42.

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Page 14

		1.2.2— Examples of Self-Similarity in Space

		Examples of statistical self-similarity in space are:

		1. The branching patterns of the arms (dendrites) of nerve cells growing in the retina in the eye or growing in a nutrient medium in a plastic culture dish,

		2. The arteries and veins in the retina, and

		3. The tubes that bring air into the lungs.

		These objects are self-similar because the pattern of the branching of the large structures is repeated in the branching of the ever smaller structures.

		The fractal analysis of these branching patterns sheds light on how the dendrites of the nerve cell grow and how the airways in the lung are formed in the embryo. Determining the fractal properties of the blood vessels in the retina may be useful in diagnosing diseases of the eye or in determining the severity of the disease.

		The analysis of nerve cells and blood vessels in the retina and in the nutrient medium of a culture dish is simplified by the fact that the retina and the nutrient media are both very thin. Thus the branching pattern is 2-dimensional. Analysis of a photograph of a 3-dimensional pattern would have to compensate for the images of the branches projected on top of each other.

 

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