HAT FRACTAL DIRECTIONS

Open Geometer's Sketchpad,and open a new scetch and a new script. Click record on the script before you begin to construct on the sketch. Follow the directions below to create a hat fractal.

1. Construct two points and the segment between them. Mark the left point as the center and dilate the right point by a factor of 2/3. Then mark the right point as the center and dilate the left point by a factor of 2/3. (To mark a point as a center, double-click on it. The dilate tool is found under the transform menu) This action trisects the segment.

2. Next, rotate the second point (from the left) -90 degrees about the third point, and rotate the third point 90 degrees about the second point. (using the rotate function under the transform menu, making sure to mark the center of rotation)


3. Now, hide the original segment, and construct segments between the points as pictured below.

4. Beginning on the left, highlight the first and second points (holding down the shift key). Click on your script that is recording the construction, and click "loop." Go back to your scetch, and highlight the second and third points and again, loop. Do the same for each set of consecutive points (3rd and 4th, 4th and 5th, and 5th and 6th). Then hide all the points except the original endpoints, and finally click "stop" on your script. Now you have recorded a recursive script that will create your fractal.

5. To play your script, open a new scetch, and construct two points. Highlight them both and click "fast" on your script. It will ask you how many recursions you would like. Recursions take a lot of memory, so don't choose too many (your computer will tell you if you have). The following picture was made with 3 recursions:

THE KOCH CURVE

Using the same method of recording a script and recursing, try to create a script to generate the following fractal, called the Koch curve.

Now, using the same script, try to generate a Koch snowflake:



Now, create your own fractal, and scripts to construct it. Write directions as to how to create a script to construct your fractal, and give the directions to a friend and see if they're able to make your fractal.

List your instructions below, and print a picture of your fractal and attatch it to this paper.


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