Fractal Dimension
This is a Helper Page for:


Koch Snowflake 
Blue Fern 
Sierpinski's Triangle 
Henon Attractor 
HarterHeighway Dragon 
Lévy's Ccurve 
Lorenz Attractor 
Strange Attractors 
Contents
What is Fractal Dimension?
The fractal dimension, , of a particular fractal is a measure of how the complexity of the figure increases as it scales. The dimension is the exponent that relates the scaling factor to the measure of the figure. That is, scale = number of copies of the figure.
Or, , where N is the number of copies of the figure and e is scale.
Example: Sierpinski's Triangle
For example, consider Sierpinski's triangle. If we double its size (as in the picture to the right), we create three copies of it. So its dimension can be calculated by . So .