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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image returns to yesterday's scene in the Seahorse Valley complex of the Z2+C Julibrot. I zoomed in on the lower right part of yesterday's image and turned the view upside down to produce an image that gives the impression of massive striped arms floating above an infinite depth. No wonder I named the image "Depths Without End". I created the banded effect by hand rather than using the banding feature included in the program. Though the view is double-rotated only two degrees or so (my estimate) from the Julia orientation, the ghostly remains of Mandelbrot buds are clearly visible along the top of the image. The fact that the circular bud outlines are undistorted showsthat both parts of the double rotation are equal. (Mandel-bud remains are impossible in the exact Julia orientation because their outlines have enlarged to infinity.) I rated the image at a 7.5. Despite its several flaws, it still has something to offer. Just to the right of the center of today's image lies a cluster of tiny bright dots. These dots are actually holes in the surface stuff. Beneath the surface at this location lies a minibrot with its main bud facing left. When blown up, these holes prove to be Julia sets of whatever part of the underlying minibrot they happen to be on top of. The minibrot itself is located somewhere in Seahorse Valley, though I have not the slightest idea of its actual Mandelbrot coordinates. The calculation time of the included parameter file is only 3/100 of a second in excess of 5 minutes, a bit slow but nothing that cannot be quickly accomplished. The finished GIF image is or soon will be posted on the FOTD web site at: Monday was a repeat of Sunday here at Fractal Central, though with a few more clouds and a bit higher humidity. With all the sun, the temperature reached 84F 29C. Now, at post time, the wind is stirring and lightning is flashing in the distant west. Rain is threatening, but the day is finished, so let it rain. The fractal cats have their eyes on the sky however. The next FOTD will be posted in 24 hours. Until then, take care, and if you can't find the fourth dimension, try to be satisfied with the third. It's only a consolation prize, but it's still better than nothing. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Depths_Without_End { ; time=0:05:00.03-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=EvenMoreSlices logmap=22 periodicity=10
params=2/0/0/0.15/-0.78/0/0/0 float=y maxiter=15000
center-mag=0.953034/-0.257883/17.1836/1/-167.8/0
passes=t inside=255
colors=000088re8097re70A6rg60B6rh50C5rj40D4ql30E4p\
k50F5oj60G6ni70H7mh80I9lg90JAkfA1KBjeB2LCidD2MDhcE\
3MEgbF4MFeaG5MHd`H5MIb_I6MJaZJ7MK`YK7ML_XM8MMZWN9M\
NZVO9MOZUPAMQZTQBMRZSRCMSZRSCMTZQUDMUZPVEMVZOWEMWY\
NXFMYXMYGMZWLZGL_VK_GK`UL_HK`TK`HKaSKaIKbRKbIJcQJc\
IJdPJdIJdOJeJIeNIfJIfMIgJIgLIhKIhKHiKHiKHiLHjLHjLH\
kLGkLGlLGlMGmMGmMGmMFnMFnMFoNFoNFpNFpNFqNEqOErOErO\
ErOEsOEsODtPDtPDuPDuPDvPDvOCwPDvPDvPDuQEuQEuQEtREt\
RFtRFsRFsSFrSGrSGrTGqTHqTHqTHpUHpUIpUIoVIoVInVJnVJ\
nWJmWJmWKmXKlXKlXLlXLkYLkYLjYMjZMjZMiZMwZNw_Nw_Nw_\
Ow`Ow`Ow`Ow`PwaPwaPwaPwbQwbQwbQwaRwbQwbQwbQwcQwcQw\
cQwdPwdPwdPwePweQweRwfSwfTwfUwgVwgWzgWzhWzhWzhWziW\
ziWziWziWzjWzjWzjWzkWzkWzkWzlWzlWzlWzmWzmWzmWznWzn\
WznWzoWzoWzoWzpWzpWzpWzrWzqWzpWzpWzoWzoWznWznWzmWz\
mWzlWzlWzkWzjWzjWziWziWzhWzhWzgWzgWzfWzfWzeWzeWzdW\
zcWzcWzbWzbWzaWzaWz`Wzmzz }
frm:EvenMoreSlices {; Jim Muth
; P1--exponent, P2--angle,
; P3--M center, P4--J center,
z=pixel+(p4), c=p3+(pixel*p2):
z=(-z)^(p1)+c,
|z| < 16 }
END PARAMETER FILE=========================================
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times.
