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Fractal Growth on the Surface of a Planet and in Orbit Around It
Wilfrid Laurier University Scholars Commons @ Laurier Physics and Computer Science Faculty Publications Physics and Computer Science 10-2014 Fractal Growth on the Surface of a Planet and in Orbit around It Ioannis Haranas Wilfrid Laurier University, [email protected] Ioannis Gkigkitzis East Carolina University, [email protected] Athanasios Alexiou Ionian University Follow this and additional works at: https://scholars.wlu.ca/phys_faculty Part of the Mathematics Commons, and the Physics Commons Recommended Citation Haranas, I., Gkigkitzis, I., Alexiou, A. Fractal Growth on the Surface of a Planet and in Orbit around it. Microgravity Sci. Technol. (2014) 26:313–325. DOI: 10.1007/s12217-014-9397-6 This Article is brought to you for free and open access by the Physics and Computer Science at Scholars Commons @ Laurier. It has been accepted for inclusion in Physics and Computer Science Faculty Publications by an authorized administrator of Scholars Commons @ Laurier. For more information, please contact [email protected]. 1 Fractal Growth on the Surface of a Planet and in Orbit around it 1Ioannis Haranas, 2Ioannis Gkigkitzis, 3Athanasios Alexiou 1Dept. of Physics and Astronomy, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada 2Departments of Mathematics and Biomedical Physics, East Carolina University, 124 Austin Building, East Fifth Street, Greenville, NC 27858-4353, USA 3Department of Informatics, Ionian University, Plateia Tsirigoti 7, Corfu, 49100, Greece Abstract: Fractals are defined as geometric shapes that exhibit symmetry of scale. This simply implies that fractal is a shape that it would still look the same even if somebody could zoom in on one of its parts an infinite number of times. -
Object Oriented Programming
No. 52 March-A pril'1990 $3.95 T H E M TEe H CAL J 0 URN A L COPIA Object Oriented Programming First it was BASIC, then it was structures, now it's objects. C++ afi<;ionados feel, of course, that objects are so powerful, so encompassing that anything could be so defined. I hope they're not placing bets, because if they are, money's no object. C++ 2.0 page 8 An objective view of the newest C++. Training A Neural Network Now that you have a neural network what do you do with it? Part two of a fascinating series. Debugging C page 21 Pointers Using MEM Keep C fro111 (C)rashing your system. An AT Keyboard Interface Use an AT keyboard with your latest project. And More ... Understanding Logic Families EPROM Programming Speeding Up Your AT Keyboard ((CHAOS MADE TO ORDER~ Explore the Magnificent and Infinite World of Fractals with FRAC LS™ AN ELECTRONIC KALEIDOSCOPE OF NATURES GEOMETRYTM With FracTools, you can modify and play with any of the included images, or easily create new ones by marking a region in an existing image or entering the coordinates directly. Filter out areas of the display, change colors in any area, and animate the fractal to create gorgeous and mesmerizing images. Special effects include Strobe, Kaleidoscope, Stained Glass, Horizontal, Vertical and Diagonal Panning, and Mouse Movies. The most spectacular application is the creation of self-running Slide Shows. Include any PCX file from any of the popular "paint" programs. FracTools also includes a Slide Show Programming Language, to bring a higher degree of control to your shows. -
An Image Cryptography Using Henon Map and Arnold Cat Map
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 05 Issue: 04 | Apr-2018 www.irjet.net p-ISSN: 2395-0072 An Image Cryptography using Henon Map and Arnold Cat Map. Pranjali Sankhe1, Shruti Pimple2, Surabhi Singh3, Anita Lahane4 1,2,3 UG Student VIII SEM, B.E., Computer Engg., RGIT, Mumbai, India 4Assistant Professor, Department of Computer Engg., RGIT, Mumbai, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - In this digital world i.e. the transmission of non- 2. METHODOLOGY physical data that has been encoded digitally for the purpose of storage Security is a continuous process via which data can 2.1 HENON MAP be secured from several active and passive attacks. Encryption technique protects the confidentiality of a message or 1. The Henon map is a discrete time dynamic system information which is in the form of multimedia (text, image, introduces by michel henon. and video).In this paper, a new symmetric image encryption 2. The map depends on two parameters, a and b, which algorithm is proposed based on Henon’s chaotic system with for the classical Henon map have values of a = 1.4 and byte sequences applied with a novel approach of pixel shuffling b = 0.3. For the classical values the Henon map is of an image which results in an effective and efficient chaotic. For other values of a and b the map may be encryption of images. The Arnold Cat Map is a discrete system chaotic, intermittent, or converge to a periodic orbit. that stretches and folds its trajectories in phase space. Cryptography is the process of encryption and decryption of 3. -
