Edit Profile (opens in new tab) Barnsley, Michael Fielding Compute Distance To: Compute Author ID: barnsley.michael-fielding Published as: Barnsley, Michael F.; Barnsley, M. F.; Barnsley, Michael; Barnsley, M.; Barnsley, Michael Fielding; Barnsley, M. F more...less External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 116 Publications since 1973, including 9 Books 5 Contributions as Editor · 1 Further Contribution Co-Authors: 53 Co-Authors with 95 Joint Publications 1,054 Co-Co-Authors all top 5 Co-Authors 22 single-authored 18 Vince, Andrew 14 Harrington, Andrew N. 13 Geronimo, Jeffrey S. 12 Robinson, Peter D. 5 Demko, Stephen G. 5 Elton, John H. 5 Harding, Brendan 5 Leśniak, Krzysztof 4 Hardin, Douglas P. 3 Devaney, Robert L. 3 Falconer, Kenneth J. 3 Herod, James V. 3 Hutchinson, John Edward 3 Igudesman, Konstantin B. 3 Massopust, Peter R. 3 Passty, Gregory Bohdan 3 Rypka, Miroslav 3 Stenflo, Orjan 3 Vrscay, Edward Robert 2 Bandt, Christoph 2 Barnsley, Louisa F. 2 Cornille, Henri 2 Dager, L. D. 2 Frame, Michael Lee 2 Hegland, Markus 2 Hurd, Lyman P. 2 La Torre, Davide 2 Mosher, D. L. 2 Mumford, David Bryant 2 Saupe, Dietmar 2 Stewart, Ian Nicholas 2 Turchetti, Giorgio 2 Wilson, David C. 1 Alligood, Kathleen T. 1 Anson, Louisa F. 1 Atkins, Ross 1 Baker, George Allen jun. 1 Barrallo, Javier 1 Berger, Marc A. 1 Bessis, Daniel 1 Branner, Bodil 1 Brothers, Harlan J. 1 Cohen, Nathan 1 Coppens, Marc-Olivier 1 Deliu, Anca 1 Duffin, Richard James 1 Eglash, Ron 1 Epstein, Saul T. 1 Ervin, Vincent J. 1 Fisher, Yuval 1 Freiberg, Uta Renata 1 Furstenberg, Hillel 1 Harrison, Jenny C. 1 Holmes, Philip J. 1 Howe, Roger Evans 1 Jaffard, Stéphane 1 Jory, Virginia Vickery 1 Kannan, V. 1 Keen, Linda 1 Keesling, James Edgar 1 Kumar, P. B. Vinod 1 Lesmoir-Gordon, Nigel 1 Mandelbrot, Benoit B. 1 McGuire, Michael 1 Mihalache-Ciurdea, Nicolae 1 Morley, Thomas D. 1 Moussa, Pierre 1 Peitgen, Heinz-Otto 1 Raddatz, W. 1 Roychowdhury, Mrinal Kanti 1 Soner, Halil Mete 1 Steiner, Wolfgang 1 Viswanathan, Puthan Veedu 1 Voss, Richard F. 1 West, Bruce J. 1 Xie, Ruifeng 1 Yorke, James Alan all top 5 Serials 8 Journal of Mathematical Physics 4 Notices of the American Mathematical Society 3 Journal of the Institute of Mathematics and its Applications 3 Journal of Approximation Theory 3 Transactions of the American Mathematical Society 3 Ergodic Theory and Dynamical Systems 3 Constructive Approximation 3 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 2 American Mathematical Monthly 2 Bulletin of the Australian Mathematical Society 2 Communications in Mathematical Physics 2 Journal of Mathematical Analysis and Applications 2 Journal of Statistical Physics 2 Journal of Physics A: Mathematical and General 2 Proceedings of the National Academy of Sciences of the United States of America 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 SIAM Journal on Mathematical Analysis 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Fractals 2 SIAM Journal on Imaging Sciences 1 Advances in Applied Probability 1 Houston Journal of Mathematics 1 Letters in Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Rocky Mountain Journal of Mathematics 1 Chaos, Solitons and Fractals 1 Advances in Mathematics 1 Geometriae Dedicata 1 Journal of Functional Analysis 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Numerical Analysis 1 Discrete & Computational Geometry 1 Forum Mathematicum 1 The Journal of Geometric Analysis 1 Annals of Physics 1 Linear Algebra and its Applications 1 Bulletin of the American Mathematical Society. New Series 1 Russian Mathematics 1 Topology Proceedings 1 Probability in the Engineering and Informational Sciences 1 Lobachevskii Journal of Mathematics 1 Journal of Nonlinear and Convex Analysis 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 The IMA Volumes in Mathematics and its Applications 1 Proceedings of Symposia in Applied Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Symmetry 1 Bulletin of Mathematical Sciences 1 Springer Proceedings in Mathematics & Statistics 1 International Journal of Applied Nonlinear Science all top 5 Fields 46 Measure and integration (28-XX) 46 Dynamical systems and ergodic theory (37-XX) 19 Approximations and expansions (41-XX) 18 Functions of a complex variable (30-XX) 15 Computer science (68-XX) 11 General and overarching topics; collections (00-XX) 11 Operator theory (47-XX) 11 Probability theory and stochastic processes (60-XX) 8 Real functions (26-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Information and communication theory, circuits (94-XX) 6 Combinatorics (05-XX) 6 Partial differential equations (35-XX) 6 Convex and discrete geometry (52-XX) 6 General topology (54-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Numerical analysis (65-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Fluid mechanics (76-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Ordinary differential equations (34-XX) 4 Integral equations (45-XX) 3 Special functions (33-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Integral transforms, operational calculus (44-XX) 2 Functional analysis (46-XX) 2 Quantum theory (81-XX) 1 Number theory (11-XX) 1 Difference and functional equations (39-XX) 1 Mechanics of particles and systems (70-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 96 Publications have been cited 2,345 times in 1,350 Documents Cited by ▼ Year ▼ Fractals everywhere. Zbl 0691.58001Barnsley, Michael 593 1988 Fractal functions and interpolation. Zbl 0606.41005Barnsley, Michael F. 265 1986 Iterated function systems and the global construction of fractals. Zbl 0588.28002Barnsley, M. F.; Demko, Stephen 198 1985 The calculus of fractal interpolation functions. Zbl 0693.41008Barnsley, Michael F.; Harrington, Andrew N. 108 1989 Recurrent iterated function systems. Zbl 0659.60045Barnsley, Michael F.; Elton, John H.; Hardin, Douglas P. 108 1989 Hidden variable fractal interpolation functions. Zbl 0704.26009Barnsley, M. F.; Elton, J.; Hardin, D.; Massopust, P. 88 1989 Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities. Zbl 0653.60057Barnsley, M. F; Demko, S. G.; Elton, J. H.; Geronimo, J. S. 84 1988 Fractals everywhere. Revised with the assistance of Hawley Rising III. Answer key by Hawley Rising III. 2nd ed. Zbl 0784.58002Barnsley, Michael F. 81 1993 Solution of an inverse problem for fractals and other sets. Zbl 0613.28008Barnsley, M. F.; Ervin, V.; Hardin, D.; Lancaster, J. 50 1986 A new class of Markov processes for image encoding. Zbl 0643.60050Barnsley, Michael F.; Elton, John H. 42 1988 Superfractals. Zbl 1123.28007Barnsley, Michael Fielding 38 2006 Orthogonal polynomials associated with invariant measures on Julia sets. Zbl 0509.30023Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 34 1982 \(V\)-variable fractals: Fractals with partial self similarity. Zbl 1169.28006Barnsley, Michael F.; Hutchinson, John E.; Stenflo, Örjan 33 2008 Bilinear fractal interpolation and box dimension. Zbl 1315.28003Barnsley, Michael F.; Massopust, Peter R. 32 2015 Fractal image compression. Illustrations by Louisa F. Anson. Zbl 0796.68186Barnsley, Michael F.; Hurd, Lyman P. 31 1993 A fractal valued random iteration algorithm and fractal hierarchy. Zbl 1304.28004Barnsley, Michael; Hutchinson, John; Stenflo, Örjan 28 2005 The chaos game on a general iterated function system. Zbl 1221.37079Barnsley, Michael F.; Vince, Andrew 26 2011 Developments in fractal geometry. Zbl 1275.28006Barnsley, Michael; Vince, Andrew 22 2013 Infinite-dimensional Jacobi matrices associated with Julia sets. Zbl 0535.30025Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 20 1983 The science of fractal images. With contributions by Yuval Fisher and Michael McGuire. Ed. by Heinz-Otto Peitgen and Dietmar Saupe. (Based on notes for the course fractals - introduction, basics and pespectives given as part of the SIG-GRAPH ’87, Anaheim, Calif. course program). Zbl 0683.58003Barnsley, Michael F.; Devaney, Robert L.; Mandelbrot, Benoit B.; Peitgen, Heinz-Otto; Saupe, Dietmar; Voss, Richard 20 1988 The Conley attractors of an iterated function system. Zbl 1417.37080Barnsley, Michael F.; Vince, Andrew 20 2013 Fractal image compression. Zbl 1114.68568Barnsley, M.; Barnsley, L. 19 1997 On the invariant sets of a family of quadratic maps. Zbl 0535.30024Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 16 1983 Bivariational bounds. Zbl 0295.49022Barnsley, M. F.; Robinson, P. D. 16 1974 The chaos game on a general iterated function system from a topological point of view. Zbl 1304.28003Barnsley, Michael F.; Leśniak, Krzysztof 15 2014 Fractal image compression. Zbl 1044.94501Barnsley, Michael F. 14 1996 A characterization of hyperbolic affine iterated function systems. Zbl 1196.28011Atkins, Ross; Barnsley, Michael F.; Vince, Andrew; Wilson, David C. 14 2010 Fractal continuation. Zbl 1279.28013Barnsley, Michael F.; Vince, Andrew 14 2013 Almost periodic