Complex-valued quadratic maps either converge to fixed points, enter into periodic cycles, show aperiodic behavior, or diverge infinity. Which of these scenarios takes place depends on the map’s complex-valued parameter c and initial conditions. The Mandelbrot set is defined by values for which map remains bounded when initiated at origin complex plane. In this study, we analyze dynamics a coup...

PURPOSE Fractal analysis is a mathematical method used to describe the internal architecture of complex structures such as trabecular bone. Fractal analysis of panoramic radiographs of implant recipient sites could help to predict the quality of the bone prior to implant placement. This study investigated the correlations between the fractal dimension values obtained from panoramic radiographs ...

Along with the intensification of global competition and the complexity of manufacturing products, cooperation among enterprises becomes more intimately, and the range of quality control extends from internal to the external enterprises. Consequently, previous quality control methods for internal enterprise have been difficult to meet the demands of extended enterprises. To effectively realize ...

This paper is an attempt to attain a new and profound model of the nature’s structure using a vortex-fractal theory (VFT). Scientists try to explain some phenomena in Nature that have not been explained so far. The aim of this paper is the vortex-fractal modeling of vortex-ring fractal structure of atoms, molecules, and a creation of elements in the Mendeleev’s periodic table with vortex-ring p...