A new iterative approach to fractal models |
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| Authors: | SL Singh |
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| Institution: | a Department of Mathematics, Walter Sisulu University, Nelson Mandela Drive, Private Bag X1, Mthatha 5117, South Africa
b Department of Applied Mathematics, Walter Sisulu University, Nelson Mandela Drive, Private Bag X1, Mthatha 5117, South Africa |
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| Abstract: | Mandelbrot is best appreciated for his broad attempt to describe irregular shapes in nature. He founded fractal geometry in 1975. Subsequently the whole fractal theory developed using one-step feedback systems. In 2002, an attempt was made to study and analyze fractal objects using two-step feedback systems. Researchers used superior iteration methods to implement two-step feedback systems. This was the beginning of a new iterative approach in the study of fractal models, and it seems promising to extend fractal theory. The purpose of this paper is to present a review of literature in fractal analysis using this new iterative approach and explore its potential applications. |
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| Keywords: | Fractal Superior Julia set Superior Mandelbrot set Escape-time fractal Cantor set Koch curve L-system Strange attractor Logistic map V-variable fractal Superfractal |
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