WHAT IS a CHAOTIC ATTRACTOR? 1. Introduction J. Yorke Coined the Word 'Chaos' As Applied to Deterministic Systems. R. Devane
WHAT IS A CHAOTIC ATTRACTOR? CLARK ROBINSON Abstract. Devaney gave a mathematical definition of the term chaos, which had earlier been introduced by Yorke. We discuss issues involved in choosing the properties that characterize chaos. We also discuss how this term can be combined with the definition of an attractor. 1. Introduction J. Yorke coined the word `chaos' as applied to deterministic systems. R. Devaney gave the first mathematical definition for a map to be chaotic on the whole space where a map is defined. Since that time, there have been several different definitions of chaos which emphasize different aspects of the map. Some of these are more computable and others are more mathematical. See [9] a comparison of many of these definitions. There is probably no one best or correct definition of chaos. In this paper, we discuss what we feel is one of better mathematical definition. (It may not be as computable as some of the other definitions, e.g., the one by Alligood, Sauer, and Yorke.) Our definition is very similar to the one given by Martelli in [8] and [9]. We also combine the concepts of chaos and attractors and discuss chaotic attractors. 2. Basic definitions We start by giving the basic definitions needed to define a chaotic attractor. We give the definitions for a diffeomorphism (or map), but those for a system of differential equations are similar. The orbit of a point x∗ by F is the set O(x∗; F) = f Fi(x∗) : i 2 Z g. An invariant set for a diffeomorphism F is an set A in the domain such that F(A) = A. -
The Age of Addiction David T. Courtwright Belknap (2019) Opioids
The Age of Addiction David T. Courtwright Belknap (2019) Opioids, processed foods, social-media apps: we navigate an addictive environment rife with products that target neural pathways involved in emotion and appetite. In this incisive medical history, David Courtwright traces the evolution of “limbic capitalism” from prehistory. Meshing psychology, culture, socio-economics and urbanization, it’s a story deeply entangled in slavery, corruption and profiteering. Although reform has proved complex, Courtwright posits a solution: an alliance of progressives and traditionalists aimed at combating excess through policy, taxation and public education. Cosmological Koans Anthony Aguirre W. W. Norton (2019) Cosmologist Anthony Aguirre explores the nature of the physical Universe through an intriguing medium — the koan, that paradoxical riddle of Zen Buddhist teaching. Aguirre uses the approach playfully, to explore the “strange hinterland” between the realities of cosmic structure and our individual perception of them. But whereas his discussions of time, space, motion, forces and the quantum are eloquent, the addition of a second framing device — a fictional journey from Enlightenment Italy to China — often obscures rather than clarifies these chewy cosmological concepts and theories. Vanishing Fish Daniel Pauly Greystone (2019) In 1995, marine biologist Daniel Pauly coined the term ‘shifting baselines’ to describe perceptions of environmental degradation: what is viewed as pristine today would strike our ancestors as damaged. In these trenchant essays, Pauly trains that lens on fisheries, revealing a global ‘aquacalypse’. A “toxic triad” of under-reported catches, overfishing and deflected blame drives the crisis, he argues, complicated by issues such as the fishmeal industry, which absorbs a quarter of the global catch. -
MA427 Ergodic Theory
MA427 Ergodic Theory Course Notes (2012-13) 1 Introduction 1.1 Orbits Let X be a mathematical space. For example, X could be the unit interval [0; 1], a circle, a torus, or something far more complicated like a Cantor set. Let T : X ! X be a function that maps X into itself. Let x 2 X be a point. We can repeatedly apply the map T to the point x to obtain the sequence: fx; T (x);T (T (x));T (T (T (x))); : : : ; :::g: We will often write T n(x) = T (··· (T (T (x)))) (n times). The sequence of points x; T (x);T 2(x);::: is called the orbit of x. We think of applying the map T as the passage of time. Thus we think of T (x) as where the point x has moved to after time 1, T 2(x) is where the point x has moved to after time 2, etc. Some points x 2 X return to where they started. That is, T n(x) = x for some n > 1. We say that such a point x is periodic with period n. By way of contrast, points may move move densely around the space X. (A sequence is said to be dense if (loosely speaking) it comes arbitrarily close to every point of X.) If we take two points x; y of X that start very close then their orbits will initially be close. However, it often happens that in the long term their orbits move apart and indeed become dramatically different. -
