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## Прекрасная фрактальная математика и ее приложения

С. 58-65.

In this chapter the application of fractal geometry in such unusual areas such as architecture, art, design, jewelry, video, show describes.

### In book

М. : МИЭМ НИУ ВШЭ, 2013

Trubochkina N. K., Качество. Инновации. Образование 2012 Т. 84 № 5 С. 76-82

Scientific and exploratory research and mathematical simulation of a fractal designresults are presented. Decorative fractal patterns for textile and construction industries (models, murals, stained glass) have been developed. Fractals, which can be attributed to a class of fractal artdeveloped. Technology of frost-and water-resistant seamless large area fractal frescoes developed. Technology cost much less than for ...

Added: November 21, 2012

Isopeskul O., Экономика и предпринимательство 2013 № 2 С. 374-379

The concept of the conjunctual attractor of the organizational culture as a composite element in a simple attractor decomposition is introduced in the article. Organizational culture is considered as one of the fractals of the fractal structure "global culture of mankind", which can be characterized by covariant nature of self-similarity, oppennes and recursive ability ...

Added: November 3, 2014

Trubochkina N. K., Rolich A., В кн. : Запись и воспроизведение объёмных изображений в кинематографе, науке, образовании и в других областях: XI Международная научно-практическая конференция, Москва, 18–19 апреля 2019 г.: Материалы и доклады. : М. : ИПП «КУНА», 2019. Гл. 9. С. 109-124.

The article describes experiments to determine the system of optimal synthesis parameters for fractal and mixed content that meets the requirements of its comfortable viewing in stand-alone helmets of virtual reality. ...

Added: October 30, 2019

Gladkov N., Kolesnikov A., Zimin A., Calculus of Variations and Partial Differential Equations 2019 Vol. 58 No. 173 P. 1-33

The multistochastic (n, k)-Monge–Kantorovich problem on a product space ∏ni=1Xi∏i=1nXi is an extension of the classical Monge–Kantorovich problem. This problem is considered on the space of measures with fixed projections onto Xi1×⋯×XikXi1×⋯×Xik for all k-tuples {i1,…,ik}⊂{1,…,n}{i1,…,ik}⊂{1,…,n} for a given 1≤k<n1≤k<n. In our paper we study well-posedness of the primal and the corresponding dual problem. Our central result describes a solution ππ to the following important model ...

Added: October 9, 2019

Springer Nature Switzerland AG, 2019

Gathering the proceedings of the 11th CHAOS2018 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the ...

Added: October 29, 2021

Tikhonov K., Mirlin A. D., Physical Review B: Condensed Matter and Materials Physics 2016 Vol. 94 P. 184203-1-184203-16

We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave-function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity ...

Added: March 9, 2017

Isopeskul O., Экономика и предпринимательство 2013 Т. 7 № 3 С. 252-257

The article interprets the organizational culture as a fractal unit within the global fractal structure “human culture”, defines its place and aspects of the interaction with other fractal constructs. Besides the article characterizes various types of management influence on this organizational phenomenon considering its self-regulating character. ...

Added: March 29, 2013

Zybin K., Sirota V. A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2013 Vol. 88 No. 4

The appearance of vortex filaments, the power-law dependence of velocity and vorticity correlations and their multiscaling behavior are derived from the Navier-Stokes equation. This is possible due to interpretation of the Navier-Stokes equation as an equation with multiplicative noise and remarkable properties of random matrix products. ...

Added: October 20, 2014

Trubochkina N. K., Лиховцева А. В., Мир техники кино / World of Technique of Cinema (WTC). Россия. ISSN: 1991-3400 2015 № 2(36) С. 11-18

The article describes a method of producing three-dimensional video using fractal mathematics and information technologies. Various 3D visualization technologies of three-dimensional fractals, both in static and dynamic form are considered. Methods of three-dimensional fractal video synthesis used for various applications are described. One of the applications is a 3D cinema with glasses, where the background ...

