DOCSLIB.ORG

Insieme Di Mandelbrot - Wikipedia

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Insieme Di Mandelbrot - Wikipedia Insieme di Mandelbrot - Wikipedia https://it.wikipedia.org/wiki/Insieme_di_Mandelbrot Insieme di Mandelbrot Da Wikipedia, l'enciclopedia libera. L'insieme di Mandelbrot o frattale di Mandelbrot è uno dei frattali più popolari, conosciuto anche al di fuori dell'ambito matematico per le suggestive immagini multicolori che ne sono state divulgate.[1] È l'insieme dei numeri complessi per i quali la successione definita da: [2] è limitata. Nonostante la semplicità della Una rappresentazione dell'insieme di definizione, l'insieme ha una forma Mandelbrot. complessa il cui contorno è un frattale. Solo con l'avvento del computer è stato possibile visualizzarlo. L'insieme prende il nome da Benoît Mandelbrot, colui che nel suo libro Les Objects Fractals: Forme, Hazard et Dimension (1975) rese popolari i frattali. Indice 1 Storia 2 Definizione formale 3 Rappresentazione grafica 4 Relazione con gli insiemi di Julia 5 Galleria d'immagini 6 Note 7 Bibliografia 8 Voci correlate 9 Altri progetti 10 Collegamenti esterni Storia 1 di 8 27/12/2016 10:55 Insieme di Mandelbrot - Wikipedia https://it.wikipedia.org/wiki/Insieme_di_Mandelbrot L'insieme di Mandelbrot si colloca nel campo della dinamica complessa, il cui studio inizia con i matematici francesi Pierre Fatou e Gaston Julia all'inizio del XX secolo. I primi disegni dell'insieme di Mandelbrot risalgono al 1978 e fanno parte di uno studio di Robert Brooks e Peter Matelski riguardante i gruppi kleiniani;[3] è Benoît Mandelbrot nel 1980 a visualizzare per primo la forma che oggi porta il suo nome e a riconoscere che si tratta di un frattale.[4][5] Lo studio approfondito di questo insieme La prima immagine pubblica dell'insieme comincia nel 1984 con il lavoro dei di Mandelbrot creata da Robert W. Brooks e matematici Adrien Douady e John H. Hubbard, che ne scoprono molte Peter Matelski nel 1978 fondamentali proprietà e gli danno il nome di Mandelbrot.[6] L'articolo di copertina del numero di Scientific American dell'agosto 1985, tradotto in italiano su Le Scienze nell'ottobre dello stesso anno, rappresenta un'immagine creata da Benoît Mandelbrot, Heinz-Otto Peitgen e John H. Hubbard; in quell'articolo l'insieme è definito "l'oggetto più complesso esistente in matematica" e, grazie anche alle colorate immagini che accompagnano l'articolo, inizia la popolarità dell'insieme anche presso il grande pubblico.[7][8][9] I matematici Heinz-Otto Peitgen e Peter Richter diventano famosi promuovendo l'insieme con fotografie, libri e raccolte d'immagini.[10] Il lavoro di Douady e Hubbard coincide con una grande crescita d'interesse nella dinamica complessa e lo studio dell'insieme di Mandelbrot è subito un elemento centrale di questo campo. Una lista completa di tutti i matematici che da allora contribuiscono alla comprensione di questo insieme è al di là degli scopi di questa voce, ma una tale lista includerebbe senz'altro ai primi posti Mikhail Lyubich,[11][12] Curt McMullen, John Milnor, Mitsuhiro Shishikura e Jean-Christophe Yoccoz. Definizione formale L'insieme di Mandelbrot è definito a partire da una famiglia di polinomi quadratici complessi: nella forma: 2 di 8 27/12/2016 10:55 Insieme di Mandelbrot - Wikipedia https://it.wikipedia.org/wiki/Insieme_di_Mandelbrot dove è un parametro complesso. Per ogni si considera il comportamento della successione ottenuta iterando a partire dal punto ; questa può o divergere all'infinito oppure essere limitata. L'insieme di Mandelbrot è definito come l'insieme dei punti tali che la corrispondente successione è limitata. Una