Recursive scene graphs for art and design

We analyze a minimal model of iterated function systems (IFS) and show possibilities for controlling properties of the fractal signals they generate. Applications for signal modeling and spread-spectrum communications illustrate the potentialities of IFS for signal processing.

# Structure of Genetic Regulatory Networks: Evidence for Scale Free Networks (L S Liebovitch et al.) # Modelling Fractal Dynamics (B J West) # Fractional Relaxation of Distributed Order (R Gorenflo & F Mainardi) # Fractional Time: Dishomogeneous Poisson Processes vs. Homogeneous Non-Poisson Processes (P Allegrini et al.) # Markov Memory in Multifractal Natural Processes (N Papasimakis & F Pallikari) # Description of Complex Systems in Terms of Self-Organization Processes of Prime Integer Relations (V Korotkikh & G Korotkikh) # Dynamical Decomposition of Multifractal Time Series as Fractal Evolution and Long-Term Cycles: Applications to Foreign Currency Exchange Market (A Turiel & C Perez-Vicente) # Fractal Sets from Noninvertible Maps (Ch Mira) # A Generative Construction and Visualization of 3D Fractal Measures (T Martyn) # Complexity in Nature and Society: Complexity Management in the Age of Globalization (K Mainzer) # Fractals, Complexity and Chaos in Supply Chain Networks (M Pearson) # The Effects of Different Competition Rules on the Power-Law Exponent of High Income Distribution (K Yamamoto et al.) # Synergetics on Its Way to the Life Sciences (H Haken) # Complexity, Fractals, Nature and Industrial Design: Some Connections (N Sala) # Modelling Pattern Formation Upon Laser-Induced Etching (A Mora et al.) # Fractal Properties of Some Machined Surfaces (T R Thomas & B-G Rosen) # Fractals, Morphological Spectrum and Complexity of Interfacial Patterns in Non-Equilibrium Solidification (P K Galenko & D M Herlach) # Competition of Doublon Structure in the Phase-Field Model (S Tokunaga & H Sakaguchi) # Study of Thermal Field in Composite Materials (P Stefkova et al.) # Simulation of Geochemical Banding in Acidization-Precipitation Experiments In Situ (M Msharrafieh et al.) # Bulk Mediated Surface Diffusion: Non Markovian and Biased Behavior (J A Revelli et al) # Multifractal Formalism for Remote Sensing: A Contribution to the Description and the Understanding of Meteorological Phenomena in Satellite Images (J Grazzini et al.) # The Distance Ratio Fractal Image (X-Z Zhang et al.) # Iterated Function Systems in Mixed Euclidean and p-Adic Spaces (B Sing) # Multifractality of the Multiplicative Autogressive Point Processes (B Kaulakys et al.) # Analysis of Geographical Distribution Patterns in Plants Using Fractals (A Bari et al.) # Hierarchy of Cellular Automata in Relation to Control of Chaos or Anticontrol (M Markus et al.) # Fractal Analysis of the Images Using Wavelet Transformation (P Jerabkova et al.) # Clustering Phenomena in the Time Distribution of Lightning (L Telesca et al.) # A Cornucopia of Connections: Finding Four Familiar Fractals in the Tower of Hanoi (D R Camp) # Monitoring the Depth of Anaesthesia Using Fractal Complexity Method (W Klonowski et al.) # The Complex Couplings and Gompertzian Dynamics (P Waliszewski & J Konarski)

Cloud computing is expected to grow consider- ably in the future because it has so many advantages with regard to sale and cost, change management, next generation architectures, choice and agility. However, one of the principal concerns for users of the Cloud is lack of control and above all, data security. This paper considers an approach to encrypting information before it is 'placed' on the Cloud where each user has access to their own encryption algorithm, an algorithm that is based on a set of iterated function systems that outputs a chaotic number stream, designed to produce a cryptograph- ically secure cipher. We study cryptographic systems using finite-state approximations to chaos or 'pseudo-chaos' and develop an approach based on the concept of multi-algorithmic cryptography that exploits the properties of pseudo-chaos. Although such algorithms can be taken to be in the public domain in order to conform with the Kerchhoff-Shannon principal, i.e. the enemy knows the system, their combination can be used to secure data in a way that is unique to each user. This provides the potential for users of the Cloud to upload and transfer data in the knowledge that they are encrypting their data in a way that is algorithm as well key dependent, thereby defeating a known algorithm attack. This paper reports on one application of this approach called Crypstic in which the encryption engine is mounted on a USB memory stick and where the key is automatically generated by the characteristics of the plaintext/ciphertext file.

