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Newton Basins
Newton Basins
http://aleph0.clarku.edu/~djoyce/newton/newton.html
Article about the basins of attraction for the Newton's method for finding roots of equations and th eir resulting representation in the complex plane. Includes mathematical framework and examples.
newton, solution, initial, method, complex, eventually, basins, closer, happens, estimate, basins, i mages, examples, solutions, newton, guesses, interesting, fractals, beautifully, intricate, boundari es, mathematics, allows, polynomials, generation, djoyce, copyright, aleph0, address, create, unders tand, background, clarku, possibilities, browse, involved, quickly, equations, finding, references, fantastic, applied, number, functions, details, technical, university, august, generation, backgroun d, introduction
clarku.edu - rank der domain 90062 (34477 in US)
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Kleinian Groups Pictures
http://klein.math.okstate.edu/kleinian/
Discusses the mathematical theory of Kleinian groups. Includes illustrations, examples, formalism an d program source code.
okstate.edu - rank der domain 26946 (9970 in US)
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The Dynamical Systems and Technology Project
Dynamical Systems and Technology Project
http://math.bu.edu/DYSYS/dysys.html
Educational resource from the Boston University. Includes mathematical framework and formulation, an imated illustrations and calculation spreadsheets.
students, mathematics, mandelbrot, teachers, university, fractals, behind, school, dynamical, techno logy, systems, designed, several, devaney, project, interactive, boston, october, topics, systems, f ractal, fractal, mathematics, celest, thomasina, annual, method, readers, arcadia, stoppard, fractal s, comments, images, geometry, center, mathematical, iterated, dynamics, events, zooming, triangles, dancing, sierpinski, project, science, applets, function, tuesday, concerning, fairly, spreadsheets
bu.edu - rank der domain 8169 (3097 in US)
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Science/Math/Chaos_and_Fractals
Science/Math/Chaos_and_Fractals
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Fractal Dimensions
Cynthia Lanius' Fractals Unit: Fractal Dimension
http://math.rice.edu/~lanius/fractals/dim.html
Easy to comprehend mathematical approach to understanding the significance of the applied study of f ractals and attractors. Includes didactic examples and illustrations.
dimension, length, copies, fractals, sierpinski, triangle, doubling, figure, fractal, double, lanius , similar, exponent, fractal, original, really, dimension, infinitely, dimensions, height, fractals, cynthia, figure, copies, between, triangles, fractional, closer, information, triangle, number, seg ment, similarity, square, remember, better, answer, smaller, segment, another, infinity, investigate , lanius, infinite, logarithms, iteration, teachers, teacher, studied, snowflake, extending
rice.edu - rank der domain 15813 (5869 in US)
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Efg's Computer Lab: Fractals and Chaos
efg's Fractals and Chaos Page
http://www.efg2.com/Lab/FractalsAndChaos
Software and information resource on the Mandelbrot set, geometrical explosion sets, and attractors. Includes diagrams and mathematical backgrounds.
fractals, lyapunov, sierpinski, wavelengthtorgb, rainbow, pf32bit, fractals, mandelbrot, keywords, f unction, program, description, similarity, hausdorff, compute, source, display, logistic, strange, m athematical, recursion, pantograph, digital, mapping, dimension, library, gallery, scientific, expon ents, section, recreations, american, transform, flights, fractal, exponents, originally, developed, curiosities, attractors, reference, maryland, science, lorenz, tp7strng, center, single, forcing, p eriodic, interesting, graphics
efg2.com - rank der domain 929216 (379482 in US)
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Mathematical Figures Using Mathematica
The Math Forum: Mathematical Figures by Robert M. Dickau
http://mathforum.org/advanced/robertd/
Collection of sets and attractors. Includes Mathematica source code, mathematical formulations and i llustrations.
Fractals and combinatorics diagrams created using Mathematica.
fractals chaos Mathematica combinatorics Bell Stirling Catalan Delannoy Motzkin Newton Mandelbrot Ju lia Sierpinski Lozi Rossler Euler numbers permutations derangements
numbers, diagrams, shortest, attractor, sierpinski, systems, method, figures, newton, stirling, math ematical, robert, dickau, numbers, diagram, motzkin, delannoy, zigzag, stacking, harmonic, fibonacci , problem, second, mathforum, rights, reserved, research, professional, studies, college, goodwin, e ducational, enterprise, university, library, privacy, policy, reference, drexel, search, variation, tetrahedron, sponge, randelbrot, menger, chaotic, magnetic, carpet, pendulum, similar, subject
mathforum.org - rank der domain 32496 (12109 in US)
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Fractal Map
Fractal Map
http://frac.samurajdata.se/
Interactive online Mandelbrot and Julia generator.
