Morphological Modeling Using Fractal Geometries
Thomas R. Nelson · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1988
The application of fractal concepts to the analysis of non-linear dynamics and morphology has expanded our insight into many diverse natural phenomena. Fractal mathematics provides new methods of analysis also applicable to biophysical phenomena including the structure and function of systems comprising the human body. The brain, heart and the tracheo-bronchial tree possess characteristics common to fractal objects including: (a) a large degree of heterogeneity, (b) self-similar structures over many size scales, and (c) no well defined (characteristic) scale of measure. The fractal dimension, DF is a measure of the structural complexity. This paper presents an overview of some of the general concepts underlying fractals and their relationship to non-linear dynamics and morphology. Areas of investigation that benefit from the application of these concepts to biological phenomena and modeling are discussed and an algorithm for modeling lung development based on fractal concepts is presented. Structures that are in good agreement with actual morphological data may be generated using simple recursive algorithms and constraints.