Dynamic Fractal Mathematical Model

Abstract

Matter structure (atoms and molecules) represents a material's physical properties. Hence, matter structure study provides new materials and new properties. Generally, the matter structure investigation approach is stationary (neglects time) because of the unpredictable movement of particles. Currently, the untraceable movement of particles is assumed chaos, and probability is the most efficient mathematical approach for studying. But, nanoparticles harmonic behaviors show matter as a system. In other words, it seems nanoparticles are fractals, not fragments. Therefore, a novel doctrine is necessary. In this article, the matter system approach and dynamic topology provide the Dynamic Fractal mathematical model that represents the dynamic structure of matter. Due to crystals' strong dependency on material structure, this doctrine could be significant for crystal and crystallization analysis. Then, more efficient products of industries as semiconductors, cutting machines, laser technology, watch industry, photovoltaic cells will be expected.