Fractal Map - A fun and addictive online fractal viewer. No Java required
Fractal, Map, Mandelbrot, Mandel, Online, Interactive, Viewer, Fractalmap, Fractint, Frac, Explorer
fractal, seeing, palette, patches, volcano, reload, visiting, cached, thanks, comments, contact, sam urajdata, refresh, switch, platform, rendered, interruption, service, cached, iterations
samurajdata.se - rank der domain 120214 (46416 in US)
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Julia and Mandelbrot Set Explorer
Mandelbrot and Julia Set Explorer
http://aleph0.clarku.edu/~djoyce/julia/explorer.html
Online navigator for various sets and attractors from the Clark University. Includes background and a short course on complex numbers.
mandelbrot, lambda, explorer, images, websites, alternate, recently, public, parameter, colors, iter ations, information, others, interesting, binary, escape, circular, through, standard, square, creat ed, feathered, pattern, copyright, science, university, worcester, computer, mathematics, purpose, w hatsoever, department, djoyce, explorer, clarku, aleph0, located, applet, generation, planes, biblio graphy, introduction, contents, references, produced, domain, images, september, copyright, stumbled , stumbleupon
clarku.edu - rank der domain 90062 (34477 in US)
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Science/Math/Chaos_and_Fractals
Science/Math/Chaos_and_Fractals
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3D Fractals Bicomplex Dynamics
3D Fractals
http://www.3dfractals.com/
Resource on the bicomplex generalization of the Mandelbrot set. Includes scientific publications, il lustrations, news and downloads.
fractals
(SLD : 3dfractals.com)
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IFS Attractors
IFS Attractors
http://www.meden.demon.co.uk/Fractals/fractals.html
Index and definition of different attractors. Includes images, plots and glossary.
technique, element, tilings, fractals, number, figures, techniques, composition, complex, conjugates , linear, higher, single, figure, several, copies, subtractive, tiling, grouped, attractors, affine, glossary, triangles, similar, attractors, october, associated, similarity, dimension, measure, line ar, topics, cyclomers, polymers, hinsley, connected, simply, attractor, stewart, uniform, include, r elated, similar, derived, mixture, sierpinski, lammering, infinite, falconer, dimers, astromers
demon.co.uk - rank der domain 17267 (441 in GB)
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Technocosm
technocosm.org - Math, Chaos, and Fractals
http://technocosm.org/chaos/
Focuses on the visualization of three dimensional attractors. Includes formula derivations and image galleries.
pictures, strange, attractor, divisibility, gallery, numbers, number, attractor, strange, please, ad agio, technocosm, divisible, evenly, remembered, tricks, responded, another, talking, fractals, befo re, childhood, friends, shortcuts, determining, remembering, learning, interested, article, holder, copyright, quickly, derived, pseudo, proofs, obviously, correct, formal, theory, mandelbrot, encount ered, sought, favorite, hojicha, dragonwell, internet, gunpowder, mathematics, fractals, supplier, e xploring
(SLD : technocosm.org)
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Iterations and the Mandelbrot Set
http://www.cut-the-knot.com/blue/Mandel.html
Discusses how differently the iterations behave depending on which portions the coefficients are plu cked from. Includes basics, concept, formulations and references.
(SLD : cut-the-knot.com)
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Fractal Foundation
FractalFoundation.org
http://www.fractalfoundation.org
Foundation with purpose of educating people about the mathematical theory and the interconnectedness of complex systems. Includes mission statement, mathematical framework, gallery and contact.
The Fractal Foundation uses the beauty of fractals to inspire interest in Science, Math and Art.
fractal, fractals, education, teaching, learning, chaos theory, children, school, schools, inspirati on, math, science, computers, technology, culture, art, public art, balloon, balloons, nonprofit, jo nathan wolfe, albuquerque, santa fe, new mexico, elementary, kindergarten, sponsorship, scholarship, creative, creativity, beauty
fractal, fractals, standards, school, foundation, fractal, challenge, fractals, friday, complex, tri angle, infinitely, trianglethon, winning, function, mygallery, startgallery, presentations, program, mountains, coastlines, rivers, canyons, including, nature, building, science, delight, patterns, co nnections, between, building, downtown, washington, rachel, grader, albuquerque, winner, largest, re mote, community, escuela, mariano, reservation, visited, harwood, category, installation, pleased, c enter, announce
fractalfoundation.org - rank der domain 967415 (419225 in US)
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The Mandelbrot and Julia Sets Anatomy
The Mandelbrot set Anatomy: Contents
http://www.ibiblio.org/e-notes/MSet/Contents.htm
Scientific publication about the anatomy of different sets and attractors and chaotic dynamics. Incl udes animated samples, articles and mathematical formulations.
