Results 91 to 100 of about 2,419 (215)

The Area of the Mandelbrot Set and Zagier's Conjecture

Integers, 2017
We prove Zagier's conjecture regarding the 2-adic valuation of the coefficients $\{b_m\}$ that appear in Ewing and Schober's series formula for the area of the Mandelbrot set in the case where $m\equiv 2 \mod 4$.
Patrick F. Bray, Hieu D. Nguyen
openaire   +4 more sources

Visualization of Mandelbrot Set [PDF]

, 2008
Šaja darba rakstits par Mandelbrota kopas vizualizešanas variacijam, izmantojot dažadas krasu pieškiršanas metodes. Klasiska metode iteraciju skaitam piekarto krasu no iepriekš definetas krasu paletes.
Dzelde, Mārtiņš
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Parameter-Driven Analysis of Complex Fractals via Picard–Abbas Iteration

Fractal and Fractional
Fractal geometry has recently been advanced through fixed-point iteration schemes, enabling new analytical approaches. In this paper, we apply the Picard–Abbas iteration process to study Mandelbrot sets, Julia sets, and biomorphs for polynomials of the ...
Bashir Nawaz, Krzysztof Gdawiec, Kifayat Ullah, Maggie Aphane   +3 more
doaj   +1 more source

Scouting the Mandelbrot set with memory

Complexity, 2014
An exploratory study is made on the dynamics of the map defining the Mandelbrot set endowed with memory (m) of past iterations, that is, , . © 2014 Wiley Periodicals, Inc.
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Escape Criteria Using Hybrid Picard S-Iteration Leading to a Comparative Analysis of Fractal Mandelbrot Sets Generated with S-Iteration

Fractal and Fractional
Fractals are a common characteristic of many artificial and natural networks having topological patterns of a self-similar nature. For example, the Mandelbrot set has been investigated and extended in several ways since it was first introduced, whereas ...
Rekha Srivastava, Asifa Tassaddiq, Ruhaila Md Kasmani   +2 more
doaj   +1 more source

On the Julia set of the perturbed Mandelbrot map [PDF]

, 2000
In this work, we present numerical results which support the smooth decomposition method of the generalized Julia set by Peintge et al., in the case of other perturbations of the Mandelbrot map studied in our previous work (Argyris J, Andreadis I ...
Argyris, J., Andreadis, I., Karakasidis, T. E.   +2 more
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Numerical simulations of seepage flow in rough single rock fractures

Petroleum, 2015
To investigate the relationship between the structural characteristics and seepage flow behavior of rough single rock fractures, a set of single fracture physical models were produced using the Weierstrass–Mandelbrot functions to test the seepage flow ...
Qingang Zhang, Yang Ju, Wenbo Gong, Liang Zhang, Huafei Sun   +4 more
doaj   +1 more source

The Mandelbrot set is universal [PDF]

, 2000
We show small Mandelbrot sets are dense in the bifurcation locus for any holomorphic family of rational maps.
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Mandelbrot in mathematica: guide to plotting the most famous instance of the mandelbrot set in mathematica [PDF]

, 2005
In this article the algorithm required for plotting the most famous picture of the Mandelbrot Set was presented and commented upon. In colouring the Mandelbrot Set, the key information required is the number of iterations after which the characteristic ...
Petrovic, Novak S.
core  

Semelhança entre o conjunto de Mandelbrot e o conjunto de Julia em pontos Misiurewicz [PDF]

Weshall prove that the Julia set Jc is asymptotically similar to the Mandelbrot set M about a Misiurewicz parameter c, using the concept of similarity and the Hausdorff-Chabauty distance. This result was originally proved by Tan Lei in 1990.
Morales, Gabriel Andrés Borges
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