rappresentazione matematica rigorosa dell'insieme di Mandelbrot M. I punti che Più formalmente, se indica l'n-esima appartengono all'insieme sono colorati di iterata di (cioè composta con sé nero, i restanti di bianco. stessa n volte), l'insieme di Mandelbrot è il sottoinsieme del piano complesso dato da: Si può dimostrare che se il modulo di è maggiore di allora la successione divergerà e quindi il punto sarà esterno all'insieme di Mandelbrot. Rappresentazione grafica Dal punto di vista matematico, l'insieme di Mandelbrot è semplicemente un insieme di numeri complessi. Ogni numero complesso può appartenere a oppure no. Una rappresentazione grafica rigorosa dell'insieme di Mandelbrot si ottiene colorando tutti i punti che appartengono a di nero e gli altri di bianco. Le immagini multicolori che si vedono sono generate colorando i punti esterni all'insieme in dipendenza di "quanto velocemente" la sequenza diverge all'infinito. Il minimo valore di per cui Zoom nell'insieme è un indice di quanto "lontano dal contorno" si trova un punto e viene utilizzato per la rappresentazione "a colori". 3 di 8 27/12/2016 10:55 Insieme di Mandelbrot - Wikipedia https://it.wikipedia.org/wiki/Insieme_di_Mandelbrot Paradossalmente, i punti colorati che conferiscono il fascino al frattale di Mandelbrot sono proprio quelli che non appartengono all'insieme.[13] Relazione con gli insiemi di Julia L'insieme di Mandelbrot permette di indicizzare gli insiemi di Julia. Ad ogni punto del piano complesso corrisponde un diverso insieme di Julia; tale insieme è connesso se il punto in questione appartiene all'insieme di Mandelbrot, ed è invece non connesso se il punto non vi appartiene. Intuitivamente, gli insiemi di Julia più interessanti (ovvero quelli dalle forme meno banali) corrispondono a punti che si trovano vicino al bordo dell'insieme di Mandelbrot, mentre punti molto all'interno generano insiemi di Julia dalle forme geometriche semplici e i punti esterni, lontani dal bordo, generano insiemi di Julia formati da molti piccoli insiemi connessi. Galleria d'immagini Inizio Passo 1 4 di 8 27/12/2016 10:55 Insieme di Mandelbrot - Wikipedia https://it.wikipedia.org/wiki/Insieme_di_Mandelbrot Passo 2 Passo 3 Passo 4 Passo 5 Passo 6 Passo 7 Passo 8 Passo 9 5 di 8 27/12/2016 10:55 Insieme di Mandelbrot - Wikipedia https://it.wikipedia.org/wiki/Insieme_di_Mandelbrot Passo 10 Passo 11 Passo 12 Passo 13 Passo 14 Note 1. ^ Unione matematica italiana, Bollettino della Unione matematica italiana: Matematica nella società e nella cultura, Bologna, N. Zanichelli, 2001, p. 236. 2. ^ (EN) Mandelbrot Set Explorer: Mathematical Glossary , math.bu.edu. URL consultato il 7 ottobre 2007. 3. ^ Robert Brooks e Peter Matelski, The dynamics of 2-generator subgroups of PSL(2,C), in "Riemann Surfaces and Related Topics", ed. Kra and Maskit, Ann. Math. Stud. 97, 65–71, ISBN 0-691-08264-2 4. ^ (EN) Benoît Mandelbrot, Fractal aspects of the iteration of for complex 6 di 8 27/12/2016 10:55 Insieme di Mandelbrot - Wikipedia https://it.wikipedia.org/wiki/Insieme_di_Mandelbrot , Annals NY Acad. Sci. 357, 249/259 5. ^ (EN) R.P. Taylor & J.C. Sprott, Biophilic Fractals and the Visual Journey of Organic Screen- savers (PDF), su Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 12, No. 1, Society for Chaos Theory in Psychology & Life Sciences, 2008. URL consultato il 1º gennaio 2009. 6. ^ (FR) Adrien Douady e John H. Hubbard, Etude dynamique des polynômes complexes, Prépublications mathémathiques d'Orsay 2/4 (1984 / 1985) 7. ^ (EN) John Briggs, Fractals: The Patterns of Chaos. 1992, p 80. 8. ^ Archimede, Voll. 39-40; Le Monnier, 1987. p. 109. 