GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION

Abstract

In this paper, we introduce the [Formula: see text]-circle inversion which generalizes the classical inversion with respect to a circle ([Formula: see text]) and the taxicab inversion [Formula: see text]. We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the [Formula: see text]-circle inversion.

El Efecto de la aplicación de mezclas de sustitutos de grasa sobre algunas propiedades funcionales del helado de vainilla

“…Para determinar el efecto de la sustitución de grasa láctea por I, O y/o M sobre los parámetros de calidad o propiedades funcionales del helado, se realizaron muestreos al azar para que fueran representativos. Cada una de las unidades debía tener la misma probabilidad que las demás para llegar a ser parte de la muestra al azar, las unidades que conformaron la muestra fueron numeradas al azar (Ramírez et al, 2015). En total se realizaron 7 unidades experimentales por triplicado, para un total de 21 experimentos.…”

On The Maximum Spherical Inversions

“…It was systematically developed by Steiner in the 1830s. It can be used to examine some theorems and problems in geometry, for example the Pappus chain theorem, Feuerbach's theorem, Ptolemi theorem, Steiner Porism, Apollonoius's problem, (Ramirez et al, 2015). There are many generalizations of the inversion map in the literature.…”

“…1995;Ramirez, 2013;Gdawiec, 2014;Ramirez, 2014;Ramirez and Rubian, 2014). The new inversion maps have been defined by taking different distance function such as taxicab distance, p-distance, Chinese Checkers distance, α -distance, (Bayar ve Ekmekçi, 2014;Gelişgen ve Ermiş, 2019;Nickel, 1995;Pekzorlu, 2019;Ramirez et al, 2015;Yüca ve Can, 2020). The spherical inversion has been defined as the generalization of the circle inversion in the three dimensional Euclidean space and its properties have been given, in (Ramirez and Rubian, 2016).…”

On The Chinese Checkers Spherical Inversions in Three Dimensional Chinese Checkers Space

“…In three-dimensional space a generalization of the spherical inversion is given in [16]. Also, the inversions with respect to the taxicab distance, alpha-distance [17], [21], [19] or in general a p-distance [20]. The circle inversion have been generalized in three-dimensional space by using a sphere as the circle of inversion [16].…”