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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Take four lines with a length of -1 meter and arrange them as the sides of a square. The result is a square with an area of one square meter and four sides that measure one meter less than nothing. This is not only getting something from nothing; it is getting something from less than nothing. Then take six of these square meters with sides less than zero and arrange them as the sides of a cube. The result is a cube with a volume of one cubic meter less than nothing. I shall not attempt to describe this incredible beast, but I shall note that if eight of these weird cubes were arranged as the cells of a 4-D hypercube, that unimaginable object would have a hypervolume of 1 quartic meter more than nothing. This situation is mathematically correct, though I have yet to see a line with a length of -1 meter. It simply shows that much mathematics extends far beyond the everyday world in which we live. I have also never seen a real-life fractal, though I have seen hundreds of thousands of pictures of fractals. Today's image simply adds one more fractal picture to the ever-growing list. The image is a scene in the fractal created by the formula (Z^3)+0.4(Z^5)+C. I named it "Stems" because of the sprawling stem-like features surrounding the midget at the center. Like so many other recent FOTD images, today's image rates a nominal 6. The render time of 2 minutes makes running the parameter file not too great a task. And as always, the GIF file of the completed image is available on Paul's web site at: The fractal weather Wednesday was very warm and muggy, with a temperature of 92F 33C and humidity to match. In the late afternoon a very noisy thunder-storm developed, which sent the dynamic duo of fractal cats scurrying for cover. They stayed out of sight until hunger brought them into the open around nightfall. As for myself, as is normally the case, I've got too much work to do and too little time in which to do it. The remedy for such a situation is to get busy and resume productive activity. So until Sunday June 9, take care, and be of good humor. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Stems { ; time=0:02:48.18--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix2 function=ident passes=1
center-mag=+0.54332395099606500/+0.517188441425538\
80/1.244136e+010/1/-67.5000495545287009/7.69023680\
009528476e-005 params=1/3/0.4/5/0/0/0/0 float=y
maxiter=300 inside=0 logmap=49 periodicity=10
colors=000HfuHcqH`lHYhHVcHS_HPVHNTHLRHIQKFPNHNQKNT\
NOWQQZTR`XSg`RmeQtkPzpOykQygRxcTx_UxWWwSXwPZvL_vIa\
vFbuCdu9et6gt3ht0ip8fmGdiOafW_cbYbaZa`Z`_Z___ZZ_ZY\
_YX`XX`WW`VVaUUaUUaYYY`aVcdRfhOjlKmoHpsDsvAmwFgxJa\
xOWySRyWDlT0_R6ZMCZHHYDNY8SY4TZBT_HT_NT`UU`_UaeUal\
UbrUbxVcrWclXcgYcaZcX_cR`cMacGacBiiDqoFyuGwpFulFsh\
FqdFo`FnXFlTFjPFhLFfHFeDF`KKWRPSXUNcZJibGk`DmZBoY8\
qW6rV9pXCoYEn_Hl`JkbMjcPheRgfUfhWdiZckablc`nf_ohZp\
jVqlRrnOrpKsqHsrFprEnsDlsCjtAht9fu8cu7av5_v4Yw3Ww2\
Uw1SuNHth7ti9tjBtkCtlEtmFtnHtoItoKtpMtqNtrPtsQttSt\
uTtvVtxWhzaYzfNzkCzpRzbezPtzBrzDqzEpzFozGnzHlzIkzJ\
jzKizLhzMgzPfzRfzTezVezXdzZdz`czcczebzgbziazkazm`z\
o`zqYzjVzdSzYPzSMzMJzFGz9Dz3Fz8GzCIzHJzLLzQMzUOzZP\
zbRzgSzkTzoVzkWzgYzcZz`VzaRzbNzcJzdFzeBzf7zg3zgGz`\
TzVezPdzQdzRdzSazQ_zOXzNVzLSzKQzIOzHLzFJzDGzCEzABz\
99z77z6FzHNzSVzaWzROzhHzz }
frm:MandelbrotMix2 {; 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)+(p4)),
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==================================
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