The Study on the Evaluation of Closedness and Self- Similarity of 3D Fractals
Objective: The purpose of the current study was to demonstrate a technique that shows the closeness and self-similarity of 3D fractals taken as an example by 3D Sierpinski Gasket. Methods / Statistical Analysis: The Sierpinski Gasket’s 2D and 3D images were interpreted by taking the initial generators as the basis for either the Sierpinski Triangle / Sierpinski Pyramid or the Sierpinski Carpet / Sierpinski Gasket. This method ensures the generation of the final 3D Sierpinski Gasket, which takes an exact copy of the original image. Findings: This is achieved by taking a cube as the base and applying the same algorithm through an IFS-like transformation consisting of ((x , y) rotation, z(zoom)) and changing the depth parameter from 3 to 2 to 1 in that order in a recursive manner, giving rise to a new 3D Sierpinski Gasket that is similar to an exact copy of the original 3D Sierpinski Gasket based cube. The findings represent the closeness of fractal images in the aspect of self-similarity and thus provide a real-time vision of fractal images. Application / Improvements: For more study , the findings embodied from the approach above can be useful and the extension of this work gives us more creative analysis in the field of 3D fractals and the like. The findings show the closeness of fractal images in self-similarity and thus provide a real-time vision of fractal images, and how fractal geometry is an art and a science by using theory, computation and experimentation.
Formerly Department of Computer Science and Engineering, MLR Institute of Technology, Hyderabad, Telangana, India.
View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/299