Project-Team Virtual Plants Modeling Plant Morphogenesis from Genes To
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE Project-Team Virtual Plants Modeling plant morphogenesis from genes to phenotype Sophia Antipolis THEME BIO c t i v it y ep o r t 2005 Table of contents 1. Team 1 2. Overall Objectives 2 2.1. Overall Objectives 2 3. Scientific Foundations 2 3.1. Analysis of structures resulting from meristem activity 2 3.2. Meristem functioning and development 3 3.3. A software platform for plant modeling 4 4. New Results 4 4.1. Analysis of structures resulting from meristem activity 4 4.1.1. Analysis of longitudinal count data and underdispersion 4 4.1.2. Growth synchronism between Aerial and Root Systems 4 4.1.3. Changes in branching structures within the whole plants 5 4.1.4. Growth components in trees 5 4.1.5. Markov switching models 5 4.1.6. Diagnostic tools for hidden Markovian models 5 4.1.7. Hidden Markov tree models for investigating physiological age within plants 6 4.1.8. Branching processes for plant development analysis 6 4.1.9. Self-similarity in plants 6 4.1.10. Reconstruction of plant foliage density from photographs 6 4.1.11. Fractal analysis of plant geometry 6 4.1.12. Light interception by canopy 7 4.1.13. Heritability of architectural traits 7 4.2. Meristem functioning and development 8 4.2.1. 3D surface reconstruction and cell lineage detection in shoot meristems 8 4.2.2. Simulation of auxin fluxes in the mersitem 8 4.2.3. Dynamic model of phyllotaxy based on auxin fluxes 8 4.2.4. -
Attractors and Orbit-Flip Homoclinic Orbits for Star Flows
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 141, Number 8, August 2013, Pages 2783–2791 S 0002-9939(2013)11535-2 Article electronically published on April 12, 2013 ATTRACTORS AND ORBIT-FLIP HOMOCLINIC ORBITS FOR STAR FLOWS C. A. MORALES (Communicated by Bryna Kra) Abstract. We study star flows on closed 3-manifolds and prove that they either have a finite number of attractors or can be C1 approximated by vector fields with orbit-flip homoclinic orbits. 1. Introduction The notion of attractor deserves a fundamental place in the modern theory of dynamical systems. This assertion, supported by the nowadays classical theory of turbulence [27], is enlightened by the recent Palis conjecture [24] about the abun- dance of dynamical systems with finitely many attractors absorbing most positive trajectories. If confirmed, such a conjecture means the understanding of a great part of dynamical systems in the sense of their long-term behaviour. Here we attack a problem which goes straight to the Palis conjecture: The fini- tude of the number of attractors for a given dynamical system. Such a problem has been solved positively under certain circunstances. For instance, we have the work by Lopes [16], who, based upon early works by Ma˜n´e [18] and extending pre- vious ones by Liao [15] and Pliss [25], studied the structure of the C1 structural stable diffeomorphisms and proved the finitude of attractors for such diffeomor- phisms. His work was largely extended by Ma˜n´e himself in the celebrated solution of the C1 stability conjecture [17]. On the other hand, the Japanesse researchers S. -
General Guide to the Science and Cosmos Museum
General guide to the Science and Cosmos Museum 1 Background: “Tenerife monts” and “Pico” near of Plato crater in the Moon PLANTA TERRAZA Terrace Floor 5 i 2 1 4 6 3 ASCENSOR 4 RELOJ DE SOL ECUATORIAL Elevator Analemmatic sundial i INFORMACIÓN 5 BUSTO PARLANTE Information “AGUSTÍN DE BETANCOURT” Agustín de Betancourt 1 PLAZA “AGUSTÍN DE talking bust BETANCOURT” Agustín de Betancourt 6 ZONA WI-FI Square Wi-Fi zone 2 ANTENA DE RADIOASTRONOMÍA Radioastronomy antenna 3 TELESCOPIO Telescope PLANTA BAJA Ground Floor WC 10 9 8 11 7 1 6 5 4 12 2 3 ASCENSOR Cosmos Lab - Creative Elevator Laboratory 1 EXPOSICIÓN 7 PLANETARIO Exhibition Planetarium 2 TALLER DE DIDÁCTICA 8 SALIDA DE EMERGENCIA Didactic Workshop Emergency exit 3 EFECTOS ÓPTICOS 9 MICROCOSMOS Optical illusions 10 SALÓN DE ACTOS 4 SALA CROMA KEY Assembly hall Chroma Key room 11 EXPOSICIONES TEMPORALES 5 LABERINTO DE ESPEJOS Temporary exhibitions Mirror Labyrinth 12 ZONA DE DESCANSO 6 COSMOS LAB - LABORATORIO Rest zone CREATIVO CONTENIDOS Contents 7 LA TIERRA The Earth 23 EL SOL The Sun 33 EL UNIVERSO The Universe 45 CÓMO FUNCIONA How does it work 72 EL CUERPO HUMANO The human body 5 ¿POR QUÉ PIRÁMIDES? Why pyramids? 1 Sacred places have often been con- ceived of as elevated spaces that draw the believer closer to the divi- nity. For this reason, once architec- tural techniques became sufficiently refined, mosques or cathedrals rai- sed their vaults, minarets, towers and spires to the sky. However, for thousands of years, the formula fa- voured by almost every culture was the pyramid. -
