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Jim Muth in his "FOTD -- January 24, 2008" text
says:
>some of the images appear so unlikely that I
>cannot shake the impression that they are
>artifacts of mathematical imprecision rather
>than true fractals.
My question is:
Can one determine if a fractal's features are
precision problem artifacts by computing the
fractal twice -- with two different values of
the number of arbitrary precision digits --
and then comparing the two images? <---<<
My hypothesis is that if you compare the two
images calculated in the above manner and they
are the same, then problems of precision are not
the cause of a fractal's unusual features.
Is this the case? <---<<
If this method does correctly determine whether
an image has artifacts or not, is adding the
following items to an image's parameter file a
valid way to exactly set the number of digits
of precision used in a calculation?
1st image calc:
---------------
MATHTOLERANCE=-1/-1
BFDIGITS=14
2nd image calc:
---------------
MATHTOLERANCE=-1/-1
BFDIGITS=15
I cannot find the email sent to me that tells
how to compare two images. Here is what appears
to work -- please correct me if I am wrong:
To compare two images that are in files:
- Run FRACTINT *without* the command line
parameter debug=50
- Load the first image from its file using <r>
- Type <g> and then: debug=50
- Load the second image from its file.
(Note that the File List selection page
title is now: "Select File for 3D Overlay")
- The image on the screen is the difference
between the two images. Identical pixels
in the two images are shown as color zero.
Different pixels are shown as non-zero.
- If this 'difference image' has any non-zero
pixels the two images are different.
Is the above procedure to compare two images
in files correct? <---<<
It appears that the color map of the images
is used to display the difference pixels.
If there are extremely dim color map values
in the image one could be fooled into thinking
that there were no differences between two
images when in fact there were if the
difference pixels that were displayed happened
to use dim color map values.
If this is a problem for a particular image
one could get around it by loading a garish
color map, say, a color map of 15 bright
colors and black like: GOODEGA.MAP
This makes all non-zero pixels be easily
visible against a black background.
I calculated a default Mandelbrot image at
640 x 480 using both the default integer math
and then putting float=yes in my SSTOOLS.INI
file. (I had forgotten to do this when
installing FRACTINT onto my recent computer.)
I was surprised to see a significant
number of differences between the integer and
float images. I constructed a color map
that would allow me to see the difference
image pixel values as follows:
0 0 0 This file shows the pixel values
127 0 0 1-6 as distinct recognizable
255 0 0 colors. All other pixel values are
0 127 0 dim gray, except for pixel value
0 255 0 zero which is black.
0 0 255 - HHL 1/24/08
0 0 127
64 64 64
64 64 64
64 64 64
. . .
64 64 64
The difference image showed a few dozen pixels
with values of 1 - 6 and a few hundred dim
gray pixel values with values somewhere in the
range of 7 - 255. All other pixels were black.
Is it likely that I did this comparison and
analysis incorrectly, or is this difference
between integer and float expected? <---<<
Does anyone know if the pixel values of the
difference image represent the absolute value
of the difference between the pixel values of
the two compared images as I am conjecturing
they do? <---<<
Also, am I correct in assuming that arbitrary
precision works for formula file fractals? <---<<
- Hal Lane
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# hallane(a)earthlink.net #
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