Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractals and fractal dimension of systems of blood vessels: An analogy
  between artery trees, river networks, and urban hierarchies   An analogy between the fractal nature of networks of arteries and that of
systems of rivers has been drawn in the previous works. However, the deep
structure of the hierarchy of blood vessels has not yet been revealed. This
paper is devoted to researching the fractals, allometric scaling, and hierarchy
of blood vessels. By analogy with Horton-Strahler's laws of river composition,
three exponential laws have been put forward. These exponential laws can be
reconstructed and transformed into three linear scaling laws, which can be
named composition laws of blood vessels network. From these linear scaling laws
it follows a set of power laws, including the three-parameter Zipf's law on the
rank-size distribution of blood vessel length and the allometric scaling law on
the length-diameter relationship of blood vessels in different orders. The
models are applied to the observed data on human beings and animals early given
by other researchers, and an interesting finding is that human bodies more
conform to natural rules than dog's bodies. An analogy between the hierarchy of
blood vessels, river networks, and urban systems are further drawn, and
interdisciplinary studies of hierarchies will probably provide new revealing
examples for the science of complexity.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys