  A multifractal model of neutron evolution in a reactor is considered. For
chain reactions, the dimension of the multifractal carrier, information and
correlation dimensions, the entropy of the fractal set, the maximum and minimum
values of the dimension, the multifractal spectrum function and other
characteristics of multifractal neutron behavior are found. The use of
geometric characteristics of a multifractal makes it possible to describe a
stochastic system of hierarchically subordinate statistical ensembles,
characterized by Cayley trees. A stationary distribution over hierarchical
levels is established, which reduces to the Tsallis power law. Some
possibilities for using fractal patterns in the theory of nuclear reactors are
indicated.
