Name: _____________________ATM Mandelbrot Set Computer Explorations
WINFRACT
1.a.Open the WinFract folder, then double-click on WinFract(there’s a little M-Set picture next to it)
b. Click on Colors, Load Color Map, then select Default
c. Enlarge the window, then go to View, Image Setting, and select 800x600
d. Go to View and turn the Coordinate Box on.
Move the cursor around to get a sense of where you are on the complex plane.
Try to position it at the origin (0+0i), which is x=0, y=0 in this program
Now turn Coordinate Box off
e. Go to the View menu and select Pixel by Pixel Update (unless it is already checked)
f. Go to Fractals, Basic Options , go to Passes and click on B-trace
g. Find a place that looks interesting and...
click and drag a box out, then double click on the box to zoom, but just zoom once
2. This will become too slow quickly, so...Now turn off the Pixel by Pixel update from 1e).
3. Zoom some more, until you seem to be losing a lot of detail (it seems to be smoothing out)...then:
a) go to Fractals, Basic Options, and set MaxIter=500
Zoom a little more
b) You will now go back to the original M-Set to check out some other features...
To go back to the original...
a. Go to Fractals, Fractal Formula, and select mandel
b. You must then go to Colors and Load Color Map and use
Default (or some other) again every time!
c) Okay. Now to make your picture even cooler (and I really mean that),
go to Fractals, Basic Options, and click on epscr for Inside
d) Zoom in on this picture now a bit...
e) Once you’ve got a truly great picture...
4. Okay, now, once you’ve got a truly great picture... (UPDATE: I’m not sure this step of saving works anymore)
a) File, SaveAs, OK
b) Fractals, 3D Restore, check Spherical Project, then select OK, then set Surface Scaling at 90. Then select OK and watch the magic.
5. Now go to Fractals, Fractal Formula and select some other type of fractal (there are hundreds) and play around with the same ideas or do deep zooms. Remember that you must load the color map for each one (unfortunately). Experiment for awhile. Enjoy yourself. (Try “spider” and do some zooms into it. There are many others to try.)
If you find a picture you like a lot, you can save it as a .gif. Just go to File, Save As, ...
ULTRAFRACTAL
1. a. Open the UltraFractal folder, then click on the picture of the little M-Set,
click on I agree, then No
b. Hit Ctrl-N (=new fractal)
c. Click on Library, then Formula, then Fractint , then select Mandelbrot Z^n
d. Go to the Properties Windows on the right side of your screen- if you don't see it, go to the Fractal menu, and select Properties
e. Click on the Image tab and set the Width to 800
2. Zooming in:
a. Zoom in 6 or 7 times (when zooming, you can double-click anywhere on the picture or you can click, hold, and drag out a box, to be moved around, then click on the box)
b. When you’ve entertained yourself enough, click on the Location tab. This shows you where you are on the complex plane and shows you how many times you've magnified the original picture.
If you've magnified over 10,000 times, go to the Formula tab and under Maximum Iterations, click on “adjust automatically”
c. Once you’ve selected “adjust automatically”, zoom in one more time...
Notice that a lot more detail suddenly appeared.
d. Now zoom some more....After a few zooms, look back at the Location and(remember that, for example, E8, means x108, so 5.678E8 as 567,800,000):
e. Colors: Hit Alt-A, then G. Now try dragging the little squares around and go back to your picture to see the resulting changes.
Also try using the Gradient, menu and selecting Randomize, then try Adjust
f. Reset to the original fractal by hitting Alt-A, then L
g. Look at the little specks along the horizontal line to the left of the M-Set. Try zooming in on those, then keep zooming in on new specks.
h. Hit F10 a couple of times. What happens?
Hit F9 - what happens?
i. Reset to the original fractal by hitting Alt-A, then L
j. On the Formula tab, go to Parameter: and select Exponent. This allows you to change the exponent from just 2 to other numbers
k. Go to Exponent(Re) to and change it to 3 (this changes it from x2+S to x3+S), then try 4, 5, 6, 7, 8, 20, 100.
What is the relationship between the exponent in xnext=xn+c and the resulting picture?
l. Now look at 3.5, 5.5, 7.5, 9.5. What do you notice?
m. Now try 2.5, 4.5, 6.5, 8.5
n. Now try 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0
o. This will be cool: Try 5.3, then zoom in on left middle side where it seems kind of flat.
Once you get in there, find little islands and try zooming in on them, then zoom on the islands within the islands.
p. Reset to the original fractal by hitting Alt-A, then L
Now try Exponent(Re): 2, 1, 0, -1, -2, -3, -4, -5
Now try Exponent (Re): 4 and Exponent(Im): .01, then .1, .2, .3, .4, .5, .6
Now zoom in to see what havoc you have wreaked on the poor M-set
q. go to Library, Formula, and select formulas to explore...
FRACTAL EXPLORER
1. Open the Fractal Explorer folder, then click on the picture of little M-Set
2. Go to Options, then Fractal Size, then select 640x640
3. Hit Alt-L, then S (Select Fractal)
Click on the different Fractal Types and notice the preview in the lower left corner
a. Select Classic Mandelbrot from the very top of the list
b. On that same screen go to Filter Properties, scroll way down the list and select anything with stalks or tentacles. Click on Select to see the fractal and zoom in on it.
c. Another cool thing to explore is in the top right of the Select Fractal screen, called Parameters.go to Functions and change to anything and watch how the picture changes
Click select to see the picture, then you can zoom
Fractal EXTREME (this is the best!!!!)
1. Open the Fractal eXtreme folder and Click on the picture of the “fX”
2. Click on “Use Fractal Extreme” and “Okay” and “Close”
3. Go to Options and click on Fractal Size and set at 800x600
Also enlarge the window
4. a) You can zoom by double clicking on the picture and you can also click, hold, and drag the image to shift around, try it.
b) Also: click on the minus sign on your keyboard to zoom out and the = to zoom in
5. Go to Options, Color Palette, and select Cycle Colors
6. Zoom in many times, then click on Render and Make Zoom Movie, then wait for the movie to begin.
Notice that if you used the suggestion in 4b) the movie is even cooler, because it changes where you are zooming in to.
While the movie is playing, Click on Cycle colours
Also, you can alter the Zooms Per Second: slow it all the way down with color cycle on, then speed it way up
Any of these programs can be used to create and save images of the fractals you have created/explored/discovered.
Saving fractal files is different from saving images. If you save a file, it means you can come back to it and zoom in on it. If you save an image, it can be altered, displayed, sent via email,etc...