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		1.2.6— More Examples of Self-Similarity

		1— Self-Similarity in Space

		We have already seen that there are self-similar patterns in the branching of the arms (dendrites) of nerve cells, the arteries and the veins in the retina, and the tubes that bring air into the lungs.

		Additional examples of self-similarity in space are the branching structures of the conduction fibers in the heart (His-Purkinje system) that spread the wave of muscle contraction during the heartbeat; the tubes (ducts) in the liver that bring the bile to the gallbladder; and the arteries and the veins throughout the body.

		Many surfaces in the body have self-similar undulations with ever finer fingers or pockets. These ever finer structures increase the area available for the exchange of nutrients, gasses, and ions. These surfaces include the lining of the intestine, the boundary of the placenta, and the membranes of cells.

		These properties are self-similar in physical space. There are also self-similar properties in more abstract spaces such as the energy space used to characterize molecules. For example, the distribution of the spacing between energy levels in some proteins is self-similar.

		2— Self-Similarity in Time

		We have already seen that there are self-similar patterns in time in the motion of the heights of cells above the dish in which they are growing, in the variation of the voltage across the cell membrane, and in the timing of the switches between the open and closed states of an ion protein.

		Additional examples of self-similarity in time include the electrical signal generated by the contraction of the heart and the volumes of breaths over time drawn into the lung.

 

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