9. ^ Mandelbrot, p. 259 10. ^ (EN) James Gleick, Chaos: Making a New Science, 1987. p. 229. 11. ^ Lyubich, Mikhail, Six Lectures on Real and Complex Dynamics , maggio-giugno, 1999. URL consultato il 4 aprile 2007. 12. ^ Mikhail Lyubich, Regular and stochastic dynamics in the real quadratic family (PDF), in Proceedings of the National Academy of Sciences of the United States of America, vol. 95, novembre 1998, pp. 14025-14027, DOI:10.1073/pnas.95.24.14025 . URL consultato il 4 aprile 2007. 13. ^ M. Rita Laganà,, Marco Righi; Francesco Romani, Informatica. Concetti e sperimentazioni, 2ª ed., Apogeo Editore, 2007, p. 145. Bibliografia (EN) Benoît Mandelbrot, Fractals and chaos: the Mandelbrot set and beyond, Springer, 2004, ISBN 0-387-20158-0. Voci correlate Buddhabrot Burning ship Costanti di Feigenbaum Altri progetti Wikimedia Commons (https://commons.wikimedia.org/wiki/?uselang=it) contiene immagini o altri file sugli insiemi di Mandelbrot (https://commons.wikimedia.org/wiki/Category:Mandelbrot_sets?uselang=it) Collegamenti esterni Benoit Mandelbrot: Frattali e l'arte della rugosità (http://www.ted.com/talks/lang/it /benoit_mandelbrot_fractals_the_art_of_roughness.html) , TED Chaos and Fractals , su Open Directory Project, Netscape Communications. (Segnala (http://www.dmoz.org/public/suggest?cat=Science/Math/Chaos_and_Fractals/) su DMoz un 7 di 8 27/12/2016 10:55 Insieme di Mandelbrot - Wikipedia https://it.wikipedia.org/wiki/Insieme_di_Mandelbrot collegamento pertinente all'argomento "Chaos and Fractals") Estratto da "https://it.wikipedia.org/w/index.php?title=Insieme_di_Mandelbrot& oldid=84448351" Categoria: Frattali | [altre] Questa pagina è stata modificata per l'ultima volta il 24 nov 2016 alle 14:20. Il testo è disponibile secondo la licenza Creative Commons Attribuzione-Condividi allo stesso modo; possono applicarsi condizioni ulteriori. Vedi le Condizioni d'uso per i dettagli. Wikipedia® è un marchio registrato della Wikimedia Foundation, Inc. 8 di 8 27/12/2016 10:55.
Load more

Recommended publications
  • 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.
    [Show full text]
  • Learning from Benoit Mandelbrot
    2/28/18, 7(59 AM Page 1 of 1 February 27, 2018 Learning from Benoit Mandelbrot If you've been reading some of my recent posts, you will have noted my, and the Investment Masters belief, that many of the investment theories taught in most business schools are flawed. And they can be dangerous too, the recent Financial Crisis is evidence of as much. One man who, prior to the Financial Crisis, issued a challenge to regulators including the Federal Reserve Chairman Alan Greenspan, to recognise these flaws and develop more realistic risk models was Benoit Mandelbrot. Over the years I've read a lot of investment books, and the name Benoit Mandelbrot comes up from time to time. I recently finished his book 'The (Mis)Behaviour of Markets - A Fractal View of Risk, Ruin and Reward'. So who was Benoit Mandelbrot, why is he famous, and what can we learn from him? Benoit Mandelbrot was a Polish-born mathematician and polymath, a Sterling Professor of Mathematical Sciences at Yale University and IBM Fellow Emeritus (Physics) who developed a new branch of mathematics known as 'Fractal' geometry. This geometry recognises the hidden order in the seemingly disordered, the plan in the unplanned, the regular pattern in the irregularity and roughness of nature. It has been successfully applied to the natural sciences helping model weather, study river flows, analyse brainwaves and seismic tremors. A 'fractal' is defined as a rough or fragmented shape that can be split into parts, each of which is at least a close approximation of its original-self.
