COSC 231 Programming Project GUI for Two Fractals
Distributed: 24 November 2009
Due: 10 December 2009
Write a GUI that will display, with certain user-controlled parameters, the Sierpinski
gasket and a Mandelbrot set.
Sierpinski triangle (gasket)
The Sierpinski triangle generation algorithm is given in Savitch’s book (3rd edition) on pp
1061-2. That text is reproduced here.
Write a program that draws a Sierpinski gasket. A Sierpinski gasket or
triangle is a type of fractal. It is an example of how an orderly structure
can be created as a result of random, chaotic behavior.
The creation of a Sierpinski gasket is fairly simple. There are three points
that form the corners of a triangle. In the figure below, they are labeled as
A, B, and C.
To draw the Sierpinski gasket follow the algorithm:
1. Randomly pick one of the three corners. Call this the current point.
(Alternatively, you could also randomly select any point inside the
triangle).
2. Randomly pick one of the three corners. Call this the target point.
3. Calculate the midpoint between the current point and the target point.
4. Draw a single pixel at the midpoint.
5. Set the current point to the midpoint.
6. Go back to step 2 and repeat many times (e.g., 50,000 iterations).
It would seem like you should get a random mess of dots since the
algorithm randomly picks a target corner each time. Instead, if this process
is repeated many times, you will get a very orderly picture with a
A
B
C
