Look at a GSP constuction of this famous fractal.
 
 

To construct using GSP:

1.  Construct an equilateral triangle.
    -(equilateral triangle:  construct a segment, construct two circles by center and radius--do this using the endpoints, construct the point of intersection of the two circles.

2.  Find the midpoints of each side.

3.  Connect the midpoints of each side.  Now you should have four equilateral triangles.

4.  Construct a polygon interior using the triangle in the center.

5.  Repeat the process as many times as you desire-----these "times" are called iterations.
 
 
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