  As a classic self-similar network model, Sierpinski gasket network has been
used many times to study the characteristics of self-similar structure and its
influence on the dynamic properties of the network. However, the network models
studied in these problems only contain a single self-similar structure, which
is inconsistent with the structural characteristics of the actual network
models. In this paper, a type of horizontally segmented 3 dimensional
Sierpinski gasket network is constructed, whose main feature is that it
contains the locally self-similar structures of the 2 dimensional Sierpinski
gasket network and the 3 dimensional Sierpinski gasket network at the same
time, and the scale transformation between the two kinds of self-similar
structures can be controlled by adjusting the crosscutting coefficient. The
analytical expression of the average trapping time on the network model is
solved, which used to analyze the effect of two types of self-similar
structures on the properties of random walks. Finally, we conclude that the
dominant self-similar structure will exert a greater influence on the random
walk process on the network.

Statistical Mechanics