On Julia and Mandelbrot sets of gamma and beta functions for fractal images (Journal of Pure and Applied Sciences (Science Forum), 2026)
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 varoius 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 functions was exploited to obtain the Lanczos approximation for beta function.