TIPS and HINTS for using the Mandelbrot set Dictionary:
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It is not necessary to wait for the image to be completed before you start
your next magnification. It is advised that as soon as you see something in
the image you'd like to magnify, that you save the current image, and then
Magnify the place you'd like to magnify, along with increasing the number of
iterations by about 100 for every 10 X magnification increase.
If you have color, and monochrome screens and wish to produce a highly
magnified image for printing, the following procedure is recommended:
1.) Get a general idea of what you want to produce by using the low
resolution screen, and the "Accelerate" function to check various places in the
image for interesting things.
2.) Once you sort of know what the color image looks like, use "Plotting
info" to determine its X,Y and Vertical window size. The X,Y are written in
the form X + Yi, so you'll see it in the middle of the second Information
screen. It'll usually be the longest number on the screen so you shouldn't
miss it. If the number for instance says 0.1234 + -0.5678i then X = 0.1234 and
Y=-0.5678. The numbers are accurate to 11 decimal places.
3.) Boot up with the monochrome screen, choose the "Custom image" option
and type in the X,Y and Vertical size parameters you found from the color
image. If you know you're going to like the black and white image, you might
even consider making a BigScreen black and white image.
4.) Wait for about an hour to see what kind of image is being produced; if
you're getting a lot of black stuff, then lower the Threshold, or increase the
Overflow. If you're not seeing anything Raise the Threshold, or lower the
Overflow. Don't lower the overflow too much though or else you're going to get
black no matter what you do. Follow the guidelines in MD.DOC for adjusting
these things.
* Note: I haven't tried this yet, but I believe that if you RAISE the
Threshold and LOWER the Overflow at a nice distance from the Mandelbrot set you
might get branching (like trees), I haven't tried this yet, but try it an see
if you like it. (Try say a Threshold of 5 and overflow of 10000, I don't
really know, if you find out tell me!)
What magnification means:
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Magnification as seen in the "Plotting info" option, mean how many times
the image is magnified if the Mandelbrot set were plotted on the screen using
the screen as a grid where each pixel represents one integer. To fill the
screen with an image of the Mandelbrot set therefore requires a Magnification
of around 100 X on a low resolution screen and 200 X on a high resolution
screen. The 300,000,000 X image in MANDLBRC.ARC is actually as you will
notice, 30,000,000,000 X in the Plotting info screen. Since it is a color
picture, I chopped off to zeros to get a magnification number with a screen
filled Mandelbrot set representing 1 X. You must also remember that this means
magnification in each direction, so the area has actually increased
900,000,000,000,000,000,000 times! (nine hundred quintillion times!) If figure
that if you saw a picture of the earth on your screen, at approximately 12,000
km. if we magnified it 300,000,000 times, we'd do the following calculation:
12,000 km = 12,000,000 m = 12,000,000,000 mm, then take 12,000,000,000 and
divide it by 300,000,000 to get 40 mm = 4 cm.!!!! That means the image across
your screen could now be the calculator on your desk and you'd be reading HUGE
DIGITS!!!!! You could SEE THE LIQUID CRYSTALS!! It would be like seeing your
calculator ENLARGED on earth from the moon!!
The time factor:
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As the magnification increases to 100,000,000 X and up be prepared for an
image to take at least over night to process. Distance estimate plots take at
least twice as long. The image DE1_5.PI3 from the MANDLBRM.ARC file, took 2
weeks (on and off during overnight runs) to process, and it isn't even entirely
complete. Of course DE1_5.PI3 is no ordinary image either, it's taken me a
whole YEAR just to find out where it was! That'll tell you something about the
complexity of the Mandelbrot set!
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But most importantly:
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HAVE FUN!
=) Smile!