Formation of superior mineral deposit and fractal approaches

Metals can solidify and form patterns specific to their own species with the formation of natural diffusion and precipitation conditions or chemical and thermal conditions in the fabrication production process. The pattern formation of the metal on any surface varies according to the weave structure and basic properties of the surface. These patterns can be densely blotched, linear, branched, and dendritic, some of which are described by the concept of fractal. In this thesis, the patterns formed by the diffusion and precipitation of manganese and iron metals on the chalcedony surface are called manganese dendrites. Statistics is studied with the scaling theory used in physics. For this purpose, chalcedony surface images were transferred to digital media by using photometric methods. Superficial surface particle density and fractal dimension values of selected patterned regional surfaces were calculated. In addition, it has been shown that the relationship between superficial surface particle density and fractal dimension can be determined by a numerical model defined by a 4th-order polynomial function. In addition, according to the scaling theory, the critical exponent values of the perimeter-area relationship of the patterns and the fractal dimension values associated with these values were compared and their formations vary according to the surface structure. Sub-pattern superficial pore density is predicted to affect formations. This thesis study can be useful in terms of scaling patterns and pore structure in different systems and using photometric methods in terms of method.