Fractals in microscopy

Abstract

Fractal geometry, developed by B. Mandelbrot, has provided new key concepts necessary to the understanding and quantification of some aspects of pattern and shape randomness, irregularity, complexity and self-similarity. In the field of microscopy, fractals have profound implications in relation to the effects of magnification and scaling on morphology and to the methodological approaches necessary to measure self-similar structures. In this article are reviewed the fundamental concepts on which fractal geometry is based, their relevance to the microscopy field as well as a number of technical details that can help improving the robustness of morphological analyses when applied to microscopy problems.