June 9, 2010: Beyond the Horizon | June
8 |
June 10 | 2010 | FOTD Home |
Fractal
visionaries
and enthusiasts:
Today's formula, the FinDivBrot-2, certainly creates some interesting
and unexpected parent fractals -- and it's only 4 lines long. (I
have always avoided those overblown formulas with 40 or 50 lines, most
of which are devoted to coloring tricks. I much prefer the
coloring tricks to come from the fractal math, not the fractal artist.)
Today's formula, along with the type=Mandel, MandAutoCritInZ,
MandelbrotBC3, and SliceJulibrot4 formulas (formulae) are the ones I
turn to almost automatically when I boot the Fractintprogram.
They rarely disappoint me.
In today's FOTD, the FinDivBrot-2 formula produced a parent fractal
that resembles a Mandelbrot set pretty closely until its main stem is
examined. Instead of one main stem, this parent has two main
stems, both of them infinitely divided into ever-smaller curled
stems. Today's image is located in the East Valley area of the
minibrot on the northern main stem.
I named the image "Beyond the Horizon" because I did go a bit beyond
the limit of perfect definition to find the scene. The rating of
a 7 means the image is kind of good, but nothing to get excited about.
Another picture perfect day prevailed here at Fractal Central on
Tuesday, an exact repeat of Monday. The fractal cats, now
convinced that the unwanted intruder cat has moved on, spent most of
the day sleeping. My day was busier than Monday, but still left
lots of time for fractal diversions. The next FOTD will be posted
in 24 hours. Until then, take care, and pass the time pleasantly.
P.S. If a Klein bottle is given an extra twist, the result is a
surface known as a 'projective plane', which needs a full five
dimensions to be seen in its full unsquashed, non-intersecting
glory. But don't ask me to describe the shape of this
surface. Describing the Klein bottle is hard enough. And
unless I'm mistaken, a projective plane may also be created by widening
a Mobius strip until the single edge closes on itself to form a
single-sided edgeless surface.
Jim Muth
jamth@mindspring.com
jimmuth@aol.com
START PARAMETER FILE=======================================
Beyond_the_Horizon { ; time=0:03:54.18-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2 function=recip logmap=506
center-mag=-1.418212964957334/+0.03225319123708284\
/1.626e+013/1/167.5/-0 params=-0.05/-10/0/0 float=y
maxiter=1500 inside=0 mathtolerance=0.05/1
colors=000L1UK1SK1QJ1OJ1MI1KH1IH1GG1EG1CF1AE19E18D\
07D06C05B04B03A02001A00900800800700700600500500400\
40030020020010010000000000000000000000000000000000\
0000000000000000000000000000000000000000000000IwzF\
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7Uz5Uz3Uz1UzUUzTUzSUzRUzRUzzzEzzEzzEzzDzz1zz1zz0zz\
0zz0zz0zz0zz0zz0zz0zz0zz0 }
frm:FinDivBrot-2 { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }
END PARAMETER FILE=========================================