mandelbrot, points, dynamics, period, renormalization, complex, period, iterations, doubling, quadra tic, periodicity, bifurcations, orbits, periodic, scaling, windows, midgets, cascade, tuplings, orde ring, embedded, symbolic, preperiodic, similarity, cascades, external, 350x450, douglas, external, r everse, boundary, interior, crises, cantor, approximation, universal, ravenel, polynomial, fagella, theorem, introduction, anatomy, bifurcation, contents, periodic, primary, caterpillar, estimator, al gorithms, tracing, distance
ibiblio.org - rank der domain 13741 (5140 in US)
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3D Mountains
3D Mountains
http://www.ibiblio.org/e-notes/3Dapp/Mount.htm
Shows how to create fractal mountains, three-dimensional Mandelbrot and Julia sets, convex, stellate d and polyhedra. Includes pictures, plots and mathematical formulations.
rotate, mountain, number, points, fractal, controls, increase, decrease, hidden, mountains, surface, removal, lorenz, algorithms, terrains, random, status, explanations, updated, polyhedra, mountains, equation, couple, mandelbrot, terrain, terrains, examples
ibiblio.org - rank der domain 13741 (5140 in US)
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Fractals Unleashed
Fractals Unleashed - Team 26242
http://library.thinkquest.org/26242/
Tutorial covering the different types of sets and attractors. Includes mathematical formulations, ap plets, programs, gallery and an art contest. [English, Russian, Ukrainian]
algorithms,anatomy,applets,applications,art,astronomy,attractors,base,biology,box-counting,brownian, canopies,chaos,chemistry,children,clouds,clusters,contest,dimension,downloads,dragon,dusts,economy,f olding,formula,fractals,functions,gallery,generator,geometry,henon,ifs,island,iteration,java,julia,k ids,koch,l-systems,landscapes,levy,lorenz,mandelbrot,math,megner,motif,movies,music,paper,peano,plan ts,plasma,programming,pyramid,pythagoras,quaternions,rossler,russian,self-similarity,sets,sierpinski ,snowflake,sponge,star,strange,sweeps,trees,trek,triangle,tutorial,types,ukrainian,uses,weierstrass
ukrainian, russian, fractals, drawtop, unleashed, english
thinkquest.org - rank der domain 8380 (3180 in US)
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Chaos, Fractals, and Arcadia
Chaos, fractals, and Arcadia
http://math.bu.edu/DYSYS/arcadia/
Article on the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Includes examples, illustrations and references.
arcadia, university, mathematical, boston, introduction, thomasina, stoppard, devaney, dynamical, sy stems, technology, robert, sierpinski, irregular, formulas, hexagon, appendix, geometry, references, summary, valentine, grouse, feedback, suggestions, comments, return, section, welcome, please, mate rial, pictures, description, animated, lurking, background, access, department, fractals, fractals, mathematics, software, discussion, mathematical, sciences, california, institute, research, together , contained, images, generates
bu.edu - rank der domain 8169 (3097 in US)
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Fractal Geometry
Fractal Geometry
http://classes.yale.edu/fractals/
An educational resource on the mathematical framework and formalism from the Yale University, coveri ng the concept of self similarity. Includes topical examples, images, algorithms and software.
geometry, fractal
yale.edu - rank der domain 4799 (1793 in US)
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Wikipedia: Fractals
Fractal - Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Fractals
Free encyclopedia article covering historical aspects and mathematical formulations. Includes two an d three dimensional illustration sets.
fractal, fractals, fractal, player, fractals, similar, dimension, similarity, mandelbrot, wikipedia, nature, hausdorff, example, topological, vector, function, patterns, include, objects, sierpinski, wikipedia, scales, snowflake, geometric, examples, systems, cantor, called, system, appear, curves, described, created, examples, computer, program, triangle, related, applications, simplesearch, hilb ert, african, geometry, theory, recursive, article, iteration, considered, further, mediawiki, defin ition
wikipedia.org - rank der domain 6 (5 in US)
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Mathematics: Stilldreamer
Mathematics: Stilldreamer
http://www.stilldreamer.com/mathematics/
Explains the basics of Sierpinski systems and other sets. Includes interactive example programs with source code.