    [Show full text]
  • Role of Nonlinear Dynamics and Chaos in Applied Sciences
    v.;.;.:.:.:.;.;.^ ROLE OF NONLINEAR DYNAMICS AND CHAOS IN APPLIED SCIENCES by Quissan V. Lawande and Nirupam Maiti Theoretical Physics Oivisipn 2000 Please be aware that all of the Missing Pages in this document were originally blank pages BARC/2OOO/E/OO3 GOVERNMENT OF INDIA ATOMIC ENERGY COMMISSION ROLE OF NONLINEAR DYNAMICS AND CHAOS IN APPLIED SCIENCES by Quissan V. Lawande and Nirupam Maiti Theoretical Physics Division BHABHA ATOMIC RESEARCH CENTRE MUMBAI, INDIA 2000 BARC/2000/E/003 BIBLIOGRAPHIC DESCRIPTION SHEET FOR TECHNICAL REPORT (as per IS : 9400 - 1980) 01 Security classification: Unclassified • 02 Distribution: External 03 Report status: New 04 Series: BARC External • 05 Report type: Technical Report 06 Report No. : BARC/2000/E/003 07 Part No. or Volume No. : 08 Contract No.: 10 Title and subtitle: Role of nonlinear dynamics and chaos in applied sciences 11 Collation: 111 p., figs., ills. 13 Project No. : 20 Personal authors): Quissan V. Lawande; Nirupam Maiti 21 Affiliation ofauthor(s): Theoretical Physics Division, Bhabha Atomic Research Centre, Mumbai 22 Corporate authoifs): Bhabha Atomic Research Centre, Mumbai - 400 085 23 Originating unit : Theoretical Physics Division, BARC, Mumbai 24 Sponsors) Name: Department of Atomic Energy Type: Government Contd...(ii) -l- 30 Date of submission: January 2000 31 Publication/Issue date: February 2000 40 Publisher/Distributor: Head, Library and Information Services Division, Bhabha Atomic Research Centre, Mumbai 42 Form of distribution: Hard copy 50 Language of text: English 51 Language of summary: English 52 No. of references: 40 refs. 53 Gives data on: Abstract: Nonlinear dynamics manifests itself in a number of phenomena in both laboratory and day to day dealings.
    [Show full text]
  • 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.
    [Show full text]
  • Mild Vs. Wild Randomness: Focusing on Those Risks That Matter
    with empirical sense1. Granted, it has been Mild vs. Wild Randomness: tinkered with using such methods as Focusing on those Risks that complementary “jumps”, stress testing, regime Matter switching or the elaborate methods known as GARCH, but while they represent a good effort, Benoit Mandelbrot & Nassim Nicholas Taleb they fail to remediate the bell curve’s irremediable flaws. Forthcoming in, The Known, the Unknown and the The problem is that measures of uncertainty Unknowable in Financial Institutions Frank using the bell curve simply disregard the possibility Diebold, Neil Doherty, and Richard Herring, of sharp jumps or discontinuities. Therefore they editors, Princeton: Princeton University Press. have no meaning or consequence. Using them is like focusing on the grass and missing out on the (gigantic) trees. Conventional studies of uncertainty, whether in statistics, economics, finance or social science, In fact, while the occasional and unpredictable have largely stayed close to the so-called “bell large deviations are rare, they cannot be dismissed curve”, a symmetrical graph that represents a as “outliers” because, cumulatively, their impact in probability distribution. Used to great effect to the long term is so dramatic. describe errors in astronomical measurement by The good news, especially for practitioners, is the 19th-century mathematician Carl Friedrich that the fractal model is both intuitively and Gauss, the bell curve, or Gaussian model, has computationally simpler than the Gaussian. It too since pervaded our business and scientific culture, has been around since the sixties, which makes us and terms like sigma, variance, standard deviation, wonder why it was not implemented before. correlation, R-square and Sharpe ratio are all The traditional Gaussian way of looking at the directly linked to it.
