Results 181 to 190 of about 6,088,715 (228)

Mandelbrot set and Julia sets of fractional order

Nonlinear dynamics, 2022
In this paper, the fractional-order Mandelbrot and Julia sets in the sense of q -th Caputo-like discrete fractional differences, for $$q\in (0,1)$$ q ∈ ( 0 , 1 ) , are introduced and several properties are analytically and numerically studied.
Marius-F. Danca, Michal Feckan
semanticscholar   +1 more source

Efficient Computation of Mandelbrot Set Generation with Compute Unified Device Architecture (CUDA)

2022 6th International Conference on Informatics and Computational Sciences (ICICoS), 2022
Compute Unified Device Architecture (CUDA) is one of the standards for interfaces in parallel programming implemented into NVIDIA's GPUs. GPU (Graphics Processing Unit) is a processor of many smaller, more specialized cores.
Vandicco Maris Siregar, Kenny Anaga, Tsaqif Muhammad Arkan, David Pebrianto Pakpahan, Rara Ariefftah, A. Sugiharto, F. A. Nugroho   +6 more
semanticscholar   +1 more source

A NEW METHODOLOGY TO ANALYZE THE DYNAMIC OF DAILY POWER DEMAND WITH ATTRACTORS INTO THE MANDELBROT SET

Fractals, 2020
The time series plot of electricity daily load demand is seasonal as shown by its regular repetitive pattern during the same period each year. Its behavior is determined by phase-space diagrams that are able to identify any of the following states of the
Héctor A. TABARES-OSPINA, F. Angulo, M. Osorio   +2 more
semanticscholar   +1 more source

A NEW STABLE INTERNAL STRUCTURE OF THE MANDELBROT SET DURING THE ITERATION PROCESS

, 2020
In this paper, we focus on the periodic points during the iteration process to understand the convergence characteristics of the Mandelbrot set. A new internal structure of the Mandelbrot set is obtained.
Dakuan. Yu, Wurui Ta
semanticscholar   +1 more source

3D RENDERING OF THE QUATERNION MANDELBROT SET WITH MEMORY

Fractals
In this paper, we explore the quaternion equivalent of the Mandelbrot set equipped with memory and apply various visualization techniques to the resulting [Formula: see text]-dimensional geometry.
Ricardo Fariello, Paul Bourke, Gabriel V. S. Abreu   +2 more
semanticscholar   +1 more source

Pseudo-monodromy and the Mandelbrot set

Transactions of the American Mathematical Society
We investigate the discontinuity of codings for the Julia set of a quadratic map. To each parameter ray, we associate a natural coding for Julia sets on the ray.
Yutaka Ishii, Thomas Richards
semanticscholar   +1 more source

The Mandelbrot Set

1986
For polynomials of second order, p(x) = a2x2 + a1x + ao, an almost complete classification of the corresponding Julia sets can be given in terms of the Mandelbrot set. First note that p(x is conjugate to p c (z)=z2 + c by means of the coordinate transformation \( x \mapsto z = a_2 x + a_1 /2,with{\text{ }}c = a_0 a_2 + \frac{{a_1 }} {2}\left( {1 ...
Heinz-Otto Peitgen, Peter H. Richter
openaire   +1 more source

On the Mandelbrot set of zp+

Mathematics and Computers in Simulation, 2023
Muhammad Tanveer, W. Nazeer, Krzysztof Gdawiec   +2 more
semanticscholar   +2 more sources

π IN THE MANDELBROT SET

Fractals, 2001
The Mandelbrot set is arguably one of the most beautiful sets in mathematics. In 1991, Dave Boll discovered a surprising occurrence of the number π while exploring a seemingly unrelated property of the Mandelbrot set.1 Boll's finding is easy to describe and understand, and yet it is not widely known — possibly because the result has not been ...
openaire   +2 more sources

Additive perturbed generalized Mandelbrot–Julia sets

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Xing-Yuan, Chang, Pei-Jun, Gu, Ni-Ni   +2 more
openaire   +1 more source