Articles which pertain mostly to mathematics, often with sample programs.
mathematics, sierpinski, triangle, stilldreamer, substitution, system, building, triangle, pascal, p rogramming, substitution, properties, exploration, search, contents, licensed, bastien, moduli, prog rams, sample, content, sorted, mathematics, articles, pertain, mostly, cellular, fractal, island, au tomaton, cellular, automaton, dimensional, elementary
(SLD : stilldreamer.com)
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Dan Freeland
http://homepage.ntlworld.com/daniel.freeland/
Explains the basics. Includes gallery and free software for exploring different sets and singulariti es.
ntlworld.com - rank der domain 9546 (262 in GB)
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Bitshifters
BitShifters SoftSource Factals
http://bitshifters.com/fractal.html
Images generated by different commercial applications. Includes FAQs and tutorial.
These images are of the Mandelbrot set, a fractal generated from a simple mathematical formula. The y were produced by DRAWING Librarian Professional (DP).
fractile,fractiles,Drawing Librarian,CAD based graphics,streograms,fractiles,topographs,AutoCAD,cadd , drafting,translation,translator,engineering,computer aided drafting
generate, fractal, images, images, mandelbrot, softsource, numbers, drawing, fractal, librarian, pro fessional, 1502161525944, 791032671785, 0946979351544, 0000000355566, 000000441162, 7649598805986, c ontact, example, 7910322074096, 0000000158077, 1502158760371, products, general, regarding, question s, 0000000000326, 075895926312, 6605057308991, 000850078, 0000480167014, 7455175495712, produced, ex amine, factals, bitshifters, generated, formula, mathematical, simple, detail, length, followed, com mand, script, parentheses, corner, indicate, coordinates, picture, location
(SLD : bitshifters.com)
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Images From Chaos
Images from chaos
http://www.cps.unizar.es/~jlsubias/
Gallery of chaotic and complex systems and attractors from the University of Zaragoza, Spain.
images, nevageador, subias, flotantes, marcos, admite, 003300, decoration, weight
unizar.es - rank der domain 15838 (262 in ES)
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Tetrabrot Fractal Videos
page1
http://www.javaspider.com/jfract
Collection of videos made by rotation, zooming, and cycling through the four-dimensional Tetrabrot s ets. Includes basics, mathematical formulations and descriptions.
tetrabrot, numbers, hypercomplex, tetrabrot, hypercomplex, complex, decoration, complex, quaternions , tables, multiplication, images, videos, vectors, higher, dimensions, creating, extend, represented , exponent, variations, cycling, quaternion, fractal, movies, movies, jfract, javaspid, manipulation s, fractal, generate, rotated, addition, shifted, quaternion, dimensional, objects, fractals, genera ted, elements, relation, recursion, weight, family, normal, height, margin, mandelbrot, famous, numb er, iteration
(SLD : javaspider.com)
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Homepage of Kristian Gustavsson
Homepage of Kristian Gustavsson
http://www.dd.chalmers.se/~f99krgu/main/index.html
Weblog about the mathematical background of different sets and attractors in the complex plane. Incl udes downloadable generator and gallery.
Project about fractals and chaos. The fractal generator FracZoom. Project in genetic computation: A selfprogramming Nintendo player.
Fractal, Chaos, image, animation, FracZoom, Nintendo, Nintendo player, Genetic programming, Kristian Gustavsson
gustavsson, kristian, homepage
chalmers.se - rank der domain 60165 (284 in SE)
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Fractal Brownian Archipelago
Fractal Brownian Islands exhibit - Fractional Brownian Motion - fractals and coastline
http://swiss.csail.mit.edu/~rauch/islands/
Shows how brownian motion can model the shape of coastlines. Includes interactive demonstration and a collection of island set.
fractal,fractals,brownian,motion,mandelbrot,island,coastline,coast,coastlines
brownian, particle, motion, dimension, fractal, scales, islands, trails, correlated, moving, benoit, mandelbrot, island, detail, britain, islands, points, direction, following, different, structure, n atural, simple, shapes, coastlines, fractals, fractional, making, inordinately, question, motion, fa mous, conventional, examples, connection, internet, coastline, pictures, introduction, general, cont inuum, larger, 2000x2000, although, browser, version, explore, scrolling, exhibit, generated, fracta l
mit.edu - rank der domain 1198 (505 in US)
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Quantum Jumps, EEQT and the Five Platonic Fractals
Quantum Jumps, EEQT and the Five Platonic Fractals
http://quantumfuture.net/quantum_future/papers/qfract/
Explains how quantum jumps generate new family of fractals on spherical canvas. Includes graphics in several formats, mathematical framework and bibliography.
