would help. I guess this ; proves I'm a non-caring right-wing extremist. Oh well, on to ; the fractals. At least fractals are non-political. ; ; I enjoy doing variations of the Mandelbrot set, and today's old ; retired formula, which for some reason I named "MytestAG", does ; a very interesting and unexpected variation. When I wrote the ; formula I must have been thinking of the fact that an imaginary ; number multiplied by an imaginary number gives a real number, so ; in the formula I raised Z to an imaginary power, then raised the ; result to a second imaginary power to see what kind of real- ; number fractals would result. ; ; Since 2 raised to the power of 1 equals 2, it is not surprising ; that the Mandelbrot set appears in today's image. What is sur- ; prising is all the extra decorative stuff that has mysteriously ; appeared in the M-set. Our old friend has become a Christmas- ; tree set, decorated with infinite arcs and rings. Its basic ; shape is still there but all the fine details have been oblitera- ; ted by the spurious stuff that has appeared. Even more surpris- ; ing is the fact that these arcs and circles continue unchanged ; as deep as one decides to search. Of course, in the world of ; fractals, nothing should be considered truly surprising. ; ; The iterated line in today's formula is z=(z^a)^(-b)+c. When I ; saw this, I wondered why I wrote -b instead of b. After all, I ; could get the same result by writing the even simpler expression ; z=(z^a)^(b)+c, and entering -1 instead of 1 as the value of b. ; Before writing today's parameter file, I made this slight change ; to the formula, fully expecting no change in the image. But the ; image did change. It was a small change but a change indeed. ; This leads me to suspect that much if not all of today's image ; is an artifact of math imprecision. Switching the changeable ; parameters also makes a change in the image, which would also ; seem to indicate that the image is an artifact. But artifact or ; not, it is a worthy image that rates a 7. ; ; I named the image "Mandel Variation-1". The extra 1 was added ; to the name just in case I decide to investigate other varia- ; tions, which at the present time I do not expect to do. ; ; The render time of 12 seconds is about as fast as a fractal can ; be. On the most advanced 'state-of-the-art' units, the image, ; if it runs at all, will likely be completed before the video ; switches to the chosen mode. Those with handicapped units that ; choke when the word 'Fractint' is mentioned may see the festive ; Mandelbrot set by downloading the finished image from the FOTD ; web site at: ; ; ; ; The cloudy, coolish and wet conditions prevailed all day Monday ; here at the center of the fractal world. The cats dwelling at ; the center were notably unhappy. Tippy was so unhappy that he ; leaped into the refrigerator when I opened the door for an after- ; noon snack, and almost got himself shut in. Thomas slept on the ; window shelf most all day. ; ; Today is starting cloudy with light rain about. The rain is due ; to continue, so the cats' bad mood will likely continue also. ; For me it looks like a rather busy day in store. The next FOTD ; will appear in 24 hours. Until then, take care, and regardless ; of where one travels, he always finds himself at the apparent ; center of the universe. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Mandel_Variation-1 { ; time=0:00:12.24--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=MytestAG center-mag=-0.5/0/0.6296 params=2/1 float=y outside=tdis maxiter=255 inside=0 logmap=2 symmetry=xaxis periodicity=10 colors=000GRUDCWWbN_TJcJFgACkGInLOqRTtWZwadzfir_lj\ TobMrfVmicilleoualsXjqThoOfnKdlFbjB`i7ri2rh6rgArfE\ reIrdMrdPtfOvhOwjNylNznNqlMiIEhLGhOHaVJV`KOgLHmMb`\ EwO7xS6xW5x_4yc3yg2yk1yn1mj4ag6Rd9FaB4ZDIdIViMgoRt\ tVvlJwd7vbCuaHu_LtZQsXVsWZrUcrTgveozqwwmctjLqg2neA\ lcIjaPg_XeYdcWk_PfWIbSBYP4UXHOdUIlfDfgHahLXiPSjTNk\ XIl`DmcFf_H`XJUTLOQNHMPBJXHGcMDkSArX8iSA`NCSJDb50Y\ BFWEEVGETJESLERNDPQDOSDNUDIZUDcj8gzHgoPgeYgVegLdbN\ cZPcURbQTaLVaHX`CZ`8_V9YP9WK9UEAS8AQ3APBF_JKjROtL_\ lGkeRjXajOljFjdPhZZfTheOrgPqhPqiPpjQpkQolQomQopPer\ OWuNMwMDqOGlQJfSMaUOWWRRYUM_WRWZVS`ZPcbLefHhjEjkDi\ lCimBhnAho9gp8gq7fq7fhDh_IjRNkLVdGbZAjS5rM0yG1qH2j\ I3cJ4XJ5PK6IL7BM74MX4Yu4ikN5BwSCqVDkYEf`F`cGVfGQiF\ WlE`nDfqCksBqvBvxqWGmSIjOKgKMdGO`CQY8SV4US1VVD`XOf\ Z_l`jrDKXLKRTKL`KGhKAoK5y9ZyCVyFRyHNyKJyNFyPBpTMhX\ W``eTdoLgyKfrKfkKfdKfYKfS } frm:MytestAG {; Jim Muth z=c=pixel, a=flip(real(p1)), b=flip(imag(p1)): z=(z^a)^(-b)+c, |z|<=100 } ; END PARAMETER FILE========================================= ; ;