Determination of Heterogeneity for Manganese Dendrites Using Lacunarity Analysis

Abstract

The surface patterns of natural and experimental deposits are important as they result from the internal microstructure. For this purpose, lacunarity analysis is applied to determine the heterogeneous nature of deposit surface patterns. In this study, images were digitally moved onto the square mesh to determine the heterogeneous situation of manganese dendrite patterns on the natural magnesite surface. The relation between the lacunarity values of the images and the box size was examined. The lacunarity values corresponding to the box size values were estimated using the gliding-box algorithm. This relation was determined numerically as a power-law function using nonlinear regression method. It has been shown that the system examined with the generated numerical model function can be defined with three specific parameters. As a result, it has been shown that it is possible to describe the relationship between numerical solution-based lacunarity-box size and a third-order nonlinear differential equation. With this study, the lacunarity-box size value on different system images can be determined by using the gliding box algorithm and calculating the coefficient value from the power-law relationship.

Keywords

• Fractal and geometric patterns
• Lacunarity
• Mathematical model

References

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