On Self‐Affine and Self‐Similar Graphs of Fractal Interpolation Functions Generated from Iterated Function Systems

This chapter provides a brief and coarse discussion on the theory of fractal interpolation functions and their recent developments including some of the research made by the authors. It focuses on fractal interpolation as well as on recurrent fractal interpolation in one and two dimensions. The resulting self‐affine or self‐similar graphs, which usually have non‐integral dimension, were generated through a family of (discrete) dynamic systems, the iterated function system, by using affine transformations. Specifically, the fractal interpolation surfaces presented here were constructed over triangular as well as over polygonal lattices with triangular subdomains. A further purpose of this chapter is the exploration of the existent breakthroughs and their application to a flexible and integrated software that constructs and visualises the above‐mentioned models. We intent to supply both a panoramic view of interpolating functions and a useful source of links to assist a novice as well as an expert in fractals. The ideas or findings contained in this paper are not claimed to be exhaustive, but are intended to be read before, or in parallel with, technical papers available in the literature on this subject

Enhancing Primary School Teaching through Virtual Reality

In this day and age, the usage of computers as well as Internet combined with mobile devices is an integral part of our routine especially for adolescents and younger children. Thus, it puts forward a multitude of challenges and advances for educational institutions. The purpose of this article is to explore the current use of virtual reality in order to support teaching and learning along with presenting a teaching proposal concerning the utilisation of CoSpace Edu software on the subject of Religious Affairs

Scale-free fractal interpolation

An iterated function system that defines a fractal interpolation function, where ordinate scaling is replaced by a nonlinear contraction, is investigated here. In such a manner, fractal interpolation functions associated with Matkowski contractions for finite as well as infinite (countable) sets of data are obtained. Furthermore, we construct an extension of the concept of α-fractal interpolation functions, herein called R-fractal interpolation functions, related to a finite as well as to a countable iterated function system and provide approximation properties of the R-fractal functions. Moreover, we obtain smooth R-fractal interpolation functions and provide results that ensure the existence of differentiable R-fractal interpolation functions both for the finite and the infinite (countable) cases

How Are Fractal Interpolation Functions Related to Several Contractions?

This chapter provides an overview of several types of fractal interpolation functions that are often studied by many researchers and includes some of the latest research made by the authors. Furthermore, it focuses on the connections between fractal interpolation functions resulting from Banach contractions as well as those resulting from Rakotch contractions. Our aim is to give theoretical and practical significance for the generation of fractal (graph of) functions in two and three dimensions for interpolation purposes that are not necessarily associated with Banach contractions

Fractal-Based Image Encoding and Compression Techniques

In computer science and information theory, data compression, source coding, or bit-rate reduction is the process of encoding digital information using fewer bits than the original representation. Specifically, digital-image compression is important due to the high storage and transmission requirements. Various compression methods have been proposed using different techniques to achieve high compression ratios. Fractal image encoding is a technique based on the representation of an image by contractive transformations. Fractal-based image compression methods belong to different categories according to the different theories they are based on. In this article, first we try to clarify the terminology used and then to comprehensively unveil the mathematical principle behind fractal image compression as well as to briefly overview a variety of schemes that have been investigated

Educational social networking services: The case of edmodo in the teaching practice

In recent years, there has been a strong education interest in second generation World Wide Web (Web 2.0) applications such as blogs, social networking, information sharing tools, social bookmarking and more. This article presents a case of using an online social learning network offering communication, collaboration and coaching tools to K-12 schools and teachers as well as a means of communication among pupils themselves. Given the students’ familiarity with computers and the internet, it was considered that using these tools in teaching would motivate them during the lesson, and, in particular, it would benefit the weakest students who often maintain a non-positive attitude towards the traditional (conventional) face-to-face lesson. In order to achieve this goal, Edmodo has been selected from all the available as a technology based educational learning tool, thanks to the ability of using the Greek language since the summer of 2011. The features of this social learning tool and the experience of using it in Secondary Education within the course “Informatics Applications” are reported here: during one school year, and some examples of its use in everyday teaching. The advantages of using it both pedagogically and practically, as well as some problems encountered by students and teachers during their practicum studies, are presented. The purpose of this article is to present in general terms the use of the Edmodo platform in the course of Informatics in a real class of the Evening Vocational Lyceum (EPAL).</p

Approximation by non-self-referential bivariable fractal functions

Fractal functions defined through iterated function systems provide a new technique for the approximation of functions. Non-self-referential bivariable fractal functions which approximate a given continuous function defined on a rectangle in $$\mathbb {R}^2$$ are developed herein. Moreover, by imposing suitable conditions on the scaling factors and on base functions, we study $$\mathcal {C}^r$$-non-self-referential bivariable fractal functions

Electrodeposition of thin film semiconductors in the presence of metallocenes

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Επιστήμη και Τεχνολογία Υλικών

Line Clipping in 3D: Overview, Techniques and Algorithms

Clipping algorithms essentially compute the intersection of the clipping object and the subject, so to go from two to three dimensions we replace the two-dimensional clipping object by the three-dimensional one (the view frustum). In three-dimensional graphics, the terminology of clipping can be used to describe many related features. Typically, “clipping” refers to operations in the plane that work with rectangular shapes, and “culling” refers to more general methods to selectively process scene model elements. The aim of this article is to survey important techniques and algorithms for line clipping in 3D, but it also includes some of the latest research performed by the authors