Jacobi matrices associated with Julia sets for polynomials. Zbl 0574.58016Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 14 1985 Chaos game for IFSs on topological spaces. Zbl 1341.37013Barnsley, Michael F.; Leśniak, Krzysztof; Rypka, Miroslav 13 2016 \(V\)-variable fractals: dimension results. Zbl 1244.28008Barnsley, Michael; Hutchinson, John E.; Stenflo, Örjan 13 2012 Geometry, electrostatic measure and orthogonal polynomials on Julia sets for polynomials. Zbl 0566.41033Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 13 1983 Some recent progress concerning topology of fractals. Zbl 1322.54002Barnsley, Michael F.; Wilson, David C.; Leśniak, Krzysztof 12 2014 Real projective iterated function systems. Zbl 1256.28002Barnsley, Michael F.; Vince, Andrew 12 2012 How to transform and filter images using iterated function systems. Zbl 1246.37024Barnsley, Michael F.; Harding, Brendan; Igudesman, Konstantin 12 2011 Transformations between self-referential sets. Zbl 1229.28009Barnsley, Michael F. 11 2009 Erratum: Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities. Zbl 0715.60086Barnsley, M. F.; Demko, S. G.; Elton, J. H.; Geronimo, J. S. 10 1989 Fractal tilings from iterated function systems. Zbl 1336.28006Barnsley, Michael; Vince, Andrew 10 2014 The bounding properties of the multipoint Padé approximant to a series of Stieltjes on the real line. Zbl 0279.41013Barnsley, Michael 10 1973 Measure-valued images, associated fractal transforms, and the affine self-similarity of images. Zbl 1175.94022La Torre, D.; Vrscay, E. R.; Ebrahimi, M.; Barnsley, M. F. 9 2009 The Diophantine moment problem and the analytic structure in the activity of the ferromagnetic Ising model. Zbl 0454.44006Barnsley, M.; Bessis, D.; Moussa, P. 9 1979 Moments of balanced measures on Julia sets. Zbl 0512.30014Barnsley, M. F.; Harrington, A. N. 9 1984 Numerics and fractals. Zbl 1305.28015Barnsley, Michael F.; Hegland, Markus; Massopust, Peter 9 2014 On the continuity of the Hutchinson operator. Zbl 1371.54130Barnsley, Michael F.; Leśniak, Krzysztof 8 2015 Theory and applications of fractal tops. Zbl 1192.37010Barnsley, Michael 7 2005 The entropy of a special overlapping dynamical system. Zbl 1290.37017Barnsley, Michael; Harding, Brendan; Vince, Andrew 7 2014 Correction terms for Padé approximants. Zbl 0298.41007Barnsley, M. F. 7 1975 On a class of solutions of the Krook-Tjon-Wu model of the Boltzmann equation. Zbl 0443.76066Barnsley, M.; Cornille, H. 6 1980 General solution of a Boltzmann equation, and the formation of Maxwellian tails. Zbl 0488.76081Barnsley, M.; Cornille, H. 6 1981 The eigenvalue problem for linear and affine iterated function systems. Zbl 1229.15008Barnsley, Michael; Vince, Andrew 6 2011 Condensed Julia sets, with an application to a fractal lattice model Hamiltonian. Zbl 0565.30018Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 6 1985 Pointwise bivariational bounds on solutions of Fredholm integral equations. Zbl 0395.65066Robinson, Peter D.; Barnsley, Michael F. 6 1979 Mixing Markov chains and their images. Zbl 1134.68576Barnsley, Michael F.; Berger, Marc A.; Soner, H. Meté 5 1988 Some tree-like Julia sets and Padé approximants. Zbl 0532.41023Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 5 1983 Old wine in fractal bottles. I: Orthogonal expansions on self-referential spaces via fractal transformations. Zbl 1372.28006Bandt, Christoph; Barnsley, Michael; Hegland, Markus; Vince, Andrew 5 2016 Fractal homeomorphism for bi-affine iterated function systems. Zbl 1291.28007Barnsley, Michael; Vince, Andrew 5 2013 Geometrical and electrical properties of some Julia sets. Zbl 0548.30021Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 5 1984 Self-similar polygonal tiling. Zbl 1391.52026Barnsley, Michael; Vince, Andrew 4 2017 The Tjon-Wu equation in Banach space settings. Zbl 0471.34046Barnsley, M. F.; Herod, J. V.; Jory, V. V.; Passty, G. B. 4 1981 Fast basins and branched fractal manifolds of attractors of iterated function systems. Zbl 1359.37037Barnsley, Michael F.; Vince, Andrew 4 2015 Approximation of rough functions. Zbl 1350.26003Barnsley, M. F.; Harding, B.; Vince, A.; Viswanathan, P. 4 2016 Topological contractive systems. Zbl 1253.37012Barnsley, M.; Igudesman, K. 4 2011 A study of Boltzmann energy equations. Zbl 0591.76134Barnsley, Michael F.; Turchetti, Giorgio 4 1985 Chaotic dynamics and fractals. (Proceedings of a Conference on Chaotic Dynamics, Georgia