Results 11 to 20 of about 6,037,193 (187)
Review of "Fractals and Chaos: The Mandelbrot Set and Beyond", by B. Mandelbrot [PDF]
BioMedical Engineering OnLine, 2005 Diaspro Alberto
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A study of Mandelbrot and Julia Sets via Picard-Thakur iteration with s-convexity. [PDF]
PLoS OneNawaz B, Gdawiec K, Ullah K, Aphane M.
europepmc +3 more sources
Generalized Mandelbrot Sets of a Family of Polynomials Pnz=zn+z+c;n≥2
International Journal of Mathematics and Mathematical Sciences, 2022 In this paper, we study the general Mandelbrot set of the family of polynomials Pnz=zn+z+c;n≥2, denoted by GM(Pn). We construct the general Mandelbrot set for these polynomials by the escaping method.
Salma M. Farris
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Topics in Cognitive Science, EarlyView., 2023 Abstract Fractal fluctuations are a core concept for inquiries into human behavior and cognition from a dynamic systems perspective. Here, we present a generalized variance method for multivariate detrended fluctuation analysis (mvDFA). The advantage of this extension is that it can be applied to multivariate time series and considers intercorrelation ...
Sebastian Wallot +5 more
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Fixed point results of an implicit iterative scheme for fractal generations
AIMS Mathematics, 2021 In this paper, we derive the escape criteria for general complex polynomial $ f(x) = \sum_{i = 0}^{p}a_{i}x^{i} $ with $ p\geq2 $, where $ a_{i} \in \mathbb{C} $ for $ i = 0, 1, 2, \dots, p $ to generate the fractals.
Haixia Zhang +4 more
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Topics in Cognitive Science, EarlyView., 2023 Abstract Representational drift is a phenomenon of increasing interest in the cognitive and neural sciences. While investigations are ongoing for other sensory cortices, recent research has demonstrated the pervasiveness in which it occurs in the piriform cortex for olfaction.
Ann‐Sophie Barwich +1 more
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Computational Geometry of Period-3 Hyperbolic Components in the Mandelbrot Set
Mathematics, 2021 A parametric theoretical boundary equation of a period-3 hyperbolic component in the Mandelbrot set is established from a perspective of Euclidean plane geometry.
Young-Hee Geum, Young-Ik Kim
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Quadratic dynamics over hyperbolic numbers: a brief survey [PDF]
Surveys in Mathematics and its Applications, 2022 Hyperbolic numbers, also called split complex or perplex numbers in the literature, are a variation of complex numbers established as a theory primarily by W. Clifford in the nineteenth century who applied them to mechanics.
Sandra Hayes
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Exploring parameter spaces in complex dynamics
Selecciones Matemáticas, 2023 We show the structure of the parameter space for a family of rational maps containing Blaschke products. Through numerical simulations using the orbit of a single critical point, we reveal the existence of infinitely many Mandelbrot-like sets along the ...
Pedro Iván Suárez Navarro
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Fractals via Generalized Jungck–S Iterative Scheme
Discrete Dynamics in Nature and Society, 2021 The purpose of this research is to introduce a Jungck–S iterative method with m,h1,h2–convexity and hence unify different comparable iterative schemes existing in the literature.
Zhihua Chen +3 more
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