Wyniki wyszukiwania - Biblioteka Nauki

1

Deterministic fractals based on Archimedean solids

100%

Katunin A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2011

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tom Vol. 10, nr 1

93-100

EN

In the present work, the construction of fractals based on Archimedean solids was discussed. The methods of 3D fractals construction based on uniform polyhedra were presented. It was shown that the contraction mapping procedure for the construction of fractals with non-overlapping or -disjointed contractions could be applied only for a limited number of the polyhedra. The contraction ratios and the Hausdorff dimensions were determined for the existing fractals with adjacent contractions based on Archimedean solids.

2

Growing a class of fractals based on combination of classical fractals and recursive mathematical series in L-systems

80%

Bisoi A. K. , Mishra S. N. , Mishra J.

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tom Vol. 13, No. 3

275-288

EN

L-systems can be used to generate fractals. In this paper L-systems with a standard turtle alphabet are combined with L-systems which emulate simple number sequences. The combination of two such L-systems is achieved by concatenating their axioms as well as merging their rule sets. This can happen in several ways, depending in part on the sequence in which axioms and right-hand sides of rules are concatenated. The purpose of this paper is to combine these two applications of L-systems to generate novel fractals. A turtle interpretation is applied to the yield of the generated hybrid L-systems resulting in new fractal images.

3

On a visualization of the convergence of the boundary of generalized Mandelbrot set to (n-1)-sphere

80%

Katunin A. , Fedio K.

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tom Vol. 14, nr 1

63--69

EN

In this article we analyze the generalized Mandelbrot set in higher-order hypercomplex number spaces following both the Cayley-Dickson construction algebraic spaces and the spaces defined by Clifford algebras. The particular case of the generalized 3D quasi-Mandelbrot set was also considered. In particular, we investigated the increase of power of the iterated variable and proved that when this power tends to infinity, the Mandelbrot set is convergent to the unit circle. The same is true for the generalized Mandelbrot sets in higher-dimensional hypercomplex number spaces, i.e. when the power of iterated variable tends to infinity, the generalized Mandelbrot set is convergent to the unit (n-1)- sphere. The results of our investigation were visualized for the generalized Mandelbrot set in a complex number space and the generalized quasi-Mandelbrot set in a 3D Euclidean space.

4

Image generation by Petri nets

80%

Lumini A. , Maio D.

Machine Graphics and Vision

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1998

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tom Vol. 7, No. 1/2

221-232

EN

This paper presents a new approach to computer image generation. The basic idea is to translate the evolution of a Petri net into a graphic output. In particular, we focus on three methods for image generation which exhibit a certain analogy whit fractals. Some experimental results are reported together whit a brief investigation on the relationships between generated images and thier corresponding Petri nets.

5

Fractal palettes for medical imaging

80%

Nikiel S. , Kirby G. H.

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tom Vol. 7, No. 4

743-750

EN

A fractal colour model used for medical imaging is discussed in this paper. Presented method should lead to better understanding of displays of complex and ambiguous medical data sets. A simple technique for generation of fractal paletters with different "irregularity is presented together with sample images. The method was tested with real life datasets. Obtained results shown that the fractal colour model can be used as an additional interactive tool for medical visualisation purposes. This tool is especially useful in enhancing detail visibility within uncertain regions of computer tomography magnetic resonance and X-ray mammography images.

6

Fractal images with inverse replicas

80%

Bisoi A. K. , Mishra J.

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tom Vol. 8, No. 1

77-82

EN

Fractals are famous for thier beauty and fractal techniques are employed for less storage space requirement while storing images. The fractal comtain thier scale down, rotate and skew replicas embedded in them. The concept of multiple reduction copy machine (MRCM) has been used for creating fractals since long. A modified MRCM has been designed to generate fractal images having inverse replicas embedded in them along with the scale down, rotate, translate and skew replicas. We restrict our experiments only to binary images in order to compare the results with the existing regular fractals. This paper only demonstrates the generation of fractal images with inverse replcas.

7

Interated function systems for terrain synthesis

80%

Nikiel S. S. , Kirby G. H.

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tom Vol. 9, No. 1/2

47-55

EN

This paper discusses terrain synthesis using IFS interpolation techniques by extending them from two- to three-dimensional cases. The method is not intended to be started from a purey random set of points, rather from some real or meaningful heightfield. The method is suited to near real-time computing, is deterministic, context dependent and provides control over the nature of roughness of rendered furfaces. Its speed and flexibility on standard deskop computers open up the possibility of terrain engineering.

8

Korelacja wybranych charakterystyk mechanicznych i fraktalnych dla stali 40 H

80%

Kotowski P.

Zeszyty Naukowe Politechniki Białostockiej. Mechanika

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2001

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tom Z. 24

PL

W pracy przedstawiono zależności wymiaru fraktalnego powierzchni pęknięcia i wybranych wielkości mechaniki pękania. W szczególności dla stali 40H po obróbce cieplnej, zbadano korelację między współczynnikiem intensywności naprężeń oraz prędkością wzrostu szczeliny zmęczeniowej a wymiarem fraktalnym przełomu. Prezentowana praca zmierza więc do opisu zjawisk pękania przy pomocy fraktalnego języka pojęć.