Added: July 10, 2015

Decrouez G. G., Amblard P. O., Brossier J. M. et al., Journal of Physics A: Mathematical and Theoretical 2009 Vol. 42 No. 9 P. 1-17

Iterated function systems (IFS) are interesting parametric models for generating fractal sets and functions. The general idea is to compress, deform and translate a given set or function with a collection of operators and to iterate the procedure. Under weak assumptions, IFS possess a unique fixed point which is in general fractal. IFS were introduced ...

Added: October 2, 2014

Gladkov N., Kolesnikov A., Zimin A., Journal of Mathematical Analysis and Applications 2022 Vol. 506 No. 2 Article 125666

The multistochastic Monge–Kantorovich problem on the product X=∏i=1nXi of n spaces is a generalization of the multimarginal Monge–Kantorovich problem. For a given integer number 1≤k<n we consider the minimization problem ∫cdπ→inf on the space of measures with fixed projections onto every Xi1×…×Xik for arbitrary set of k indices {i1,…,ik}⊂{1,…,n}. In this paper we study basic properties of the multistochastic problem, including well-posedness, existence of a dual solution, boundedness and continuity of a dual ...

Added: December 4, 2021

Chernyshov A., Kozelov B. V., Mogilevsky M. M., Journal of Atmospheric and Solar-Terrestrial Physics 2017 Vol. 161 P. 127-133

In this work, values of the fractal dimension and the connectivity index characterizing the structure of Hall conductivities on the night side of the auroral ionosphere are derived in general form. Restrictions imposed on fractal structure of the ionospheric conductivity are analyzed in terms of the percolation of the ionospheric Hall currents. It is shown ...

Added: November 28, 2019

Silaev A. M., International Research Journal of Finance and Economics 2012 No. 100 P. 12-18

The paper introduces the idea of using fractals for stylized facts modelling. Since the behavior of financial markets is hard to predict, there have appeared new financial assets models, based, first of all, on empirically revealed properties or stylized empirical facts. We have found the correspondence between four types of fractals and four main empirical ...

Added: November 6, 2012

Gladkov N., Kolesnikov A., Zimin A., On multistochastic Monge-Kantorovich problem, bitwise operations, and fractals / Cornell University. Series arXiv "math". 2018.

The multistochastic (n,k)-Monge--Kantorovich problem on a product space ∏ni=1Xi is an extension of the classical Monge--Kantorovich problem. This problem is considered on the space of measures with fixed projections onto Xi1×…×Xik for all k-tuples {i1,…,ik}⊂{1,…,n} for a given 1≤k<n. In our paper we study well-posedness of the primal and the corresponding dual problem. Our central result describes a solution π to the following important model case: n=3,k=2,Xi=[0,1], ...

Added: July 31, 2018

Molchanov S., Chen J., Teplyaev A., Journal of Physics A: Mathematical and Theoretical 2015 Vol. 48 No. 39 P. 1-22

...

Added: June 22, 2016

Knyazeva H., Философия и культура 2013 № 6 С. 736-745

Atomism and holism are considered as two opposite by implication but complementary approaches in the modern theory of complex self-organizing systems (theory of complexity). Atomism is connected with the consideration of nesting of complex structures in the world, their fractal organization, where we can reach elementary, further indivisible structural fragments on those basis complex scale ...

Added: November 13, 2013

Linetskiy B., Sedova T.L., Tikhonov А. N. et al., , in : Innovative Information Technologies: Materials of the International scientific–practical conference. Part 2. * 2.: M. : HSE, 2014. P. 219-226.

This article consider The project of the scientific and educational Center for integration of multimedia technologies in science, education and culture, as space-technological environment for the implementation of innovative scientific and educational projects of the 21st century, which should become the support for the master's programs, especially interdisciplinary; at the intersection of science, art and ...

Added: May 21, 2014

Dmitrii Sidorenko, ORGANIZATIONAL CULTURE: ESTABLISHING FRACTAL STRUCTURE FRAMEWORK / Высшая школа экономики. Series MAN "Management". 2014.

This research is aimed at the establishment of fractal structure framework that is based on fractal geometry applied to organizational culture. It presents different approach to the problem of cultural integrity – integration vs. differentiation perspective – by studying culture as unity and plurality simultaneously.
Proposed framework is tested on the case of National Research University ...

Added: October 25, 2014