Results 61 to 70 of about 1,561 (174)
Natural Sciences, Volume 6, Issue 3, July 2026.Within quantum chemistry, density functional theory (DFT) is a revolution. This serves as an example of a multitude of other scientific events, supporting the idea that revolutions are always large, if observed with the appropriate magnification. ABSTRACT Distinguishing scientific revolutions from normal science is a subjective, conflicting matter ...
Sebastian Kozuch
wiley +1 more source
Generalized Logistic Maps in the Complex Plane: Structure, Symmetry, and Escape-Time Dynamics
AxiomsIn this paper, we introduce a generalised formulation of the logistic map extended to the complex plane and correspondingly redefine the classical Mandelbrot and Julia sets within this broader framework.
Krzysztof Gdawiec, Muhammad Tanveer
doaj +1 more source
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
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Generalized Scaling of Blue Metabolism in River Basins
Water Resources Research, Volume 62, Issue 7, July 2026.Abstract River networks play a central role in regulating biogeochemical transformations at the catchment scale, yet a general scaling theory linking network structure to integrated metabolic function is still lacking. By positing the fundamental differences between blue (fluvial) and green (terrestrial) metabolisms in river basins, we focus on the ...
G. Nicoletti +6 more
wiley +1 more source
Alexandria Engineering JournalWith a generalized setting of transcendental functions associated with a non-linear variable, we have observed the combinatorial structures of the fractals of Julia sets and Mandelbrot sets due to the function zκcos(zκ)+pz2+q, in the complex plane with p,
Santanu Nandi +2 more
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Meteoritics &Planetary Science, Volume 61, Issue 7, Page 1355-1385, July 2026.Abstract We investigated the structural framework of the north–northwestern Paraná Basin in Brazil to test whether the pre‐impact structures in this region may have had any influence on the first‐order formation and morphostructure of the Araguainha impact structure (AIS).
Renato B. Bernardes +5 more
wiley +1 more source
When integers embrace the beauty of complex numbers [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамикаPurpose. This article investigates how fixed-point arithmetic and discrete recursive models can reveal structured behaviours in systems traditionally considered chaotic. Methods.
Alcover-Garau, Pedro-Maria +1 more
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Newton-Mandelbrot set and Murase-Mandelbrot set
We obtain four extended Newton's methods and three extended Mandelbrot's recurrence formulas from the Wasan (Japanese mathematics in the Edo period (1603-1868)). Furthermore, two extended Newton's methods relate to one of the extended Mandelbrot's recurrence formulas. We lead four types of extended Mandelbrot recurrence formulas.
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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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Parameter-Driven Analysis of Complex Fractals via Picard–Abbas Iteration
Fractal and FractionalFractal 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 +3 more
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