MME 518

Fractal Dimension

Below are shown various classical fractals. Your job is to utilize the notion of fractal dimension and compute the value for each object shown. To do this, you should first understand what recursive scheme is being used.

Problem 1: Miscellaneous Curves

a. Koch Curve

Problem 2: The Cantor Set

Problem 3: The Sierpinski Triangle:

Problem 4: The Sierpinski Carpet:

Problem 5: The Sierpinski Pyramid:

Problem 6: The Menger Sponge:

after more iterations:

Problem 7: Koch Snowflake