    [Show full text]
  • Transformations)
    TRANSFORMACJE (TRANSFORMATIONS) Transformacje (Transformations) is an interdisciplinary refereed, reviewed journal, published since 1992. The journal is devoted to i.a.: civilizational and cultural transformations, information (knowledge) societies, global problematique, sustainable development, political philosophy and values, future studies. The journal's quasi-paradigm is TRANSFORMATION - as a present stage and form of development of technology, society, culture, civilization, values, mindsets etc. Impacts and potentialities of change and transition need new methodological tools, new visions and innovation for theoretical and practical capacity-building. The journal aims to promote inter-, multi- and transdisci- plinary approach, future orientation and strategic and global thinking. Transformacje (Transformations) are internationally available – since 2012 we have a licence agrement with the global database: EBSCO Publishing (Ipswich, MA, USA) We are listed by INDEX COPERNICUS since 2013 I TRANSFORMACJE(TRANSFORMATIONS) 3-4 (78-79) 2013 ISSN 1230-0292 Reviewed journal Published twice a year (double issues) in Polish and English (separate papers) Editorial Staff: Prof. Lech W. ZACHER, Center of Impact Assessment Studies and Forecasting, Kozminski University, Warsaw, Poland ([email protected]) – Editor-in-Chief Prof. Dora MARINOVA, Sustainability Policy Institute, Curtin University, Perth, Australia ([email protected]) – Deputy Editor-in-Chief Prof. Tadeusz MICZKA, Institute of Cultural and Interdisciplinary Studies, University of Silesia, Katowice, Poland ([email protected]) – Deputy Editor-in-Chief Dr Małgorzata SKÓRZEWSKA-AMBERG, School of Law, Kozminski University, Warsaw, Poland ([email protected]) – Coordinator Dr Alina BETLEJ, Institute of Sociology, John Paul II Catholic University of Lublin, Poland Dr Mirosław GEISE, Institute of Political Sciences, Kazimierz Wielki University, Bydgoszcz, Poland (also statistical editor) Prof.
    [Show full text]
  • Bézier Curves Are Attractors of Iterated Function Systems
    New York Journal of Mathematics New York J. Math. 13 (2007) 107–115. All B´ezier curves are attractors of iterated function systems Chand T. John Abstract. The fields of computer aided geometric design and fractal geom- etry have evolved independently of each other over the past several decades. However, the existence of so-called smooth fractals, i.e., smooth curves or sur- faces that have a self-similar nature, is now well-known. Here we describe the self-affine nature of quadratic B´ezier curves in detail and discuss how these self-affine properties can be extended to other types of polynomial and ra- tional curves. We also show how these properties can be used to control shape changes in complex fractal shapes by performing simple perturbations to smooth curves. Contents 1. Introduction 107 2. Quadratic B´ezier curves 108 3. Iterated function systems 109 4. An IFS with a QBC attractor 110 5. All QBCs are attractors of IFSs 111 6. Controlling fractals with B´ezier curves 112 7. Conclusion and future work 114 References 114 1. Introduction In the late 1950s, advancements in hardware technology made it possible to effi- ciently manufacture curved 3D shapes out of blocks of wood or steel. It soon became apparent that the bottleneck in mass production of curved 3D shapes was the lack of adequate software for designing these shapes. B´ezier curves were first introduced in the 1960s independently by two engineers in separate French automotive compa- nies: first by Paul de Casteljau at Citro¨en, and then by Pierre B´ezier at R´enault.
    [Show full text]
  • Τα Cellular Automata Στο Σχεδιασμό
    τα cellular automata στο σχεδιασμό μια προσέγγιση στις αναδρομικές σχεδιαστικές διαδικασίες Ηρώ Δημητρίου επιβλέπων Σωκράτης Γιαννούδης 2 Πολυτεχνείο Κρήτης Τμήμα Αρχιτεκτόνων Μηχανικών ερευνητική εργασία Ηρώ Δημητρίου επιβλέπων καθηγητής Σωκράτης Γιαννούδης Τα Cellular Automata στο σχεδιασμό μια προσέγγιση στις αναδρομικές σχεδιαστικές διαδικασίες Χανιά, Μάιος 2013 Chaos and Order - Carlo Allarde περιεχόμενα 0001. εισαγωγή 7 0010. χάος και πολυπλοκότητα 13 a. μια ιστορική αναδρομή στο χάος: Henri Poincare - Edward Lorenz 17 b. το χάος 22 c. η πολυπλοκότητα 23 d. αυτοοργάνωση και emergence 29 0011. cellular automata 31 0100. τα cellular automata στο σχεδιασμό 39 a. τα CA στην στην αρχιτεκτονική: Paul Coates 45 b. η φιλοσοφική προσέγγιση της διεπιστημονικότητας του σχεδιασμού 57 c. προσομοίωση της αστικής ανάπτυξης μέσω CA 61 d. η περίπτωση της Changsha 63 0101. συμπεράσματα 71 βιβλιογραφία 77 1. Metamorphosis II - M.C.Escher 6 0001. εισαγωγή Η επιστήμη εξακολουθεί να είναι η εξ αποκαλύψεως προφητική περιγραφή του κόσμου, όπως αυτός φαίνεται από ένα θεϊκό ή δαιμονικό σημείο αναφοράς. Ilya Prigogine 7 0001. 