Using the Mandelzot Program
For your project on Chapter 12, you may explore the Mandelbrot Set using the MandelZot 4.0.1 software. This is
freeware that has been loaded on to the network in the computer center. You can download the program from the
Internet or get a copy from me.
What you will need:
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Your ACC ID with a library bar code on it.
A pencil and paper.
A 3.5" computer disk.
A summary of what you are going to do:
You are going to go exploring the Mandelbrot set and write a "journal" of where you have been. You are going
to record your "travels" by "taking" pictures, keeping a "log" of your journey and writing a "journal" what you
see, both descriptively (it looks like a spiral) and mathematically (all the spirals are self-similar). You should
visit at least five (5) different "locations" (the zero magnification, original Mandelbrot Set does not count),
preferably zooms of an interesting location. Also include any impressions you have during your travels, both
mathematical and other.
My suggestion for your journey is that you pick an interesting location and zoom in four or five (or more!)
times on that particular location rather than visiting five different locations. If you use a large magnification
at each level you may run into some technical difficulties, but it can be done. I think you will find it more
enjoyable to zoom in and see what happens, but you may need to visit a couple of locations if you try to use
large magnifications. Choose what works well for you, it is your trip and you can go where you want.
How to get started on your journey:
1.
Sit down at the computer. Insert your floppy disk. If you aren't sure whether it's a Macintosh disk; initialize
it by choosing SPECIAL from the menu and selecting E r a s e D i s k . The computer may tell you that the
disk needs to be initialized. Give the disk a name (preferably your name), click E R A S E . Wait until the
computer is through.
2.
Open MandelZot 4.0.1. If you are in the computer
lab you only need to click on the icon once. The
MandelZot icon looks like this:
3.
When the menu bar appears (along the very top of the screen) choose the File menu and select "N e w ,
specify center & mag..."
The window that appears tells the program where on the complex coordinate plane you want to center
your picture on and at what magnification. You can change any value in any box. Start at the default
values (shown) for this project. When you are more comfortable with the program or need to salvage a
picture you can make other changes.
4.
Use the TAB key to move the cursor to the width box. Type in 360 for the width. TAB to the height box.
Type in 240 for the height. Use the mouse to click O k or press the return key.
The largest viewing window that the memory will handle easily is about 450 x 300.
5.
Creating the picture may go slowly, so be patient. Save the completed picture. Use a name such a "Mary0"
or "original" or "beginning."
To save - under the File menu choose S a v e . When you get a window that prompts you for a file
name, be sure that the "top" of the box has your disk name NOT the computer name; you want to save
to your disk not the hard drive. The program saves the picture, any technical (location) information
and any color change information in the same file.
6.
Select a section of the Mandelbrot Set to magnify (zoom in on).
To select section - Position the cursor (which is a cross-hair/plus sign/cross while the mouse is over the
picture) where you would like a corner of a rectangle to be. Click and hold on the mouse button. While
holding the button down drag the rectangle around what you would like to magnify. When the
rectangle is as large as you need, let go of the mouse button.
To re-position the rectangle - Press and hold the Option key, a hand will appear instead of the plus-sign
cursor. With the hand over the rectangle, click and hold the mouse button and drag the rectangle to the
desired location.
7.
Magnify the selection. Go the C a l c u l a t i o n s menu and choose "M a g n i f y s e l e c t i o n ."
The zoomed image should begin re-drawing. Don't try to zoom too much at one time or you might lose
some of the sights along the way; you will also freak out the computer (not totally) and it will take a
long time to re-draw! Initially, make good size rectangles (at least one-fourth the size of the picture
window), at least until you get a feel for what you're doing.
8.
Save the new picture using the S a v e a s command under the File menu.
If you choose S a v e you will save over the previous picture. Give this new picture a name like "#1"
or "Mary1" or "first stop". Be sure save the file as C o m p r e s s e d D w e l l s so you'll have enough
space on your disk for all your pictures.
9.
Record the technical (location) information. This can be done later, but if you crash you're in trouble.