In this paper we Ointroduce linear-spaces consisting of continuous functions whose graphs are the attactors of a special class of iterated function systems. We show that such spaces are finite dimensional and give the bases of these spaces in an implicit way. Given such a space, we discuss how to obtain a set of knots for which the Lagrange interpolation problem by the space is uniquely solvable.

Visualization of recursively defined concepts is a general problem that appears in many areas. For example, drought areas based on the standardized precipitation index (SPI) and long-term air pollution areas based on safe and critical level standards are recursively defined concepts. We develop a general and efficient representation and visualization method for recursively defined spatio-temporal concepts. We illustrate our general method by visualizing drought and pollution areas.

One of the main disadvantages of fractal image data compression is a loss time in the process of image compression (encoding) and conversion into a system of iterated functions (IFS). In this paper, the idea of the inverse problem of fixed point is introduced. This inverse problem is based on collage theorem which is the cornerstone of the mathematical idea of fractal image compression. Then this idea is applied by iterated function system, iterative system functions and grayscale iterated function system down to general transformation. Mathematical formulation form is also provided on the digital image space, which deals with the computer. Next, this process has been revised to reduce the time required for image compression by excluding some parts of the image that have a specific milestone. The neural network algorithms have been applied on the process of compression (encryption). The experimental results are presented and the performance of the proposed algorithm is discussed. Finally, the comparison between filtered ranges method and self-organizing method is introduced.

We derive tight expressions for the maximum number of k-faces, k=0,...,d-1, of the Minkowski sum, P_1+...+P_r, of r convex d-polytopes P_1,...,P_r in R^d, where d >= 2 and r < d, as a (recursively defined) function on the number of vertices of the polytopes. Our results coincide with those recently proved by Adiprasito and Sanyal [1]. In contrast to Adiprasito and Sanyal's approach, which uses tools from Combinatorial Commutative Algebra, our approach is purely geometric and uses basic notions such as f- and h-vector calculus, stellar subdivisions and shellings, and generalizes the methodology used in [10] and [9] for proving upper bounds on the f-vector of the Minkowski sum of two and three convex polytopes, respectively. The key idea behind our approach is to express the Minkowski sum P_1+...+P_r as a section of the Cayley polytope C of the summands; bounding the k-faces of P_1+...+P_r reduces to bounding the subset of the (k+r-1)-faces of C that contain vertices from each of the r polytopes. We end our paper with a sketch of an explicit construction that establishes the tightness of the upper bounds.

Generation of fractals via iterated function system of Kannan contractions in controlled metric space

Fractal geometry has provided statistical and deterministic models for classes of signals and images that represent many natural phenomena and objects. Iterated function systems (IFS) theory provides a convenient way to describe and classify deterministic fractals in the form of a recursive definition. As a result, it is conceivable to develop image representation schemes based on the IFS parameters that correspond to a given fractal image. The authors propose the use of the wavelet transform and of the moment method for the solution of the inverse problem of recovering IFS parameters from fractal images. The redundancy of a fractal with respect to scale variation is mirrored by its wavelet decomposition, thus providing a method to estimate the scaling parameters for a class of IFSs modeling the image. Displacement parameters and probabilities are then found using the moment method. Experimental results verifying the approach are presented. >

Fractal image compression using the iterative function system (IFS) is based on the collage theorem proposed by Barnsley et al. (1986). In this conventional method, the errors between the reconstructed image and original image may be greater than the errors between the collage and original image because the collage theorem does not guarantee the former errors to be smaller than the latter errors. This paper proposes an extended collage theorem. An IFS algorithm based on this theorem determines the parameters after iterations of the contraction mappings. An image reconstructed according to the new theorem has higher quality than one based on the existing collage theorem. The reconstructed image can be gotten by fewer iterations than by the conventional IFS.

Many effective methods have been proposed to solve the problem of image compression. Fractal image code can compress an image in a higher compress ratio level, the fundamental idea of fractal image compression is based on the iteration function system (IFS). In this paper, we proposed a novel method based on IFS with probabilities can be used in image compression and image retrieval, we obtain enlightenment from fractal no search methods, our method also no need to carried out searching stage when compress the image, so the consuming time with image compression is less than traditional methods. We utilized the image code as index file, and apply our method in image retrieval, experiment results indicate that our method is effective in image retrieval.

