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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's ultra-quick image is simply a new view of East Valley of the Mandelbrot set. More accurately, it's an oblique view of the East Valley complex of the Z2+C Julibrot. I named it "Bat-Fractal" after one of my favorite comic book heroes from long ago -- Batman. The large dark bat-shaped feature dominating the image inspired the name. I particularly enjoyed the Batman stories because Batman was, and still is, a mere mortal human with finely-honed but still normal human abilities as well as vulnerabilities. I could dream that one day I might be like the Batman, while heroes like Superman and Captain Marvel were total fantasies, far beyond human attainment. I also enjoyed the Green Lantern stories, about a hero who used psychokinesis, the power of his mind, to overcome his enemies. Too bad none of these old comic heroes ever heard of fractals. Well, there's not much to be said about the appearance of today's image, except that this is how one of the four-dimensional 'bridges' of East Valley appears when stretched about 100 times in the vertical direction. Some hints of the East Valley elephants are also scattered throughout the scene, though I could find no fully formed ones. Unfortunately, the image does not earn a rating, but it still has a bit of curiosity value. And the calculation time of only 3-3/4 minutes is not at all bad. The most convenient way of enjoying the image, as always, is to visit the FOTD web site at: Near perfect conditions prevailed again on Thursday here at glorious Fractal Central. The clear skies and temperature of 84F 29C made everyone including the fractal cats happy. My day would have been a bit more pleasant if the work had been a bit lighter, but I'm not complaining. The next FOTD will appear in 24 hours. Until then, take care, and do what's right. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Bat-Fractal { ; time=0:03:37.44-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2 logmap=23 periodicity=10
center-mag=+0.002707327725631/0/124.5/0.01064/-90/0
params=45/90/0/45/0.265/0/0/0 passes=1 maxiter=6400
inside=253 float=y
colors=000mJKDNRH4DBCK6KRaW9otfblcQeaDYZYh7PcEH_K9\
VRDZOAXR7VT4TVRzoInh9bbvm4wQehRbUR`FRZcjRRloKfjEae\
7W`w0t6l14f93aH2WPFkMAdQ5YU2Bt1Hl1MdmyIPgQl84`DCPI\
JDNQfsdTiaF_ZPbkHZf9VaIRMDRP9RS5RVP15DEJQvGJnLDfP7\
ZT8py5go3Ze1o11h91bH1XPpVfcUcRTaESZbaLKKuEjx9cn5Xe\
K`d2uF1jL1`RLhWbCPKcnpWLcUORTRESUh9CNINK53DDD7KNOd\
vZ7rIHgzdmj`hWYdGU`fWyWUqMTjBSc4i`3d_2_Z1VYrntdhnS\
bhEXbfSMWRPMRSBRVE9P7ITlQ3_T6ISK3T3VffGZab17KEKN9g\
CIa3Z42XC2VJ1TQp77RHKL73GCBBHI6MQpRJZROIRTA1T7AV4J\
WTCq7kQ5dT3YVDloHryBho6_e8jk4`cY1uNAlCJdJyHEpLAgP5\
ZT`F2JLIB2G7BM4JSPELHJP9NTOTjTmZJeYAYXHGIBKN6OS_RS\
ORUCRW1eBHzz9zzOzzvzzUzz2zzNzz`zzSzzJzzAzzDzzAzz7z\
z4zzFzz8zzozzyzzqzzUzzMzzFzz8zzQzzJzIDzN7zSZzqNzjC\
zcuzVLzYBzXUzvKzmAzd1zV1zWwzzUzzBz87zH4zPhzqYzkNzf\
zzwWzwXzw`zrcznfzjizfhzRhzzbzzYzzMzzBzzDzzFzzHzzIz\
zPzzVzz`zzfzzhzzM0`ozzbzz }
frm:SliceJulibrot2 {; 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=sqr(z)+c
|z| <= 9 }
END PARAMETER FILE=========================================
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times.