8 0001. Στοιχεία της τρέχουσας αρχιτεκτονικής θεωρίας και μεθοδολογίας προτείνουν μια εναλλακτική λύση στις πάγιες αρχιτεκτονικές μεθοδολογίες και σε ορισμένες περιπτώσεις υιοθετούν πτυχές του νέου τρόπου της κατανόησής μας για την επιστήμη. Αυτά τα στοιχεία εμπίπτουν σε τρεις κατηγορίες. Πρώτον, μεθοδολογίες που προτείνουν μια εναλλακτική λύση για τη γραμμικότητα και την αιτιοκρατία της παραδοσιακής αρχιτεκτονικής σχεδιαστικής διαδικασίας και θίγουν τον κεντρικό έλεγχο του αρχιτέκτονα, δεύτερον, η πρόταση μιας μεθοδολογίας με βάση την προσομοίωση της αυτο-οργάνωσης στην ανάπτυξη και εξέλιξη των φυσικών συστημάτων και τρίτον, σε ορισμένες περιπτώσεις, συναρτήσει των δύο προηγούμενων, είναι μεθοδολογίες οι οποίες πειραματίζονται με την αναδυόμενη μορφή σε εικονικά περιβάλλοντα.
    [Show full text]
  • Books in Brief Hypothesis Might Be That a New Drug Has No Effect
    BOOKS & ARTS COMMENT includes not just one correct answer, but all other possibilities. In a medical experiment, the null Books in brief hypothesis might be that a new drug has no effect. But the hypothesis will come pack- The Age of Addiction aged in a statistical model that assumes that David T. Courtwright BELKNAP (2019) there is zero systematic error. This is not Opioids, processed foods, social-media apps: we navigate an necessarily true: errors can arise even in a addictive environment rife with products that target neural pathways randomized, blinded study, for example if involved in emotion and appetite. In this incisive medical history, some participants work out which treatment David Courtwright traces the evolution of “limbic capitalism” from group they have been assigned to. This can prehistory. Meshing psychology, culture, socio-economics and lead to rejection of the null hypothesis even urbanization, it’s a story deeply entangled in slavery, corruption when the new drug has no effect — as can and profiteering. Although reform has proved complex, Courtwright other complexities, such as unmodelled posits a solution: an alliance of progressives and traditionalists aimed measurement error. at combating excess through policy, taxation and public education. To say that P = 0.05 should lead to acceptance of the alternative hypothesis is tempting — a few million scientists do it Cosmological Koans every year. But it is wrong, and has led to Anthony Aguirre W. W. NORTON (2019) replication crises in many areas of the social, Cosmologist Anthony Aguirre explores the nature of the physical behavioural and biological sciences. Universe through an intriguing medium — the koan, that paradoxical Statistics — to paraphrase Homer riddle of Zen Buddhist teaching.
    [Show full text]
  • Towards a Theory of Social Fractal Discourse: Some Tentative Ideas
    Page 1 of 16 ANZAM 2012 Towards a Theory of Social Fractal Discourse: Some Tentative Ideas Dr James Latham Faculty of Business and Enterprise, Swinburne University of Technology, Victoria, Australia Email: [email protected] Amanda Muhleisen PhD Candidate, Faculty of Business and Enterprise, Swinburne University of Technology, Victoria, Australia Email: [email protected] Prof Robert Jones Faculty of Business and Enterprise, Swinburne University of Technology, Victoria, Australia Email: [email protected] ANZAM 2012 Page 2 of 16 ABSTRACT The development of chaos theory and fractal geometry has made significant contribution to our understanding of the natural world. As students of organization, chaos theory provides an opportunity to broaden our thinking beyond the linear and predictable with its presumed stability, in order to embrace chaos rather than stability as the ‘default’ state for organization. This demands we think in new ways about organizational theory and practice. It also creates a schism in the fabric of our knowledge - a divide to be bridged. By taking the scientific concept of fractals and applying it to a social theory of discourse, this paper hopes to emerge some tentative ideas around developing a theory of social fractal discourse. Keywords: chaos theory, instability, organizing as process, critical discourse analysis, complexity The aim of this paper is to outline a number of tentative ideas around the development of a theory of social fractal discourse. It will focus on qualities and features of fractal and chaotic systems. Drawing on ideas from chaos and complexity theory, we will argue that discourse can be fractal. While there is some difference in theoretical constructs within the complexity literature, we will use the terms fractal and chaos interchangeably throughout this paper.
