Прекрасная фрактальная математика и ее приложения
In this chapter the application of fractal geometry in such unusual areas such as architecture, art, design, jewelry, video, show describes.
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 in a deterministic context, then were generalized to the random setting on abstract spaces in the early 1980s. Their adaptation to random signals was carried out by Hutchinson and Rüschendorff by considering random operators. This study extends their model with not only random operators but also a random underlying construction tree. We show that the corresponding IFS converges under certain hypothesis to a unique fractal fixed point. Properties of the fixed point are also described.
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.
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 information technologies, and implementation of innovative scientific and commercial projects, which are to become a master's thesis.
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 classical frescoes and airbrushing. As a result of the mathematical-computer experiments proposed new industrial technologies in the textile and construction industries, as well as in the architectural design of roomsbuilding interior and exterior.
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 invariant, self-similar spatio-temporal structures grow up. Besides, atomism is connected with the study of hierarchical organization of being and of elements, parts, subsystems out of which a whole structure is built. At the same time, it is shown in the article that the whole theory of complexity is penetrated by holism, and its holism is evolutionary by its character. Holism in evolution of complex self-organizing systems is coupled with the appearance of emergent properties of integral structural forms as well as with the discreteness, certain set of structures-attractors of evolution. The modern atomism can be brought into correlation with the notion of frames of perception in cognitive science. Proceeding from the system and evolutionary worldview, some arguments are put forward in favor of a hypothesis of the origins of the alphabetical writing in close connection with the studies of atoms in physical nature (Nidem, A.I. Kosyrev, V.G. Lysenko).