FOTD 06-12-04 (Un-Unity [5])

6 Dec 2004

      FOTD -- December 06, 2004 (Rating 5)

Fractal visionaries and enthusiasts:

Today's formula is not strictly an escape-time formula, but the 
type of image it draws (it draws only one image) is close enough 
to escape-time images to be included in the Fractint tour.

We learned in high school that the graph of X^2+Y^2 is a circle, 
but we never learned that it could be a fractal.  (At least I 
didn't)  As today's image shows, X^2+Y^2 makes a striking 
fractal.  All that is necessary to bring out the latent fractal 
is to make the journey to unity a bit difficult, as has been 
done in the 'unity' formula.  (An interested fractalist is also 
a help.)

The fractal is a strange one.  Features that are clear on the 
surface vanish mysteriously as we zoom in on them.  When today's 
image is rendered at a resolution of 640x480, there is an 
obvious but very narrow circle of radius 1 around the origin.  
At a resolution of 800x600 only a few scattered traces of this 
circle are visible.  And when we try to zoom in on the circle, 
it vanishes completely.  It is not only this delicate circle 
that vanishes when it is enlarged; nearly every feature in the 
interior of the circular fractal itself is unstable, almost as 
though the entire fractal were a moire pattern.

Today's image shows the entire unity fractal rotated -135 
degrees.  By setting the outside to 'atan' and turning on the 
'decomp' feature, I was able to divide the fractal into two 
contrasting semi-circles and come up with an image worthy of 
FOTD status.  The name "Un-Unity" implies that the two halves of 
the image are so different as to be separate entities.

The image is extremely fast, rendering in less than 6 seconds on 
my 7-year-old machine.  Since the 'unity' formula has no parame-
ters to tweak, and the fractal is unstable when it is zoomed 
into, I could take no credit for finding a great image.  But 
today's FOTD is a fine rendering of the basic fractal, well 
worth the rating of an average 5 that I gave it.  And when the 
hyper-fast render time is considered, the overall worth measures 
an astounding 5102.

Of course, such numbers are meaningless.  All fractals that 
complete in less that a minute should be considered 'instant' 
fractals.

Today's fractal can be seen by running the included parameter 
file or by downloading it from the FOTD web site at:

       <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

The warm sun continued all afternoon here at Fractal Central on 
Sunday, while the temperature reached a mild 54F 12C, giving the 
fractal cats all the time they wanted in the yard.  It was one 
of the best days in the past several weeks.  The day was so good 
in fact that no special treat was needed to keep the duo happy 
in the evening.  This morning is starting cloudy however, and it 
is colder.  Rain is also threatening, so I doubt that the good 
day will be repeated.

For me it will be just another workday.  When I finish, I will 
have to decide what kind of fractal theme to tackle next.  Check 
back tomorrow to see what I dream up.  Until then, take care, 
and be at unity with both yourself and the cosmos.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com

START PARAMETER FILE=======================================

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END PARAMETER FILE=========================================

Jim Muth

Charles F Crocker

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