  There are three important types of structural properties that remain
unchanged under the structural transformation of condensed matter physics and
chemistry. They are the properties that remain unchanged under the structural
periodic transformation-periodic properties. The properties that remain
unchanged under the structural multi scale transformation-fractal properties.
The properties that remain unchanged under the structural continuous
deformation transformation-topological properties. In this paper, we will
describe some important methods used so far to characterize the fractal
properties, including the theoretical method of calculating the fractal
dimension, the renormalization group method, and the experimental method of
measuring the fractal dimension. Multiscale fractal theory method,
thermodynamic representation form and phase change of multiscale fractal, and
wavelet transform of multiscale fractal. The development of the fractal concept
is briefly introduced: negative fractal dimension, complex fractal dimension
and fractal space time. New concepts such as balanced and conserved universe,
the wormholes connection to the whiteholes and blackholes for universes
communication, quantum fractals, platonic quantum fractals for a qubit, new
manipulating fractal space time effects such as transformation function types,
probabilities of measurement, manipulating codes, and hiding transformation
functions are also discussed. In addition, we will see the use of scale
analysis theory to stimulate the elements on the fractal structure: the
research on the dynamics of fractal structure and the corresponding computer
simulation and experimental research. The novel applications of fractals in
integrated circuits are also discussed in this paper.
