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Your search keyword '"PRAJAPATI, DARSHANA J."' showing total 7 results
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7 results on '"PRAJAPATI, DARSHANA J."'

1. Generation of Mandelbrot and Julia sets for generalized rational maps using SP-iteration process equipped with [formula omitted]-convexity.

Author

Rawat, Shivam, Prajapati, Darshana J., Tomar, Anita, and Gdawiec, Krzysztof

Subjects
*FRACTALS, *CONVEXITY spaces, *RESEARCH personnel
Abstract

In this paper, we introduce a generalized rational map to develop a theory of escape criterion via the SP-iteration process equipped with s -convexity. Furthermore, we develop algorithms for the exploration of unique kinds of Mandelbrot as well as Julia sets. We demonstrate graphically the change in colour, size, and shape of images with the change in values of the considered iteration's parameters. The new fractals thus obtained are visually very pleasing and attractive. Most of these newly generated fractals resemble natural objects around us. Moreover, we numerically study the dependence between the iteration's parameters and the set size. The experiments show that this dependency is non-linear. We believe that the obtained conclusions will motivate researchers who are interested in fractal geometry. [ABSTRACT FROM AUTHOR]

Published
2024
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6. MANDELBROT FRACTALS USING FIXED-POINT TECHNIQUE OF SINE FUNCTION.

Author

TOMAR, ANITA, ANTAL, SWATI, PRAJAPATI, DARSHANA J., and AGARWAL, PARVEEN

Subjects
SINE function, FIXED point theory, HINDU gods, GLASS art, TRANSCENDENTAL functions
Abstract

Here, we develop escape criteria for pc(z) = sin(z n)−az +c, a, c ∈ C, n ≥ 2, exploiting four different iterations of fixed point theory to explore various Mandelbrot sets which are different than the classical Mandelbrot set . Our concern is to utilize the lesser number of iterations that are necessary to attain the fixed point of the transcendental complex-valued sine function. Further, we investigate the effect of variables on the shape, size, color, and dynamics of fractals. Noticeably, some of the obtained fractals symbolize the Swastika (a symbol of spirituality and divinity in Indian religions), Shivling (an abstract representation of the Hindu God Shiva), flowers, spiders, butterflies, Rangoli (made mainly in the festive season in India), art on glass, and so on. Interestingly, the higher-order Mandelbrot set in Picard-orbit has a resemblance to Corona-virus. [ABSTRACT FROM AUTHOR]

Published
2022
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