    [Show full text]
  • |||GET||| Geometrical Kaleidoscope 1St Edition
    GEOMETRICAL KALEIDOSCOPE 1ST EDITION DOWNLOAD FREE Boris Pritsker | 9780486812410 | | | | | A Mathematical Kaleidoscope In Sir David Brewster conducted experiments on light polarization by successive reflections between plates of glass and first noted "the circular arrangement of the images of a candle round a center, and the multiplication of the sectors formed by the extremities of the plates of glass". Seller Inventory xr Geometrical Kaleidoscope Dover Books on Mathematics. Page Count: Most kaleidoscopes are mass-produced from inexpensive materials, and intended as children's toys. In Stock. In his Treatise on the Kaleidoscope he described the Geometrical Kaleidoscope 1st edition form with an object cell:. Institutional Subscription. Buddhabrot Orbit trap Pickover stalk. Kaleidoscope Artistry. Condition: New. View on ScienceDirect. The volume is divided into sections on individual topics such as "Medians of a Triangle," and "Area of a Quadrilateral. All of these choices strike me as entirely reasonable and appropriate for a book at this level. Buy New Learn more about this copy. Updating Results. This triggered more experiments to find the conditions for the most beautiful and symmetrically perfect conditions. An early version had pieces of colored glass and other irregular objects fixed permanently and was admired by some Members of the Royal Society of Edinburghincluding Sir George Mackenzie who predicted its popularity. Brewster thought his instrument to be of great value in "all the ornamental arts" as a device that creates an "infinity of patterns". Published by Dover Publications This text does not deal with foundations or rigorous axiomatics; statements are proved, but are done so making cheerful use of reasonable inferences from diagrams.
    [Show full text]
  • Fractal-Bits
    fractal-bits Claude Heiland-Allen 2012{2019 Contents 1 buddhabrot/bb.c . 3 2 buddhabrot/bbcolourizelayers.c . 10 3 buddhabrot/bbrender.c . 18 4 buddhabrot/bbrenderlayers.c . 26 5 buddhabrot/bound-2.c . 33 6 buddhabrot/bound-2.gnuplot . 34 7 buddhabrot/bound.c . 35 8 buddhabrot/bs.c . 36 9 buddhabrot/bscolourizelayers.c . 37 10 buddhabrot/bsrenderlayers.c . 45 11 buddhabrot/cusp.c . 50 12 buddhabrot/expectmu.c . 51 13 buddhabrot/histogram.c . 57 14 buddhabrot/Makefile . 58 15 buddhabrot/spectrum.ppm . 59 16 buddhabrot/tip.c . 59 17 burning-ship-series-approximation/BossaNova2.cxx . 60 18 burning-ship-series-approximation/BossaNova.hs . 81 19 burning-ship-series-approximation/.gitignore . 90 20 burning-ship-series-approximation/Makefile . 90 21 .gitignore . 90 22 julia/.gitignore . 91 23 julia-iim/julia-de.c . 91 24 julia-iim/julia-iim.c . 94 25 julia-iim/julia-iim-rainbow.c . 94 26 julia-iim/julia-lsm.c . 98 27 julia-iim/Makefile . 100 28 julia/j-render.c . 100 29 mandelbrot-delta-cl/cl-extra.cc . 110 30 mandelbrot-delta-cl/delta.cl . 111 31 mandelbrot-delta-cl/Makefile . 116 32 mandelbrot-delta-cl/mandelbrot-delta-cl.cc . 117 33 mandelbrot-delta-cl/mandelbrot-delta-cl-exp.cc . 134 34 mandelbrot-delta-cl/README . 139 35 mandelbrot-delta-cl/render-library.sh . 142 36 mandelbrot-delta-cl/sft-library.txt . 142 37 mandelbrot-laurent/DM.gnuplot . 146 38 mandelbrot-laurent/Laurent.hs . 146 39 mandelbrot-laurent/Main.hs . 147 40 mandelbrot-series-approximation/args.h . 148 41 mandelbrot-series-approximation/emscripten.cpp . 150 42 mandelbrot-series-approximation/index.html .
    [Show full text]