| Abstract: | Fractals provide an innovative method for generating 3D images of real-world objects by using computational modelling algorithms based on the imperatives of self-similarity, scale invariance, and dimensionality. Images such as coastlines, terrains, cloud mountains, and most interestingly, random shapes composed of curves, sets of curves, etc. present a multi-varied spectrum of fractals usage in domains ranging from multi-coloured, multi-patterned fractal landscapes of natural geographic entities, image compression to even modelling of molecular ecosystems. Fractal geometry provides a basis for modelling the infinite detail found in nature. Fractals contain their scale down, rotate and skew replicas embedded in them. Of the many different types of fractals that have come into limelight since their origin, the Sierpinski fractal has eluded both mathematicians and computer scientists alike. And the 2D, 3D, etc. versions of the same have been realized based on the starting axioms/generators as either triangle/pyramid or square/cube. The resulting fractals are Sierpinski Triangle and Sierpinski Pyramid in case of the triangle-based generations; and Sierpinski Carpet and Sierpinski Gasket in case of the square/cube based fractals. This paper describes a methodology that illustrates the closeness in self-similarity otherwise termed as closing the self-similarity loop - of fractal images by way of generating a 3D Sierpinski Gasket fractal starting with a cube as the baseline shape and applying the same algorithm recursively by way of IFS-like transformations of ((x,y) rotation, z (zoom) ) - changing a newly introduced property called depth, from 3 to 2 to 1 in that order – to arrive at a new 3D Sierpinski Gasket that resembles a self-similar copy of the original 3D cube-based Sierpinski Gasket [9],[10],[11]. The depth property represents an additional variant which we represents an iterative- recursive execution count.
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| Keywords: | Fractals, 3D Images, Sierpinski Traingle, Sierpinski Pyramid, Sierpinski Carpet, Sierpinski Gasket, 3D rendering, Recursion, IFS.
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