To record the information - under the File menu choose G e t I n f o . From the window that appears
record C e n t e r X , C e n t e r Y , X m a g n i f i c a t i o n , Y m a g n i f i c a t i o n , and M a x
d w e l l . This is the only information necessary to re-generate your picture if you forget to save it or
save over it or something. (This information would go into the boxes of the window you get when you
choose New).
10. Repeat steps 6-9 four more times to get a total of five stops.
Other comments, trouble-shooting, technical and fun stuff:
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A note on PATIENCE. Depending on how much you zoomed, you may have to wait several minutes until the
image is finished re-drawing. Be patient! If it seems really, really slow and you didn't try an enormous zoom
(an enormous zoom means you drew a very small box to magnify) check several things:
1) under the C a l c u l a t i o n s menu, under the O r d e r sub-menu, make sure the option "R a s t e r scan" is checked, if not, select it;
2) under the C a l c u l a t i o n s menu, under the M a t h M o d e sub-menu, make sure the option
I n t e g e r is checked, if not, select it. If the option "68881 floating-point" is available
(black, not gray on the menu) select it because it is the best choice, just not always available
(dependent upon type of machine).
3) under the C a l c u l a t i o n s menu, under the A c c e l e r a t o r option, see if "S h e r m a n
c o n t o u r c r a w l e r " or "Mariani/Silver" are checked. They are the best accelerators and
may speed up the drawing.
4) under the C a l c u l a t i o n s menu select D i v i d e a n d c o n q u e r . This will allow the computer
to access all available memory to do the calculations. You won't be able to do anything else with the
computer, but it should speed up the drawing. You know the computer is through when the arrow
cursor returns from being a watch.
If you tried all of the above, just BE PATIENT!!! That's what you get for trying to magnify more than the
computer can handle! (You can always scrap this picture and do another that's not magnified as much.)
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If you get a message window that says "unable to perform the operation" (or something to that effect), do a
get info, record the information and quit the program by choosing "Quit" from the File menu. The
memory has been overloaded with junk that it can't get rid of. Quitting the program will clear the junk out of
memory. You might quit every three or four zooms, just to avoid that problem.
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You can get a change of pace by playing with the "M o n o c h r o m e b a n d s ," "P a t t e r n e d p e n ,"
and "C o l o r e d p e n " options under the Display menu.
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Improving clarity. If the images start looking "fat," i.e., what looked like two blobs now looks like one longer
blob, you're losing detail that you know or think should be there, etc.; you need to change the setting on the
M a x i m u m d w e l l option under the C a l c u l a t i o n s menu. Select a higher value than whatever is
currently displayed. This may slow the calculations some, but will provide greater clarity at large
magnifications.
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I don't want to know that all you saw are large colored squares. If that's all you have on your screen, either
you're not being patient or there's something wrong with the set-up information (check the technical stuff
above and/or below this paragraph). The computer can only calculate so fast and there's lots of calculations!!
You probably zoomed a whole bunch and want instant gratification and that ain't gonna happen!
Usually you can get rid of the squares by increasing the "E s c a p e r a d i u s . . . " option under the
C a l c u l a t i o n s menu. You only need to increase it to 2.1 or 2.2 (from the default of 2) and then choosing
D i v i d e a n d c o n q u e r or D i s c a r d u n c e r t a i n v a l u e s under the C a l c u l a t i o n s menu.
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There's no reason to mess with "S e t w i d t h o f d w e l l b a n d s … " option, under the Display
menu; it should be set to 1.
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Make sure the "U s e d i t h e r i n g o n 1 6 - c o l o r s c r e e n s " option, under the Display menu, is
checked.
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The "A l g o r i t h m t w e a k s . . . " option, under the C a l c u l a t i o n s menu, should be set to
"Mariani/Silver ("Eat my dust!")" which is the default setting.
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If the computer tells you that there's not enough room on the disk to save the picture, DON'T PANIC!!
Graphics files are very large and you've just used up your allotted disk space. For this picture, go back to the
File menu and choose S a v e a s . Change the F o r m a t window to read C o o r d i n a t e s o n l y .
Hopefully this salvage this picture. Next, you should open all your other pictures (one at a time) and make
sure they are saved as compressed dwells or coordinates only. Use the S a v e a s command and the same
name (so that the small file will overwrite the large file).