Institute of Technology, Atlanta, Georgia, March 25-29, 1985). Zbl 0593.00013 4 1986 Bivariational bounds for non-linear problems. Zbl 0383.49035Barnsley, M. F.; Robinson, P. D. 4 1977 Dual variational principles and Padé-type approximants. Zbl 0286.65035Barnsley, M. F.; Robinson, P. D. 4 1974 Bivariational bounds associated with non-self-adjoint linear operators. Zbl 0344.49032Barnsley, Michael F.; Robinson, Peter D. 4 1976 Solutions for a model Boltzmann equation by monotonicity methods. Zbl 0529.45007Barnsley, M. F.; Herod, J. V.; Mosher, D. L.; Passty, G. B. 3 1983 Chaos and fractals. The mathematics behind the computer graphics. (Lectures delivered in the AMS short course on August 6-7, 1988, given in conjunction with the AMS centennial meeting in Procidence, RI). Zbl 0677.58004 3 1989 Lecture notes on iterated function systems. Zbl 0752.58013Barnsley, Michael F. 3 1989 Iterated function systems for lossless data compression. Zbl 1030.94004Barnsley, Michael F. 3 2002 Geometry and combinatorics of Julia sets of real quadratic maps. Zbl 0588.58054Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 3 1984 Bivariational bounds in a complex Hilbert space, and correction terms for Padé approximants. Zbl 0322.41011Barnsley, M. F.; Baker, George A. jun. 3 1976 The life and survival of mathematical ideas. Zbl 1189.00011Barnsley, Michael F. 2 2010 Self-similar tilings of fractal blow-ups. Zbl 1427.52014Barnsley, M. F.; Vince, A. 2 2019 Basic topological structure of fast basins. Zbl 1432.37054Barnsley, Michael F.; Leśniak, Krzysztof; Rypka, Miroslav 2 2018 Overlapping iterated function systems on a segment. Zbl 1338.37022Barnsley, Michael; Igudesman, K. B. 2 2012 Measure preserving fractal homeomorphisms. Zbl 1317.28009Barnsley, Michael F.; Harding, Brendan; Rypka, Miroslav 2 2014 A variational approach to the theory of multipoint Padé approximants. Zbl 0279.41012Epstein, Saul T.; Barnsley, Michael F. 2 1973 Symmetric itinerary sets. Zbl 1417.37141Barnsley, Michael F.; Mihalache, Nicolae 2 2019 New results on the nonlinear Boltzmann equation. Zbl 0432.76062Barnsley, Michael F.; Turchetti, Giorgio 2 1980 Rational approximation of fractals. Zbl 0571.41010Barnsley, Michael F.; Demko, Stephen G. 2 1984 Analysis of Boltzmann equations in Hilbert space by means of a non-linear eigenvalue property. Zbl 0494.35076Barnsley, M. F.; Herod, J. V.; Mosher, D. L.; Passty, G. B. 1 1981 Fractals in multimedia. Based on a minisymposium held as part of the IMA annual program on mathematics in multimedia, Minneapolis, MN, USA, January 2001. Zbl 0996.00032Barnsley, Michael F.; Saupe, Dietmar; Vrscay, Edward R. 1 2002 Stationary stochastic processes and fractal data compression. Zbl 0899.60073Barnsley, Michael F.; Deliu, Anca; Xie, Ruifeng 1 1997 Making chaotic dynamical systems to order. Zbl 0611.58039Barnsley, Michael F. 1 1986 Critical itineraries of maps with constant slope and one discontinuity. Zbl 1376.37031Barnsley, Michael; Steiner, Wolfgang; Vince, Andrew 1 2014 Three-dimensional fractal homeomorphisms. Zbl 1331.28015Barnsley, Michael F.; Harding, Brendan 1 2015 Iterated networks and the spectra of renormalizable electromechanical systems. Zbl 0624.58038Barnsley, M. F.; Morley, T. D.; Vrscay, E. R. 1 1985 Padé-approximant bounds and approximate solutions for Kirkwood-Riseman integral equations. Zbl 0286.65063Barnsley, M. F.; Robinson, P. D. 1 1974 Padé approximant bounds for the difference of two series of Stieltjes. Zbl 0332.41014Barnsley, M. F. 1 1976 Rational approximant bounds for a class of two-variable Stieltjes functions. Zbl 0375.41006Barnsley, M. F.; Robinson, P. D. 1 1978 Bounds for the rth characteristic frequency of a beaded string or of an electrical filter. Zbl 0435.15009Barnsley, Michael F.; Duffin, Richard J. 1 1980 Tilings from graph directed iterated function systems. Zbl 1467.28006Barnsley, Michael; Vince, Andrew 1 2021 Glimpses of Benoît B. Mandelbrot (1924–2010). Zbl 1284.01047Stewart, Ian; Mumford, David; Falconer, Kenneth; Eglash, Ron; Brothers, Harlan; Lesmoir-Gordon, Nigel; Barrallo, Javier; Berry, Michael; Frame, Michael 1 2012 The influence of Benoît B. Mandelbrot on mathematics. Zbl 1284.01048Stewart, Ian; Mumford, David; Howe, Roger; Furstenberg, Hillel; Falconer, Kenneth; West, Bruce J.; Coppens, Marc-Olivier; Cohen, Nathan; Jaffard, Stéphane; Berry, Michael; Frame, Michael 1 2012 Tilings from graph directed iterated function systems. Zbl 1467.28006Barnsley, Michael; Vince, Andrew 