Math 331, Fall 2002: Problems 25-28

25.

(expires 12/13)     Construct a Cantor set whose box counting dimension is $1/2$. Explain a general algorithm for constructing a Cantor set with any given box dimension $0 < d < 1$. [You can do this on Maple or by hand.]

26.

(expires 12/13)     Write a TurtleCmd procedure that draws the $n$-th approximation of a fractal of your choice (not the one you're using for Project 3, and not the Koch curve!) and calculate its box-counting dimension.

27.

(expires 12/13)     [No Maple] Find the affine transformations that define the fractal below. For notes on affine transformations, download the Maple file: http://www.math.sunysb.edu/~mat331/Worksheets/IFS.mws.

28.

(expires 12/13)     Write an IFS procedure (see http://www.math.sunysb.edu/~mat331/Worksheets/IFS.mws) to draw the $n$-th approximation of a fractal of your choice (not the one you're using for Project 3 and not Koch or Sierpinski) and compute its box-counting dimension.