ISSN 1119-4618
 

Original Research 
JPAS. 2022; 22(2): 227-233


ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES

Zuwaira Babawuro, Manjak N. H..

Abstract
This work explores the Julia and Mandelbrot sets of the Gamma and beta functions by using lanczos approximation procedures for fractal images. Various Julia and Mandelbrot sets associated with the Gamma function are generated using the iterative function fλ(z), with various λ –values .The Lanczos approximation of the Gamma function presents an efficient and easy algorithm to compute an approximate solution of the iterative Gamma function to an arbitrary precision. The resulting images reveal that the fractal (chaotic) behavior found in elementary functions is also found in the Gamma functions. The chaotic nature of the Julia and Mandelbrot sets provides an understanding of complexity in systems as well as in shapes. The relationship between the Gamma and beta function was exploited to obtained lanczos approximation for Beta Function.

Key words: Julia Set, Mandelbrot Set, Gamma Function, Beta function, Lanczos approximation, Complex function.


 
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How to Cite this Article
Pubmed Style

ZB, H. MN, . ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES. JPAS. 2022; 22(2): 227-233.


Web Style

ZB, H. MN, . ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES. https://www.atbuscienceforum.com/?mno=127200 [Access: May 14, 2022].


AMA (American Medical Association) Style

ZB, H. MN, . ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES. JPAS. 2022; 22(2): 227-233.



Vancouver/ICMJE Style

ZB, H. MN, . ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES. JPAS. (2022), [cited May 14, 2022]; 22(2): 227-233.



Harvard Style

, Z. B., H., M. N. & (2022) ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES. JPAS, 22 (2), 227-233.



Turabian Style

, Zuwaira Babawuro, Manjak N. H., and . 2022. ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES. Science Forum (Journal of Pure and Applied Sciences), 22 (2), 227-233.



Chicago Style

, Zuwaira Babawuro, Manjak N. H., and . "ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES." Science Forum (Journal of Pure and Applied Sciences) 22 (2022), 227-233.



MLA (The Modern Language Association) Style

, Zuwaira Babawuro, Manjak N. H., and . "ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES." Science Forum (Journal of Pure and Applied Sciences) 22.2 (2022), 227-233. Print.



APA (American Psychological Association) Style

, Z. B., H., M. N. & (2022) ON JULIA AND MANDELBROT SETS OF GAMMA AND BETA FUNCTIONS FOR FRACTAL IMAGES. Science Forum (Journal of Pure and Applied Sciences), 22 (2), 227-233.