Fractal Properties and Characterizations

Abstract: 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.