|
Fractal of the Day
by Jim Muth
|
|
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 surprising 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 obliterated by the spurious stuff that has appeared. Even more surprising 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 variations, 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 afternoon 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=========================================
|
times.
