Discrete Dynamics in Nature and Society
Volume 3 (1999), Issue 4, Pages 297-306

On the fractality of the biological tree-like structures

Jaan Kalda

Institute of Cybernetics, Akadeemia tee 21, Tallinn EEO026, Estonia

Received 1 March 1999

Copyright © 1999 Jaan Kalda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The fractal tree-like structures can be divided into three classes, according to the value of the similarity dimension Ds:Ds<D,Ds=D and Ds>D, where D is the topological dimension of the embedding space. It is argued that most of the physiological tree-like structures have DsD. The notion of the self-overlapping exponent is introduced to characterise the trees with Ds>D. A model of the human blood-vessel system is proposed. The model is consistent with the processes governing the growth of the blood-vessels and yields Ds=3.4. The model is used to analyse the transport of passive component by blood.