Geometric application of a viscosity approximation- type iterative method to the generation the fractals as Julia and Mandelbrot Sets for complex function
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Keywords:
Algorithms, Escape criteria, Iterative methods, Julia sets, Mandelbrot setsAbstract
This work explores an application of novel fractal patterns, specifically Julia and Mandelbrot sets, generated by a modified class of complex function in which the traditional constant term is replaced with a logarithmic function. Utilizing a viscosity approximation-type iterative method, we develop escape criteria that enhance existing algorithms, thereby enabling the precise visualization of intricate fractal structures as Julia and Mandelbrot sets. Numerical experiments in MATLAB reveal that varying the input parameters induces significant dynamic transformations in the fractals’ morphol-
ogy. We believe that the insights gained from this study will inspire and motivate researchers and enthusiasts with a deep interest in fractal geometry.
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