EN

The presented paper aims to verify chosen mathematical models setting correspondence between quantities from fracture mechanics and fractal characteristics of observed crack. In particular for 41Cr steel, dependencies between stress-intensity factor and fractal dimension of fractured surface have been examined. Moreover dependencies between fatigue crack-growth rate and fractal dimension have been examined.

9

Electro-chemical manifestation of nanoplasmonics in fractal media

80%

Baskin E. , Iomin A.

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tom 11

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nr 6

676-684

EN

Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.

10

WYMIAR FRAKTALNY PRAWDY I KŁAMSTWA W SZTUCE FLY-BY ALFONSA VALLEJO. OD DERRIDY I LEVINASA DO TEORII SAMOPODOBIEŃSTWA JAKO METAFORY EGZYSTENCJI

80%

Szejko N.

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2016

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tom 10

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nr -

213-221

PL

Theatre of Alfonso Vallejo presents complex psychic processes and therefore is barely realistic, on the contrary, it is based upon surrealistic visions adequate to diversity of human being. Although it seems chaotic, this chaos re-sembles network of infinite connections that produce, as a consequence, infinite number of questions and possible answers. To interpret the complexity of Val-lejo's dramas we use theory of fractals and self-similarity in play Fly-by.

11

Areal field and fractal based characterization of hard surfaces produced by different machining operations

70%

Zak K.

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tom Vol. 16, No. 1

24--32

EN

This literature survey highlights the possible influences of surface roughness parameters on functional properties of surfaces produced by different finishing operations. The prediction of such functional properties as fatigue, sealing capacity, adhesion, friction, wear and corrosion resistance based on five groups of spatial (S) roughness parameters is overviewed. In contrast, traditional approach based on 2D roughness parameters is provided. Some real 3D surface topographies produced with desired functional properties by finishing cutting and abrasive operations are characterized. This survey confirms the vital role of machined surfaces in the functionality of machine components.

12

A proposition of mobile fractal image decompression

70%

Nikiel S.

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tom 17

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nr 1

129-136

EN

Multimedia are becoming one of the most important elements of the user interface with regard to the acceptance of modern mobile devices. The multimodal content that is delivered and available for a wide range of mobile telephony terminals is indispensable to bind users to a system and its services. Currently available mobile devices are equipped with multimedia capabilities and decent processing power and storage area. The most crucial factors are then the bandwidth and costs of media transfer. This is particularly visible in mobile gaming, where textures represent the bulk of binary data to be acquired from the content provider. Image textures have traditionally added visual realism to computer graphics. The realism increases with the resolution of textures. This represents a challenge to the limited bandwidth of mobile-oriented systems. The challenge is even more obvious in mobile gaming, where single image depicts a collection of shots or animation cycles for sprites and a backdrop scenery. In order to increase the efficiency of image and image texture transfer, a fractal based compression scheme is proposed. The main idea is to use an asymmetric server-client architecture. The resource demanding compression process is performed on the server side while the client part decompresses highly packed image data. The method offers a very high compression ratio for pictures representing image textures for natural scenes. It aims to minimize the transmission bandwidth that should speed up the downloading process and minimize the cost and time of data transfer. The paper focuses on the implementation of fractal decompression schemes suitable for most mobile devices, and opens a discussion on fractal image models for limited resource applications.

13

Fractal compression using random encoding algorithm

70%

Świdzińska B.

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tom Vol. 46, nr 4

525-532

EN

Fractal image compression is a promising brand new compression method. In the paper several algorithms are compared. A majority of those algorithms accelerate the encoding process by reduction of the size of the domain pool. I show in the paper that unlike assumed in many algorithms, the optimal domain block need not be located in the close neighborhood of the range block. I suggest two techniques of solving this problem: (1) domain blocks are searched in the whole image, but they do not cover it, (2) the positions of domain blocks are random. The other algorithm looks particularly promising: it is fast and the quality of reconstruction is acceptable in most cases. The numerical results for both methods are given.

14

2020 Ian Snook Prize Problem : Three Routes to the Information Dimensions for One-Dimensional Stochastic Random Walks and Their Equivalent Two-Dimensional Baker Maps

70%

Hoover W. G. , Hoover C. G.

Computational Methods in Science and Technology

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2019

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tom Vol. 25, No. 4

153--159

EN

The $1000 Ian Snook Prize for 2020 will be awarded to the author(s) of the most interesting paper exploring pairs of relatively simple, but fractal, models of nonequilibrium systems, dissipative time-reversible Baker Maps and their equivalent stochastic random walks. Two-dimensional deterministic, time-reversible, chaotic, fractal, and dissipative Baker maps are equivalent to stochastic one-dimensional random walks. Three distinct estimates for the information dimension, {0.7897, 0.7415, 0.7337} have all been put forward for one such model. So far there is no cogent explanation for the differences among these estimates. We describe the three routes to the information dimension, DI : 1) iterated Cantor-like mappings, 2) mesh-based analyses of single-point iterations, and 3) the Kaplan-Yorke Lyapunov dimension, thought by many to be exact for these models. We encourage colleagues to address this Prize Problem by suggesting, testing, and analyzing mechanisms underlying these differing results.