In this thesis, concepts for developing Spatial Data Infrastructures with an emphasis on visualizing 3D landscape and city models in distributed environments are discussed. Spatial Data Infrastructures are important for public authorities in order to perform tasks on a daily basis, and serve as research topic in geo-informatics. Joint initiatives at national and international level exist for harmonizing procedures and technologies. Interoperability is an important aspect in this context - as enabling technology for sharing, distributing, and connecting geospatial data and services. The Open Geospatial Consortium is the main driver for developing international standards in this sector and includes government agencies, universities and private companies in a consensus process. &#13;\n3D city models are becoming increasingly popular not only in desktop Virtual Reality applications but also for being used in professional purposes by public authorities. Spatial Data Infrastructures focus so far on the storage and exchange of 3D building and elevation data. For efficient streaming and visualization of spatial 3D data in distributed network environments such as the internet, concepts from the area of real time 3D Computer Graphics must be applied and combined with Geographic Information Systems (GIS). For example, scene graph data structures are commonly used for creating complex and dynamic 3D environments for computer games and Virtual Reality applications, but have not been introduced in GIS so far. &#13;\nIn this thesis, several aspects of how to create interoperable and service-based environments for 3D spatial data are addressed. These aspects are covered by publications in journals and conference proceedings. The introductory chapter provides a logic succession from geometrical operations for processing raw data, to data integration patterns, to system designs of single components, to service interface descriptions and workflows, and finally to an architecture of a complete distributed service network.&#13;\nDigital Elevation Models are very important in 3D geo-visualization systems. Data structures, methods and processes are described for making them available in service based infrastructures. A specific mesh reduction method is used for generating lower levels of detail from very large point data sets. An integration technique is presented that allows the combination with 2D GIS data such as roads and land use areas. This approach allows using another optimization technique that greatly improves the usability for immersive 3D applications such as pedestrian navigation: flattening road and water surfaces. It is a geometric operation, which uses data structures and algorithms found in numerical simulation software implementing Finite Element Methods. &#13;\n3D Routing is presented as a typical application scenario for detailed 3D city models. Specific problems such as bridges, overpasses and multilevel networks are addressed and possible solutions described. The integration of routing capabilities in service infrastructures can be accomplished with standards of the Open Geospatial Consortium. An additional service is described for creating 3D networks and for generating 3D routes on the fly. Visualization of indoor routes requires different representation techniques.&#13;\nAs server interface for providing access to all 3D data, the Web 3D Service has been used and further developed. Integrating and handling scene graph data is described in order to create rich virtual environments. Coordinate transformations of scene graphs are described in detail, which is an important aspect for ensuring interoperability between systems using different spatial reference systems. The Web 3D Service plays a central part in nearly all experiments that have been carried out. It does not only provide the means for interactive web-visualizations, but also for performing further analyses, accessing detailed feature information, and for automatic content discovery.&#13;\nOpenStreetMap and other worldwide available datasets are used for developing a complete architecture demonstrating the scalability of 3D Spatial Data Infrastructures. Its suitability for creating 3D city models is analyzed, according to requirements set by international standards. A full virtual globe system has been developed based on OpenStreetMap including data processing, database storage, web streaming and a visualization client.&#13;\nResults are discussed and compared to similar approaches within geo-informatics research, clarifying in which application scenarios and under which requirements the approaches in this thesis can be applied.&#13;\n

We consider finite approximations of a fractal generated by an iterated function system of affine transformations on \(\mathbb{R}^{d}\) as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a Fast (Fractal) Fourier Transform by choosing appropriately a second iterated function system to generate a set of frequencies for a collection of exponential functions supported on this finite approximation. Since both the data points of the fractal approximation and the frequencies of the exponential functions are generated by iterated function systems, the matrix representing the Discrete Fourier Transform (DFT) satisfies certain recursion relations, which we describe in terms of Diţǎ’s construction for large Hadamard matrices. These recursion relations allow for the DFT matrix calculation to be reduced in complexity to O(NlogN), as in the case of the classical FFT.

This paper develops an extension of the research work by Proinov to the product spaces X|I| (I is representing an indexing set). This paper also introduces a novel class of (L;Y)-contractions defined on a supremum metric (X|I|,d′). In supremum metric (X|I|,d′), several new fixed point theorems for (L;Y)-contractions have been established that generalize well-known ideas like the Banach, Geraghty, Boyd–Wong, and Wardowski principles. This paper also contributes a new iterated function system (IFS) built on the family of (L;Y)-contractions and demonstrates the existence and uniqueness of fractals (in other words, compact attractors) in a complete supremum metric (X|I|,d′). Theoretical work is illustrated with examples and graphs.

This paper addresses the equivalence between iterative function systems (IFS). It also explains how to classify and reduce the parameter space for a particular class of IFS.The proposed method generates various fractal textures for regular polygons and allows the creation of polygon-based fractal flakes, polygon-based spirals, and many other forms. It employs sth-order restriction, a new version of recurrent iterated function systems. Level-specified symmetry in the fractals is controlled through rth-level symmetrization.