Quantum Jumps, EEQT and the Five Platonic Fractals
qfr1
quantum, fractals, projections, platonic, introduction, document, bibliography, operators, projectio n, states, canvas, polyhedra, complex, projective, serves, importance, detectors, exponent, characte ristic, function, itself, measure, nonunitarity, meaning, geometrical, fuzziness, parameter, continu ous, evolution, detectors, direction, configurations, generate, through, fractals, quantum, symmetri c, jadczyk, abstract, sphere, transition, implemented, directions, probabilities, tetrahedron, icosa hedron, octahedron, project, opensource, accompanies, hilbert
quantumfuture.net - rank der domain 816125 (57155 in DE)
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The 3x+1 Fractal
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TYG-4C47CDM-5&_coverDate=06%2F30%2F2004&_alid=262438467&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=5618&_sort=d&view=c&_acct=C000043379&_version=1&_u
Paper that generalizes the Collatz problem to complex numbers. Includes insights, results and refere nces.
sciencedirect.com - rank der domain 1626 (667 in US)
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The Modular Group and Fractals
The Modular Group and Fractals
http://www.linas.org/math/sl2z.html
Explains the basics of fractals, Riemann Zeta, modular group gamma, Farey fractions and Minkowski qu estion mark. Includes publications.
An exposition of the relationship between fractals, the Riemann Zeta, the Modular Group Gamma and the Farey Fractions
Fractal, Modular Group, Fuchsian, Kleinian, Symmetry, Blancmange, SL(2,Z), Riemann Zeta, Hurwitz Zeta, Bernoulli Map, Takagi, Gauss, Kuz min, Wirsing, Minkowski, Question Mark, Farey Fraction, Farey, Farey sequence, continued fraction
riemann, function, measure, modular, minkowski, chapter, series, operator, fractions, bernoulli, fun ctions, representation, numbers, curves, kuzmin, fractal, question, fractals, operator, modular, dim ensional, provides, newton, number, theory, result, distribution, transform, certain, transfer, resu lts, transforms, hurwitz, rationals, fractals, series, dyadic, algorithm, fractions, wirsing, struct ure, appear, subset, theoretic, polylogarithm, subgroup, techniques, function, discussion, rational, theory
linas.org - rank der domain 993312 (383999 in US)
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Mandelbrot, Benoit B.
Benoit B. Mandelbrot
http://www.math.yale.edu/mandelbrot/
Founder of fractal geometry. Includes biography, vita, publications, interviews, and reviews.
Official Biography site. Benoit B. Mandelbrot is the world's foremost impetus for the advancement of Fractal Geometry. Learn about his life and work.
Benoit, Mandelbrot, fractal, Fractals, fractals, set, biography, articles, vita, contact, history, m ath, geometry, interviews
mandelbrot, benoit
yale.edu - rank der domain 4799 (1793 in US)
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Fractals: The Beautiful Complex Patterns Generated by Simple Iterative Computations
Climate dynamics, chaos and quantum mechanics
http://amselvam.webs.com
Outlines a general systems theory for chaos, quantum mechanics and gravity as applied to weather pat terns. Includes illustrations, scientific publications and references.
selvam, available, eprint, archives, systems, quantum, fractals, atmospheric, dynamics, structures, fractal, selfsimilar, modification, solitons, selfsimilar, ramachandra, meteorology, fadnavis, publi shed, fractal, dynamical, theory, mechanics, complex, computations, nature, general, weather, dynami cs, iterative, gravity, dimensional, atmospheric, unmodified, global, scales, applicable, suvarna, s ubatomic, physics, patterns, ramana, everything, iterative, spatial, structure, indian, numerical, s pacetime, seeding, correlations
webs.com - rank der domain 408 (183 in US)
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Introduction to Lacunarity
An Introduction to Lacunarity
http://groups.csail.mit.edu/mac/users/rauch/lacunarity/lacunarity.html
Analysis of the degree of gappiness of different sets. Includes mathematical aspects, results and pu blications.
fractal, lacunarity, lacunarity, mandelbrot, review, letters, physical, dimension, fractals, physics , different, fractal, texture, geometry, interdisciplinary, analysis, related, aharony, nature, frac tals, moving, lattices, middle, topics, fluids, related, statistical, random, gardner, plasmas, verl ag, plotnick, boston, construction, distribution, speaking, cantor, determined, medicine, introducti on, fournier, spiegel, counterpart, clusters, portugu, turbulence, percolation, intermittency, rough ly, hargrove, prestegaard
mit.edu - rank der domain 1198 (505 in US)
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Chaos, Economics and Stock  Markets
Ecometry
http://www.bentamari.com/
Introduction to chaos, attractors and dynamic systems theory. Includes mathematical formulation, ima ges and references.
geovisit, ecometry
(SLD : bentamari.com)
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