Fractal Dimension - Estimating From Real-world Data

Estimating From Real-world Data

The fractal dimension measures described in this article are for formally-defined fractals. However, many real-world phenomena also exhibit limited or statistical fractal properties and fractal dimensions have been estimated for sampled data from many such phenomena using computer based fractal analysis techniques. Practical dimension estimates are affected by various methodological issues, and are sensitive to numerical or experimental noise and limitations in the amount of data. Nonetheless, the field is rapidly growing and as evidenced by searching databases such as PubMed, the past decade has seen methods develop from being largely theoretical to the point where estimated fractal dimensions for statistically self-similar phenomena have many practical applications in multifarious fields including diagnostic imaging, physiology, neuroscience, medicine, physics, image analysis, acoustics, Riemann zeta zeros, and electrochemical processes.