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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.