1 2021 Self-similar tilings of fractal blow-ups. Zbl 1427.52014Barnsley, M. F.; Vince, A. 2 2019 Symmetric itinerary sets. Zbl 1417.37141Barnsley, Michael F.; Mihalache, Nicolae 2 2019 Basic topological structure of fast basins. Zbl 1432.37054Barnsley, Michael F.; Leśniak, Krzysztof; Rypka, Miroslav 2 2018 Self-similar polygonal tiling. Zbl 1391.52026Barnsley, Michael; Vince, Andrew 4 2017 Chaos game for IFSs on topological spaces. Zbl 1341.37013Barnsley, Michael F.; Leśniak, Krzysztof; Rypka, Miroslav 13 2016 Old wine in fractal bottles. I: Orthogonal expansions on self-referential spaces via fractal transformations. Zbl 1372.28006Bandt, Christoph; Barnsley, Michael; Hegland, Markus; Vince, Andrew 5 2016 Approximation of rough functions. Zbl 1350.26003Barnsley, M. F.; Harding, B.; Vince, A.; Viswanathan, P. 4 2016 Bilinear fractal interpolation and box dimension. Zbl 1315.28003Barnsley, Michael F.; Massopust, Peter R. 32 2015 On the continuity of the Hutchinson operator. Zbl 1371.54130Barnsley, Michael F.; Leśniak, Krzysztof 8 2015 Fast basins and branched fractal manifolds of attractors of iterated function systems. Zbl 1359.37037Barnsley, Michael F.; Vince, Andrew 4 2015 Three-dimensional fractal homeomorphisms. Zbl 1331.28015Barnsley, Michael F.; Harding, Brendan 1 2015 The chaos game on a general iterated function system from a topological point of view. Zbl 1304.28003Barnsley, Michael F.; Leśniak, Krzysztof 15 2014 Some recent progress concerning topology of fractals. Zbl 1322.54002Barnsley, Michael F.; Wilson, David C.; Leśniak, Krzysztof 12 2014 Fractal tilings from iterated function systems. Zbl 1336.28006Barnsley, Michael; Vince, Andrew 10 2014 Numerics and fractals. Zbl 1305.28015Barnsley, Michael F.; Hegland, Markus; Massopust, Peter 9 2014 The entropy of a special overlapping dynamical system. Zbl 1290.37017Barnsley, Michael; Harding, Brendan; Vince, Andrew 7 2014 Measure preserving fractal homeomorphisms. Zbl 1317.28009Barnsley, Michael F.; Harding, Brendan; Rypka, Miroslav 2 2014 Critical itineraries of maps with constant slope and one discontinuity. Zbl 1376.37031Barnsley, Michael; Steiner, Wolfgang; Vince, Andrew 1 2014 Developments in fractal geometry. Zbl 1275.28006Barnsley, Michael; Vince, Andrew 22 2013 The Conley attractors of an iterated function system. Zbl 1417.37080Barnsley, Michael F.; Vince, Andrew 20 2013 Fractal continuation. Zbl 1279.28013Barnsley, Michael F.; Vince, Andrew 14 2013 Fractal homeomorphism for bi-affine iterated function systems. Zbl 1291.28007Barnsley, Michael; Vince, Andrew 5 2013 \(V\)-variable fractals: dimension results. Zbl 1244.28008Barnsley, Michael; Hutchinson, John E.; Stenflo, Örjan 13 2012 Real projective iterated function systems. Zbl 1256.28002Barnsley, Michael F.; Vince, Andrew 12 2012 Overlapping iterated function systems on a segment. Zbl 1338.37022Barnsley, Michael; Igudesman, K. B. 2 2012 Glimpses of Benoît B. Mandelbrot (1924–2010). Zbl 1284.01047Stewart, Ian; Mumford, David; Falconer, Kenneth; Eglash, Ron; Brothers, Harlan; Lesmoir-Gordon, Nigel; Barrallo, Javier; Berry, Michael; Frame, Michael 1 2012 The influence of Benoît B. Mandelbrot on mathematics. Zbl 1284.01048Stewart, Ian; Mumford, David; Howe, Roger; Furstenberg, Hillel; Falconer, Kenneth; West, Bruce J.; Coppens, Marc-Olivier; Cohen, Nathan; Jaffard, Stéphane; Berry, Michael; Frame, Michael 1 2012 The chaos game on a general iterated function system. Zbl 1221.37079Barnsley, Michael F.; Vince, Andrew 26 2011 How to transform and filter images using iterated function systems. Zbl 1246.37024Barnsley, Michael F.; Harding, Brendan; Igudesman, Konstantin 12 2011 The eigenvalue problem for linear and affine iterated function systems. Zbl 1229.15008Barnsley, Michael; Vince, Andrew 6 2011 Topological contractive systems. Zbl 1253.37012Barnsley, M.; Igudesman, K. 4 2011 A characterization of hyperbolic affine iterated function systems. Zbl 1196.28011Atkins, Ross; Barnsley, Michael F.; Vince, Andrew; Wilson, David C. 14 2010 The life and survival of mathematical ideas. Zbl 1189.00011Barnsley, Michael F. 2 2010 Transformations between self-referential sets. Zbl 1229.28009Barnsley, Michael F. 11 2009 Measure-valued images, associated fractal transforms, and the affine self-similarity of images. Zbl 1175.94022La Torre, D.; Vrscay, E. R.; Ebrahimi, M.; Barnsley, M. F. 9 2009 \(V\)-variable fractals: Fractals with partial self similarity. Zbl 