Fractals, Dimension, and Nonsmooth Analysis

Intuition suggests dimension is an integer, e.g., • A line is 1-dimensional, • a plane (or square) is 2-dimensional, • a solid cube or ball is 3-dimensional, etc. What does it mean to say something is 1.5-dimensional? The example of a space-filling curve (e.g., BM, Peano): a curve so jaggedy that it " shades in " area. What is meant by dimension? Has… CONTINUE READING