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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Look at what has happened to the perfect minibrot of yesterday's image. Not only has it stretched beyond recognition, it has come apart. But this is what happens in the four-dimensional Julibrot when the Mandelbrot scene is double-rotated and sliced at a critical angle. In this case, the angle defined by the real(p1) parameter is the critical one. A change as little as 0.1 degree makes a world of difference. I was so surprised at the result that I rated the image at a !! This is a most unusual rating indeed. And I must apologize for the name "All Hell Breaks Loose". The image is not really that violent, and I doubt that any fractalists believe in the literal existence of that legendary hot place down below. As for a description of the motion known as double rotation, I am working on it, but at the same time I am finding it extremely difficult to put into words. Those in a hurry will find the calculation time of 34 seconds quite reasonable. Those even more hurried may view the finished image on the FOTD web site at: With a temperature of 63F 17C, Wednesday was mild enough here at Fractal Central in central Pennsylvania, but the clouds kept it from being ideal. The fractal cats live in an ideal world, so they were not disturbed by the grayness. My day was moderately busy, but we were irritated by an irate customer who claims he didn't get what he wanted and refuses to pay his bill. Thankfully, fractals do not incur bills, and even if they did, they would never refuse to pay. The next FOTD will be posted in 24 hours. Until then, take care, and keep going in hypercircles, whatever they are. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
AllHellBreaksLoose { ; time=0:00:34.64-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot4 maxiter=1800 logmap=181
center-mag=+0.00000000615716237/+0.000000135558534\
79/1.861013e+008/0.01308/92.6807800722809247/-33.0\
516955361447415 float=y inside=0 periodicity=10
params=-92.5/162/147/-42/-1.749446905449293/6.8348\
87985e-007/-1.749446905449293/6.834887985e-007/2.0\
000001/0
colors=0003966A79B8BC9ED9HEAKFBOFBRGCWHD`IDdNEkTFl\
aOikYftVmzSrzQvzNzzK_PHNYnLYjIYeGZaEZXBZT9_O6_K4_F\
2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcHbbI\
VaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIXNHzzztwsornk\
ieg`XcSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePDbME\
LhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH4fH\
5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBojCm\
gCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM`JI\
sSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__eY_b\
W_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCTYCU\
WDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSSbPN\
aMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOLJRL\
IVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCdcDc\
eEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzfUzX\
YzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtzroz\
hjzZezPDzrHzkLzdPzZTzSXzL }
frm:SliceJulibrot4 {; draws most slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(p5)+c
|z| <= 9 }
END PARAMETER FILE=========================================
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times.