1169.28006Barnsley, Michael F.; Hutchinson, John E.; Stenflo, Örjan 33 2008 Superfractals. Zbl 1123.28007Barnsley, Michael Fielding 38 2006 A fractal valued random iteration algorithm and fractal hierarchy. Zbl 1304.28004Barnsley, Michael; Hutchinson, John; Stenflo, Örjan 28 2005 Theory and applications of fractal tops. Zbl 1192.37010Barnsley, Michael 7 2005 Iterated function systems for lossless data compression. Zbl 1030.94004Barnsley, Michael F. 3 2002 Fractals in multimedia. Based on a minisymposium held as part of the IMA annual program on mathematics in multimedia, Minneapolis, MN, USA, January 2001. Zbl 0996.00032Barnsley, Michael F.; Saupe, Dietmar; Vrscay, Edward R. 1 2002 Fractal image compression. Zbl 1114.68568Barnsley, M.; Barnsley, L. 19 1997 Stationary stochastic processes and fractal data compression. Zbl 0899.60073Barnsley, Michael F.; Deliu, Anca; Xie, Ruifeng 1 1997 Fractal image compression. Zbl 1044.94501Barnsley, Michael F. 14 1996 Fractals everywhere. Revised with the assistance of Hawley Rising III. Answer key by Hawley Rising III. 2nd ed. Zbl 0784.58002Barnsley, Michael F. 81 1993 Fractal image compression. Illustrations by Louisa F. Anson. Zbl 0796.68186Barnsley, Michael F.; Hurd, Lyman P. 31 1993 The calculus of fractal interpolation functions. Zbl 0693.41008Barnsley, Michael F.; Harrington, Andrew N. 108 1989 Recurrent iterated function systems. Zbl 0659.60045Barnsley, Michael F.; Elton, John H.; Hardin, Douglas P. 108 1989 Hidden variable fractal interpolation functions. Zbl 0704.26009Barnsley, M. F.; Elton, J.; Hardin, D.; Massopust, P. 88 1989 Erratum: Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities. Zbl 0715.60086Barnsley, M. F.; Demko, S. G.; Elton, J. H.; Geronimo, J. S. 10 1989 Chaos and fractals. The mathematics behind the computer graphics. (Lectures delivered in the AMS short course on August 6-7, 1988, given in conjunction with the AMS centennial meeting in Procidence, RI). Zbl 0677.58004 3 1989 Lecture notes on iterated function systems. Zbl 0752.58013Barnsley, Michael F. 3 1989 Fractals everywhere. Zbl 0691.58001Barnsley, Michael 593 1988 Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities. Zbl 0653.60057Barnsley, M. F; Demko, S. G.; Elton, J. H.; Geronimo, J. S. 84 1988 A new class of Markov processes for image encoding. Zbl 0643.60050Barnsley, Michael F.; Elton, John H. 42 1988 The science of fractal images. With contributions by Yuval Fisher and Michael McGuire. Ed. by Heinz-Otto Peitgen and Dietmar Saupe. (Based on notes for the course fractals - introduction, basics and pespectives given as part of the SIG-GRAPH ’87, Anaheim, Calif. course program). Zbl 0683.58003Barnsley, Michael F.; Devaney, Robert L.; Mandelbrot, Benoit B.; Peitgen, Heinz-Otto; Saupe, Dietmar; Voss, Richard 20 1988 Mixing Markov chains and their images. Zbl 1134.68576Barnsley, Michael F.; Berger, Marc A.; Soner, H. Meté 5 1988 Fractal functions and interpolation. Zbl 0606.41005Barnsley, Michael F. 265 1986 Solution of an inverse problem for fractals and other sets. Zbl 0613.28008Barnsley, M. F.; Ervin, V.; Hardin, D.; Lancaster, J. 50 1986 Chaotic dynamics and fractals. (Proceedings of a Conference on Chaotic Dynamics, Georgia Institute of Technology, Atlanta, Georgia, March 25-29, 1985). Zbl 0593.00013 4 1986 Making chaotic dynamical systems to order. Zbl 0611.58039Barnsley, Michael F. 1 1986 Iterated function systems and the global construction of fractals. Zbl 0588.28002Barnsley, M. F.; Demko, Stephen 198 1985 Almost periodic Jacobi matrices associated with Julia sets for polynomials. Zbl 0574.58016Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 14 1985 Condensed Julia sets, with an application to a fractal lattice model Hamiltonian. Zbl 0565.30018Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 6 1985 A study of Boltzmann energy equations. Zbl 0591.76134Barnsley, Michael F.; Turchetti, Giorgio 4 1985 Iterated networks and the spectra of renormalizable electromechanical systems. Zbl 0624.58038Barnsley, M. F.; Morley, T. D.; Vrscay, E. R. 1 1985 Moments of balanced measures on Julia sets. Zbl 0512.30014Barnsley, M. F.; Harrington, A. N. 9 1984 Geometrical and electrical properties of some Julia sets. Zbl 0548.30021Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 5 1984 Geometry and combinatorics of Julia sets of real quadratic maps. Zbl 0588.58054Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 3 1984 Rational approximation of fractals. Zbl 