15

Algorithms and methods for analysis of the optical structure factor of fractal aggregates

70%

Mroczka J. , Woźniak M. , Onofri F. R. A.

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2012

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tom Vol. 19, nr 3

459-470

EN

We introduce numerical methods and algorithms to estimate the main parameters of fractal-like particle aggregates from their optical structure factor (i.e. light scattering diagrams). The first algorithm is based on a direct and simple method, but its applicability is limited to aggregates with large size parameter and intermediate fractal dimension. The second algorithm requires to build calibration curves based on accurate particle agglomeration and particle light scattering models. It allows analyzing the optical structure factor of much smaller aggregates, regardless of their fractal dimension and the size of the single particles. Therefore, this algorithm as well as the introduction of a criteria curve to detect the different scattering regimes, are thought to be powerful tools to perform reliable and reproducible analyses.

16

Monitoring and Biochemical Treatment of Wastewater

70%

Dychko A. , Remez N. , Kyselov V. , Kraychuk S. , Ostapchuk N. , Kniazevych A.

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2020

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tom Vol. 21, nr 4

150--159

EN

The present paper provides the methodology for the environmental monitoring of natural and engineering wastewater systems, which involves the determination of the dichotomous fractal structure of the measuring network, the boundaries of the range and the density of pollution on the Peano and Koch curves, based on the data of the measuring network and the corresponding interpolation and smoothing algorithms, as well as determination of the dynamics of the pollution range using the Bayesian theorem. On the basis of the theory of fractals and the theory of sets, the developed algorithms for monitoring allow determining the structure of the measuring network taking into account the features of the controlled range and the sets of fractal isolines of any configuration with a given accuracy of reflection, which allows predicting the change in the composition of the effluent that comes to the reservoirs from the landscapes and improving the functioning of the equipment and environmental safety of water in general. The established dependence of biogas productivity on the different methods for destruction of the active sludge microorganisms allows determining that the maximum output of biogas occurs when applying the chemical destruction of part of the sludge.

17

Roughness and fractality of fracture surfaces as indicators of mechanical quantities of porous solids

70%

Ficker T. , Martišek D.

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tom 9

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nr 6

1440-1445

EN

The 3D profile surface parameter H q and fractal dimension D were tested as indicators of mechanical properties inferred from fracture surfaces of porous solids. High porous hydrated cement pastes were used as prototypes of porous materials. Both the profile parameter H q and the fractal dimension D showed capability to assess compressive strength from the fracture surfaces of hydrated pastes. From a practical point of view the 3D profile parameter H q seems to be more convenient as an indicator of mechanical properties, as its values suffer much less from statistical scatter than those of fractal dimensions.

18

Fractal dimensions of cave for exemplary gypsum cave-mazes of Western Ukraine

70%

Andreychouk V. , Błachowicz T. , Domino K.

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tom Vol. 22

3--8

EN

Gypsum labyrinthine caves are characterized by a complex spatial structure, which can be treated as fractals and can be studied using appropriate mathematical tools. Capacitance and correlation fractal dimensions of largest gypsum caves of the Western Ukraine (as well as the World’s largest ones) were calculated. The results were used to predict findings of new, undiscovered cave mazes parts.

19

Fractal variations of the Transcarpathians, West Ukraine, seismicity and their potential relation to changing phases of local seismic cycles

70%

Gnyp A.

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tom Vol. 55, no. 3

288-301

EN

The evolution of spatial arrangement of the Transcarpathian earthquakes is studied by means of fractal analysis. Spatial correlation dimension is evaluated for a subset of fixed number of catalogue events consecutively shifted in time by one event forward. Distinctive patterns that may be related to different phases of local seismic cycle/cycles have been identified, corresponding to extreme values of the dimension. Their potential relation to evolution of the seismogenic stress field is discussed. The time it takes for the capacity dimension to reach the so-called percolation threshold is estimated for a subset consecutively extended by adding next catalogue events. Temporal and spatial frames of percolation analysis are discussed in relation to parameters of the future earthquake.

20

Microspheric continuum, rotational wave and fractal properties of earthquake and faults

70%

Nagahama H.

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tom Vol. 46, nr 3

278-294

EN

It seems that internal structures and discontinuities in the litosphere have an essential influence on the litocpheric derofmation like faulting or earthquakes. The micromorphic continuum providies a good framework to study the continnum with microstructure, such as earthquake structures. Here we briefly introduce micromorphic continuum to consider the earthquake structures (e.g., rotational wave). Then the equlibrium equation in terms of the displacements (the Navier equation) is derived from this micromorphic continuum. This equation is the generalization of Laplace equation in terms of displacements and can lead to some Laplace equation such as the local diffusion-like conservation equations. Moreover, these conservation fields bear the fractal properties of fracturing in the lithosphere in the form of facults or earthquakes. Finally some scalling laws of faults or eartquakes are discussed.