An Introduction Into Ecological Modelling for Students, Teachers & Scientists
Modelling Complex Ecological Dynamics . Fred Jopp l Hauke Reuter l Broder Breckling Editors Modelling Complex Ecological Dynamics An Introduction into Ecological Modelling for Students, Teachers & Scientists Title Drawings by Melanie Trexler Foreword by Sven Erik Jørgensen & Donald L. DeAngelis Editors Dr. Fred Jopp Dr. Hauke Reuter Department of Biology Department of Ecological Modelling University of Miami Leibniz Center for Tropical Marine Ecology P.O. Box 249118 GmbH (ZMT) Coral Gables, FL 33124 Fahrenheitstraße 6 USA 28359 Bremen [email protected] Germany [email protected] Dr. Broder Breckling General and Theoretical Ecology Center for Environmental Research and Sustainable Technology (UFT) University of Bremen Leobener St. 28359 Bremen Germany [email protected] ISBN 978-3-642-05028-2 e-ISBN 978-3-642-05029-9 DOI 10.1007/978-3-642-05029-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011921703 # Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protec- tive laws and regulations and therefore free for general use. -
Annotated List of References Tobias Keip, I7801986 Presentation Method: Poster
Personal Inquiry – Annotated list of references Tobias Keip, i7801986 Presentation Method: Poster Poster Section 1: What is Chaos? In this section I am introducing the topic. I am describing different types of chaos and how individual perception affects our sense for chaos or chaotic systems. I am also going to define the terminology. I support my ideas with a lot of examples, like chaos in our daily life, then I am going to do a transition to simple mathematical chaotic systems. Larry Bradley. (2010). Chaos and Fractals. Available: www.stsci.edu/~lbradley/seminar/. Last accessed 13 May 2010. This website delivered me with a very good introduction into the topic as there are a lot of books and interesting web-pages in the “References”-Sektion. Gleick, James. Chaos: Making a New Science. Penguin Books, 1987. The book gave me a very general introduction into the topic. Harald Lesch. (2003-2007). alpha-Centauri . Available: www.br-online.de/br- alpha/alpha-centauri/alpha-centauri-harald-lesch-videothek-ID1207836664586.xml. Last accessed 13. May 2010. A web-page with German video-documentations delivered a lot of vivid examples about chaos for my poster. Poster Section 2: Laplace's Demon and the Butterfly Effect In this part I describe the idea of the so called Laplace's Demon and the theory of cause-and-effect chains. I work with a lot of examples, especially the famous weather forecast example. Also too I introduce the mathematical concept of a dynamic system. Jeremy S. Heyl (August 11, 2008). The Double Pendulum Fractal. British Columbia, Canada. -
Pattern, the Visual Mathematics: a Search for Logical Connections in Design Through Mathematics, Science, and Multicultural Arts
Rochester Institute of Technology RIT Scholar Works Theses 6-1-1996 Pattern, the visual mathematics: A search for logical connections in design through mathematics, science, and multicultural arts Seung-eun Lee Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Lee, Seung-eun, "Pattern, the visual mathematics: A search for logical connections in design through mathematics, science, and multicultural arts" (1996). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. majWiif." $0-J.zn jtiJ jt if it a mtrc'r icjened thts (waefii i: Tkirr. afaidiid to bz i d ! -Lrtsud a i-trio. of hw /'' nvwte' mfratWf trawwi tpf .w/ Jwitfl- ''','-''' ftatsTB liovi 'itcj^uitt <t. dt feu. Tfui ;: tti w/ik'i w cWii.' cental cj lniL-rital. p-siod. [Jewy anJ ./tr.-.MTij of'irttion. fan- 'mo' that. I: wo!'.. PicrdoTrKwe, wiifi id* .or.if'iifer -now r't.t/ry summary Jfem2>/x\, i^zA 'jX7ipu.lv z&ietQStd (Xtrma iKc'i-J: ffocub. The (i^piicaiom o". crWx< M Wf flrtu't. fifesspwn, Jiii*iaiin^ jfli dtfifi,tmi jpivxei u3ili'-rCi luvjtv-tzxi patcrr? ;i t. drifters vcy. Symmetr, yo The theoretical concepts of symmetry deal with group theory and figure transformations. Figure transformations, or symmetry operations refer to the movement and repetition of an one-, two , and three-dimensional space. (f_8= I lhowtuo irwti) familiar iltjpg .