0571.41010Barnsley, Michael F.; Demko, Stephen G. 2 1984 Infinite-dimensional Jacobi matrices associated with Julia sets. Zbl 0535.30025Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 20 1983 On the invariant sets of a family of quadratic maps. Zbl 0535.30024Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 16 1983 Geometry, electrostatic measure and orthogonal polynomials on Julia sets for polynomials. Zbl 0566.41033Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 13 1983 Some tree-like Julia sets and Padé approximants. Zbl 0532.41023Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 5 1983 Solutions for a model Boltzmann equation by monotonicity methods. Zbl 0529.45007Barnsley, M. F.; Herod, J. V.; Mosher, D. L.; Passty, G. B. 3 1983 Orthogonal polynomials associated with invariant measures on Julia sets. Zbl 0509.30023Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N. 34 1982 General solution of a Boltzmann equation, and the formation of Maxwellian tails. Zbl 0488.76081Barnsley, M.; Cornille, H. 6 1981 The Tjon-Wu equation in Banach space settings. Zbl 0471.34046Barnsley, M. F.; Herod, J. V.; Jory, V. V.; Passty, G. B. 4 1981 Analysis of Boltzmann equations in Hilbert space by means of a non-linear eigenvalue property. Zbl 0494.35076Barnsley, M. F.; Herod, J. V.; Mosher, D. L.; Passty, G. B. 1 1981 On a class of solutions of the Krook-Tjon-Wu model of the Boltzmann equation. Zbl 0443.76066Barnsley, M.; Cornille, H. 6 1980 New results on the nonlinear Boltzmann equation. Zbl 0432.76062Barnsley, Michael F.; Turchetti, Giorgio 2 1980 Bounds for the rth characteristic frequency of a beaded string or of an electrical filter. Zbl 0435.15009Barnsley, Michael F.; Duffin, Richard J. 1 1980 The Diophantine moment problem and the analytic structure in the activity of the ferromagnetic Ising model. Zbl 0454.44006Barnsley, M.; Bessis, D.; Moussa, P. 9 1979 Pointwise bivariational bounds on solutions of Fredholm integral equations. Zbl 0395.65066Robinson, Peter D.; Barnsley, Michael F. 6 1979 Rational approximant bounds for a class of two-variable Stieltjes functions. Zbl 0375.41006Barnsley, M. F.; Robinson, P. D. 1 1978 Bivariational bounds for non-linear problems. Zbl 0383.49035Barnsley, M. F.; Robinson, P. D. 4 1977 Bivariational bounds associated with non-self-adjoint linear operators. Zbl 0344.49032Barnsley, Michael F.; Robinson, Peter D. 4 1976 Bivariational bounds in a complex Hilbert space, and correction terms for Padé approximants. Zbl 0322.41011Barnsley, M. F.; Baker, George A. jun. 3 1976 Padé approximant bounds for the difference of two series of Stieltjes. Zbl 0332.41014Barnsley, M. F. 1 1976 Correction terms for Padé approximants. Zbl 0298.41007Barnsley, M. F. 7 1975 Bivariational bounds. Zbl 0295.49022Barnsley, M. F.; Robinson, P. D. 16 1974 Dual variational principles and Padé-type approximants. Zbl 0286.65035Barnsley, M. F.; Robinson, P. D. 4 1974 Padé-approximant bounds and approximate solutions for Kirkwood-Riseman integral equations. Zbl 0286.65063Barnsley, M. F.; Robinson, P. D. 1 1974 The bounding properties of the multipoint Padé approximant to a series of Stieltjes on the real line. Zbl 0279.41013Barnsley, Michael 10 1973 A variational approach to the theory of multipoint Padé approximants. Zbl 0279.41012Epstein, Saul T.; Barnsley, Michael F. 2 1973 all cited Publications top 5 cited Publications all top 5 Cited by 1,473 Authors 62 Chand, Arya Kumar Bedabrata 50 Navascués, María Antonia 46 Barnsley, Michael Fielding 34 Viswanathan, Puthan Veedu 22 La Torre, Davide 22 Miculescu, Radu 22 Mihail, Alexandru 19 Vijender, Nallapu 19 Vince, Andrew 16 Mantica, Giorgio 16 Vrscay, Edward Robert 15 Mendivil, Franklin 14 Geronimo, Jeffrey S. 13 Kunze, Herb E. 13 Massopust, Peter R. 13 Strobin, Filip 12 Jørgensen, Palle E. T. 12 Sebastián, María Victoria 11 Harrington, Andrew N. 11 Kunze, Harald 11 Prasad, M. Guru Prem 10 Bandt, Christoph 10 Katiyar, Saurabh Kumar 10 Panagiotopoulos, Panagiotis D. 10 Ruan, Huo-Jun 10 Stenflo, Orjan 10 Yun, Cholhui 9 Andres, Jan 9 Bouboulis, Pantelis 9 Drakopoulos, Vasileios 9 Jha, Sangita 9 Leśniak, Krzysztof 9 Panagouli, O. K. 9 Ri, Songil 9 Wang, Hongyong 8 Dalla, Leoni 8 Gowrisankar, A. 8 Kapoor, Govind P. 8 Secelean, Nicolae-Adrian 8 Wang, Xingyuan 7 Bessis, Daniel 7 Fraser, Jonathan MacDonald 7 Hardin, Douglas P. 7 Horbacz, Katarzyna 7 Igudesman, Konstantin B. 7 Luor, Dahchin 7 Mistakidis, E. S. 7 Oliveira, Elismar