Liu, S. H. Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee.
Pietronero, L. Dipartimento di Fiscia, Universita di Roma, Roma, Italy.
- Mathematical versus natural fractals
- Fractal dimension
- Physical properties
- General applications
- Applications in physics
- Related Primary Literature
- Additional Reading
Geometrical objects that are self-similar under a change of scale, for example, magnification. The concept is helpful in many disciplines to allow order to be perceived in apparent disorder. For instance, in the case of a river and its tributaries, every tributary has its own tributaries so that it has the same structural organization as the entire river except that it covers a smaller area. The branching of trees and their roots as well as that of blood vessels, nerves, and bronchioles in the human body follows the same pattern. Other examples include a landscape with peaks and valleys of all sizes, a coastline with its multitude of inlets and peninsulas, clouds, lightning, the mass distribution within a galaxy, the distribution of galaxies in the universe, and the structure of vortices in a turbulent flow. The rise and fall of economic indices has a self-similar structure when plotted as a function of time.
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