Fractal methods and results in cellular morphology--dimensions, lacunarity and multifractals

Abstract

This paper discusses the concepts of fractal geometry in a cellular biological context. It defines the concept of the fractal dimension. D, as a measure of complexity and illustrates the two different general ways of quantitatively measuring D by length-related and mass-related methods. Then, these several Ds are compared and contrasted. A goal of the paper is to find methods other than length-related measures that can distinguish between two objects that have the same D but are structurally different. The mass-related D is shown potentially to be such a measure. The concept of lacunarity, L, is defined and methods of measuring L are illustrated. L is also shown to be a potentially distinguishing measure. Finally, the notion of multifracticality is defined and illustrated to exist in certain individual nerve and glial cells.