title: 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.
authors.affiliation: Laboratory of Neurophysiology, NINDS, National Institutes of Health, Bethesda, MD 20892, USA. tgs@codon.nih.gov
authors.forename: T G
authors.initials: TG
authors.lastname: Smith
authors.forename: G D
authors.initials: GD
authors.lastname: Lange
authors.forename: W B
authors.initials: WB
authors.lastname: Marks
mesh_terms: D048429:Cell Size; D017709:Fractals; D009457:Neuroglia / Q000166:cytology*; D009474:Neurons / Q000166:cytology*