FOTD -- May 19, 2016 (Rating A-7,M-8)
Fractal visionaries and enthusiasts:
Today's image shows a little of what can be done with minibrots
of the seventh order when they are calculated in a new way. The
formula will reveal the new way, which I discovered several
years ago while making up new random formulas, most of which
drew beautiful blank screens.
When fractals go above the quintic level, they quickly begin to
all look the same, and by the time we reach the tenth order, the
difference between orders is hard to notice. But look at what
lurks in fractals of the seventh order, (and higher orders as
well), when we do something new with them. Not only do we have
a near perfect minibrot, but there is a very interesting
extended pattern surrounding it, partly derived from the parent
quadratic Mandelbrot set.
This opens an entire new world of fractal exploration, at least
for those who seek minibrots. It is also possible to have
fractals of fractional orders without those annoying
discontinuities, as well as fractals of negative orders. I have
just recently begun exploring this stuff, and I'm sure I'll find
more new discoveries, not only with today's formula, but with
several new formulas I am working on, but have not yet worked
the bugs out of.
It's such a pleasant day here at FC that I will skip my regular
comments about controversial things and enjoy the final rays of
sunshine along with FL and the fractal cats.
Today turned out quite pleasant here at Fractal Central, with
partly cloudy skies, a temperature of 72F 22C, and sunshine that
was brilliant between the clouds. The fractal cats took full
advantage of the weather by sleeping through the afternoon,
while FL puttered in her garden and I searched the internet for
things of interest, which there is no shortage of. The next
FOTD will be posted in the not too distant future. Until then,
take care, and eventually righteousness will prevail, but how
will we recognize it when it does?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
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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=========================================