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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: After studying the "Something New" image of two days ago, I started wondering if the 4-D HyperMandelbrot set holds typical 2-D quadratic midgets. It certainly has many oddly-shaped holes, but these do not qualify as midgets. A bit of investigation soon revealed the answer. Yes, the 4-D Mandelbrot set does have midgets, but these midgets are four-dimensional things the same as their parent fractal, and when they are sliced in a direction other than straight down the middle, they take all kinds of weird shapes. Thankfully, the midget in today's image *is* sliced down the middle and appears as a normal quadratic midget. In fact, the entire scene, with its ring of basins, could easily lie in the classic Mandelbrot set. But I have not forgotten the weird-shaped slices of the 4-D midgets found in other parts of today's parent fractal. These slices are also interesting. I'll choose one of these slices as tomorrow's FOTD. I named today's image "Fractal Firestorm", probably after the 8 orangish elements surrounding the midget. I rated it at a 7 because that's what I think it's worth. The calculation time of 5-1/4 minutes is true on the 2000mhz unit. The 200mhz machine would take 25 minutes to finish the job. But the fastest way of all to see the image is to view it on the FOTD web site at: The absolutely perfect days just keep coming here at New Fractal Central. The cloudless skies, light winds and a temperature of 84F 29C were near perfect for every outdoor activity except flying kites and growing crops. It's getting quite dry and the local farmers are starting to worry. The fractal cats don't worry about weather however. They reserve their concern for more practical things such as how long it will be before their evening treats are served. My worries are more numerous than the cats', and they will not be solved by a kind pet owner. But one near-certain way to forget the problems, about which one can do nothing, is to enter the world of fractals. Speaking of fractals, the next one will appear in 24 hours. Until then, take care, and I wonder whether fractals ever exhibit quantum non-locality. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Fractal_Firestorm { ; time=0:05:17.80-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot passes=1 periodicity=0
center-mag=-0.97586929974347690/-0.003732367487476\
60/6.514006e+008/1/10/-5.09919721123075487e-005
params=0/0/-4/0/0.1/0 float=y maxiter=5000 inside=0
logmap=650
colors=000PKhkMwiOtgQqeSncUkaWheYej_bna_sccwchncmf\
coZcjRcdJc_BcV3cQ9cREcSJcSOcTUcUZcUccVhcVgcSfcQecO\
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SAYO9YL8ZH7_D7_A6`65a35a47Z58X69V6AS7BQ8CO9DM9FJAG\
HBHFCIDCJADK8EL6EM4FL5FL5FL6GL6GL6GL7GL7HL7YJTHL8H\
L8IL8IK9IK9IK9JKAJKAJKBKKBKKBKKCKKCLKCLKDLJDMJDMJE\
MJEMJENJFNJFNJGOJGOJGOJHOJHPIHPIIPIIQIIQIJQIJQIJRI\
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pzzqzzrzzszzuzzwzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:HyperMandelbrot {; periodicity must be turned off
a=(p1),b=(0,0):
q=sqr(a)-sqr(b)+pixel,
b=(p2+2)*a*b+p3,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
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times.
