  We present a new idea to understand the structure of nuclei, which is
comparing to the liquid drop model. After discussing the probability that the
nuclear system may be a fractal object with the characteristic of
self-similarity, the nuclear irregular structure properties and the
self-similarity characteristic are considered to be an intrinsic aspects of
nuclear structure properties. For the description of nuclear geometric
properties, nuclear fractal dimension is an irreplaceable variable similar to
the nuclear radius. In order to determine these two variables, a new nuclear
potential energy formula which is related to the fractal dimension is put
forward and the phenomenological semi-empirical Bethe-Weizsacker binding energy
formula is modified using the fractal geometric theory. And one important
equation set with two equations is obtained, which is related to the conception
that the fractal dimension should be a dynamical parameter in the process of
nuclear synthesis. The fractal dimensions of the light nuclei are calculated
and their physical meanings are discussed. We have compared the nuclear fractal
mean density radii with the radii calculated by the liquid drop model for the
light stable and unstable nuclei using rational nuclear fractal structure
types. In the present model of fractal nuclear structure there is an obvious
feature comparing to the liquid drop model, since the present model can reflect
the geometric informations of the nuclear structure, especially for the nuclei
with clusters, such as the {\alpha}-cluster nuclei and halo nuclei.
