The Physics Factbook™ Edited by Glenn Elert -- Written by his
students An educational, Fair Use website topic index | author
index | special index The purpose of this lab is to determine
the fractal dimension of broccoli. A fractal is an object that
has a fractional spatial dimension. The dimension of a point is
0, a line is 1, a plane is 2 and a cube is 3. The dimension of a
fractal that can be drawn from a line is between 1 and 2 and has
infinite points and finite length. The dimension of a fractal
created from a shape on a plane has a fractal dimension between
2 and 3 and has infinite length and finite area. Broccoli is a
fractal because it branches off into smaller and smaller pieces,
which are similar in shape to the original. The fractional
dimension can be calculated by: where N is the number of closed
balls of diameter S needed to cover the object. In this study,
the fractal dimension of a broccoli is determined by calculating
the slope of the graph of ln(N)/ln(S). Broccoli is especially
interesting f