FOTD -- June 18, 2008 (Rating 5)
Fractal visionaries and enthusiasts:
I seem to be in one of those occasional fractal ruts, where I
just can't seem to come up with a fractal that meets even my
lowly standards of fractal worth. Yesterday's image was
probably the least impressive FOTD of the past 11 years, and
that's talking about a lot of fractals.
Today's image is a small bit of an improvement. It is a view of
Seahorse Valley, a slit view that I can virtually guarantee has
never before been seen. The view is almost in the Rectangular
direction, oriented so close to it that it was necessary to
stretch the scene about 75 times in the vertical direction
before the remnant of Seahorse Valley became recognizable. (The
rectangular orientation is determined by the imag(z) and imag(c)
axes of the Julibrot.)
Where is the rest of the Mandelbrot set? This is a question I
cannot answer. It is probably off somewhere, a lost potentia in
a space of five or more dimensions, making the quest absolutely
futile. I have been trying unsuccessfully for 20 years or so to
visualize something with only four spatial dimensions, so far
without success. Apparently I need to have my consciousness
expanded before higher-dimensional awarenedd becomes possible.
Maybe the local mystic, Madam Zucchini, can be of help.
I named today's image "Portal to Infinity" and rated it at a 5.
The calculation time of under 2 minutes should cause no
hardships. And to be doubly sure no hardships are incurred, the
completed GIF image has been posted for instant viewing and
enjoyment on the FOTD web site at:
<
http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
A very pleasant and refreshing day here at Fractal Central on
Tuesday, with a temperature of 72F 22C, was made even fresher by
a quick shower that passed over at 6pm, followed by a brilliant
rainbow in the east. The fractal cats, not appreciating the
small pleasures of nature, slept through it all.
My day was busier than I would have preferred, but much better
than yesterday, when I posted a hasty fractal that virtually
duplicated and was a poor imitation of the not-all-that-great
image of the day before. The current work rush has about ended
however, so tomorrow's FOTD, which will appear in the usual 24
hours, will likely be a vast improvement over today's. Until
then, take care, and walk with the fractal elite.
Jim Muth
jamth@???
jimmuth@???
START PARAMETER FILE=======================================
Portal_to_Infinity { ; time=0:01:51.10-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2 passes=1 center-mag=0/0\
/33.52388/0.01407/90/0 params=89/88/0/90/-0.75/0/0\
/0 float=y maxiter=3600 inside=0 periodicity=10
colors=000JEYKGaLIfMJjNLoONsOOwRNtUNrLEDLDDLCCLBCf\
AQgCSgETgGUgIVgKWhMYhOZhQ_hS`hUaiWciYdi_eiaficgjfk\
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_eIZfIXgHWhHUiGTkGRlFQmFOnFNoELpEKqDIrDHsCFtCEuCDu\
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X_CZYBaWAcVAfT9hS8kQ7mP7oR9nTAmUClWDlYEkZGj`HibIic\
KheLgfNfhOfjPekRdmScoTcpVbrWavT_tV`sXarYbq_cpadobe\
ndfmfglghkiijkjilkhnlgpmfqnesodupaywbwtcvqdtneskfq\
hfpegnbhm`ilYjjVjiSkgPlfM }
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=========================================
