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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I named today's image "Ghostly Apparition" because the minibrot near its center barely exists. The spooky apparition manifested itself when I combined 6 negative parts of Z^(-1.66) with one negative part of Z^(-6.6) and added (1/C). The parent fractal consists of a number of irregularly shaped bays surrounded by countless interesting nooks and crannies to explore. But instead of exploring the nooks, I checked a blob of material near the inside center of the fractal, near the point where two large bays appear to merge. I found there a strange arrangement of bits and pieces, which when enlarged formed the skeletal outline of a ghostly minibrot. To return the ghost to life, I rendered the scene with the inside set to 'bof60' and the outside set to 'atan'. The result is an image different enough to rate a 8. The calculation time of under 11 seconds can hardly be a burden. And the already-calculated image is posted for instant viewing on the FOTD web site at: About a week ago I told of a 152-year-old book I recently found in a local antique emporium while tagging along with fractal lady on one of her antiquing expeditions. The book is a popularized presentation of the scientific and practical knowledge of the day. Some of the old ideas are now absurdly, almost comically wrong, while others are still totally accurate, and still others, such as how to shoe a horse, and how to bank a fire, are still true, but of importance to very few. While idly turning the weathered and stained pages, I sometimes wonder how our current scientific and practical ideas will seem 152 years from today. Will our descendants laugh at our futile search for a 'theory of (almost) everything'? Will they wonder how we could possibly fail to grasp the obvious (to them) meaning of our own quantum discoveries? Will they shake their heads at our silly addiction to 'cell phones' and the rhythmic noise we now call music? But most frightening of all, are we now seeing the beginning of a new era of techno-civilization or is it actually the start of a neo-dark age? Rain fell steadily all morning and most of the afternoon here at Fractal Central on Tuesday, while the temperature hovered just above 50F 10C. The fractal cats spent the day looking for the catnip rat, which they have somehow misplaced. I spent the day working and thinking deep (IMO) thoughts. The next FOTD will be posted in 24 hours or so. Until then, take care, and I had a clever closing comment in mind, but I forgot to write it down, and have since forgotten it. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Ghostly_Apparition { ; time=0:00:10.55-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=+0.12324718494693840/-0.146235048606272\
10/133.4492/1/50/0 params=-1/-6.6/-6/-1.66/0/0/0/0
float=y maxiter=1500 bailout=10000 periodicity=10
inside=bof60 outside=atan
colors=000v`SvYQvWPuTOuRNuPM8CmCBnGAoK9oO8pR8pQBlP\
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gVJfZHc_EeaGgbIhcJjeLkfMmgOnhPpjRrkTslUunWvoXxpZzv\
bys`yq_xnZxlYxiWwgVweUwbT }
frm:MandAutoCritInZ {; 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 PARAMETER FILE=========================================
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times.
