Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Fractional Dimensions
Name: N/A
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: N/A

I have heard that fractals can be described using units raised fractionally. For example, the two-dimensional Mendelbrot set has infinite area, described as m^2, yet zero volume, described as m^3. Some fractional power sy> (say m^2.7) could be used to describe the blank "space" in the set. While fascinating, it seems purely mathematical. Does m^2.7 represent an object existing in 2.7 dimensions; and could we exist and pass through fractional dimensions? Or is 2.7 just a number, unusable by practical physicists?

I have not been working with fractals, but I think that I can give a broad answer to your question. Yes, "fractal dimension" does have a meaningful definition. The dimension tells you, in a sense, just how "fractal" the boundary is. For a two dimensional structure, the fractal dimension tells you how fast the boundary length grows with the area of the structure,

Jack L. Uretsky

In other words, "it is just a number". It has been pointed out, however, that nature seems to like fractals. Many plants and trees seem to follow a fractal branching pattern, and you can imagine that the coastline of a country is really a fractal with no well-defined length. The practical consequence is that you have to say something like "smoothing the coastline on a length scale of 1 mile" when give a length number, because the coastline smoothed to 1 mile is considerably shorter than the coastline smoothed to 1 foot, and considerably longer than the coastline smoothed to 100 miles.

Arthur Smith

Click here to return to the Physics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory