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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image for leap-day has been named "Odd Mandelbrot". This is because it is a view of a midget sliced in an odd direction of the Julibrot somewhere between the Mandelbrot and Julia orientations. In the odd slices of the Julibrot, the midgets, or holes as they could more properly be called, can assume any shape whatever. The hole at the center of today's image is clearly not a perturbed Mandelbrot midget. Such fragmentary midgets never have the straight edges seen in today's image. Nor could it be a Julia set. They also never have features with straight edges. It is actually a slice through the Julibrot oriented half way between the Julia and Oblate orientations. (The Oblate orientation is determined by the imag(c) and real(z) axes.) The straight line through the northwest corner of the hole is an example of one of the features I have named bridges, which are actually parts of Mandelbrot valleys seen from the side. As I mentioned in recent discussions, these odd planes of the Julibrot can be rather unattractive, mostly due to the stretching, which produces a feeling of stress. After considering today's image for several minutes, I decided to rate it at a 5. When the render time time of 2-2/3 minutes is taken into consideration, the overall value registers a 187. This makes running the parameter file worth the effort. Those who would rather have their fractals already cooked may download the finished image from Paul's web site at: A nice warm late winter day with lots of sun and a temperature of 59F 15C made the fractal cats nice and happy on Saturday. They enjoyed several hours in the yard, romping as much as 13-year-old cats can romp, which is not much. When evening came and the sun went down, they strolled back indoors without complaint. Today is starting even warmer. How active can the duo get? As for me, I'm simply going to take it easy. After all, it is the seventh day of the week, a divinely ordained day of rest. Yes, I know that the calendar says it is the first day of the week, but the calendar is wrong. Creation began at 9am on a Monday. Until next fractal, take care, and see you in fractal land. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Odd_Mandelbrot { ; time=0:02:40.70--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2 passes=1
center-mag=+0.00000000000151219/-0.000000000003180\
98/1.776313e+010/0.6892/50/1.31075705844807544e-014
params=45/0/90/0/-0.6351285303263351/0.49205751226\
41822/-0.635128530326335/0.4920575122641822 float=y
maxiter=18000 inside=0 logmap=169 periodicity=10
colors=000qOPnPNkQKhRFeSCbTAZU9VU8QV7MW6HV1IW5JX9K\
XCLYGMYJNZNO_QP`UQaYRa`SadT`gU_kU_hUZkUXnMWqIVtLUw\
OTvRSvURvXQv_PvbOveQwhTwjWwlZwkawhcwebwbaw_`wX_wUZ\
xWYvXXtYWrZVp_Un`TlaSkcRidQgePefOcgNahP_hIghMbiQZg\
UUfYQeaLdeHciCbm8alA`kC_kDZjFYiHXiI_hKdgMhgNlfPpeR\
teSp`PlXMhSJdOG`JDXFAVOBTXBReBPnBOz6NwBNuGNrKMpPMm\
TMkYLhaLff8kcLdgXZXiTIjN4kU6a`7Tf9JmA9tC0zD4xF8vGC\
tIGrJKpKOnMSlNWjO_hQcfRgdSkbUi`ViWZhZWi`UjbSkePlgN\
niLplIrnGwpEzrCzlFrfIm`LhWNcQQZKTUEWP4TK9YYEbkJgxO\
ksRhoTfkWdgYbb``ZbZVeXRgVNiTQjSSkSUkSXlSZmR`mRcnRe\
oRgpReqOerMfsKgtIhuGivEjwCkxAly8mz6nz4oz2pz8qzDrzI\
szNtzSuzXvzZwz`xzayzbzzczzdzzezzfzzgzzhzzizzjzzkzz\
lzzmzzkzzjzzizzgzzfzzezzizzmzzpzzozzozzozzozzozzoz\
zozzozznzznzznzznzznzznzznzzszzpzznzzlzzjzzgzzezzc\
zzazzZzzXzzVzzTzzQzzOzzMzzIzzKzzMzzNzzPzzQzzSzzUzz\
VzzXzzfzzizzkzzmzzpzzrzzt }
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 20.0 PAR-FORMULA FILE==================================
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