R. 7 Prasad, Srijanani Anurag 7 Roychowdhury, Mrinal Kanti 7 Saltan, Mustafa 7 Trutschnig, Wolfgang 7 Tyada, K. R. 7 Uthayakumar, Ramasamy 6 Akhtar, Md. Nasim 6 Balasubramani, N. 6 Banakh, Taras Onufrievich 6 Demir, Bunyamin 6 Ioana, Loredana 6 Koçak, Şahin 6 Mathew Karakkad, Sunil 6 Matias, Edgar 6 Molter, Ursula Maria 6 Özdemir, Yunus 6 Privileggi, Fabio 6 Ruiz Galán, Manuel 6 Sarizadeh, Aliasghar 6 Serpa, Cristina 6 Shorten, Robert N. 6 Szarek, Tomasz Jakub 5 Alpan, Gökalp 5 Cabrelli, Carlos A. 5 Chitescu, Ion 5 Culik, Karel II 5 Drewes, Frank 5 Feng, Zhigang 5 Fernández-Sánchez, Juan 5 Gdawiec, Krzysztof 5 Lasota, Andrzej 5 Moussa, Pierre 5 Nia, Mehdi Fatehi 5 Nowak, Magdalena 5 Pan, Xuezai 5 Petruşel, Adrian 5 Puente, Carlos E. 5 Ri, Mi-Gyong 5 Rypka, Miroslav 5 Sirvent, Víctor F. 5 Staiger, Ludwig 5 Turchetti, Giorgio 5 Zhu, Sanguo 5 Zhuang, Zhuo 4 Bory Reyes, Juan 4 Buescu, Jorge 4 David, Claire 4 Díaz, Lorenzo Justiniano 4 Dutkay, Dorin Ervin 4 Elton, John H. 4 Fernau, Henning 4 Goncharov, Alexander P. ...and 1,373 more Authors all top 5 Cited in 329 Serials 102 Chaos, Solitons and Fractals 102 Fractals 73 Journal of Mathematical Analysis and Applications 29 Journal of Computational and Applied Mathematics 23 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 21 Communications in Nonlinear Science and Numerical Simulation 18 Applied Mathematics and Computation 18 Journal of Approximation Theory 18 Proceedings of the American Mathematical Society 17 Computers & Mathematics with Applications 17 Theoretical Computer Science 17 Ergodic Theory and Dynamical Systems 17 Physica D 16 Journal of Statistical Physics 15 Journal of Mathematical Physics 14 Results in Mathematics 14 Transactions of the American Mathematical Society 14 Topology and its Applications 13 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Mediterranean Journal of Mathematics 11 Acta Applicandae Mathematicae 11 Constructive Approximation 9 Bulletin of the Australian Mathematical Society 9 Rocky Mountain Journal of Mathematics 9 Aequationes Mathematicae 9 International Journal of Computer Mathematics 9 Discrete and Continuous Dynamical Systems 9 Chaos 9 Journal of Fractal Geometry 8 Communications in Mathematical Physics 8 Nonlinearity 8 Statistics & Probability Letters 8 Applied Mathematics Letters 8 Linear Algebra and its Applications 8 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 7 Physica A 7 Fuzzy Sets and Systems 7 Numerical Functional Analysis and Optimization 7 Indagationes Mathematicae. New Series 7 Applied Mathematics. Series B (English Edition) 7 Journal of Difference Equations and Applications 7 Qualitative Theory of Dynamical Systems 7 Fixed Point Theory and Applications 7 Journal of Fixed Point Theory and Applications 7 Nonlinear Analysis. Theory, Methods & Applications 6 Advances in Mathematics 6 Monatshefte für Mathematik 6 Numerical Algorithms 6 Russian Mathematics 6 Computational and Applied Mathematics 6 Mathematical Problems in Engineering 6 Nonlinear Dynamics 6 Abstract and Applied Analysis 5 Information Processing Letters 5 The Mathematical Intelligencer 5 Journal of Theoretical Probability 5 The Journal of Geometric Analysis 5 Stochastic Processes and their Applications 5 Applied and Computational Harmonic Analysis 5 Nonlinear Analysis. Real World Applications 5 Journal of Dynamical Systems and Geometric Theories 5 Advances in Difference Equations 5 Complex Analysis and Operator Theory 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Physics Letters. A 4 Automatica 4 Calcolo 4 Mathematics and Computers in Simulation 4 Mathematische Nachrichten 4 Advances in Applied Mathematics 4 Acta Mathematicae Applicatae Sinica. English Series 4 RAIRO. Informatique Théorique et Applications 4 Journal of Mathematical Imaging and Vision 4 The Journal of Analysis 4 Fractional Calculus & Applied Analysis 4 Dynamical Systems 4 Journal of Applied Mathematics 4 Stochastics and Dynamics 4 Bulletin of the Brazilian Mathematical Society. New Series 3 Acta Informatica 3 Applicable Analysis 3 Mathematical Biosciences 3 Ukrainian Mathematical Journal 3 Wave Motion 3 BIT 3 Geometriae Dedicata 3 Information Sciences 3 Journal of Algebra 3 Journal of Applied Probability 3 Journal of Statistical Planning and Inference 3 Mathematische Zeitschrift 3 Quaestiones Mathematicae 3 Acta Mathematica Hungarica 3 Probability Theory and Related Fields 3 Applied Mathematical Modelling 3 Pattern Recognition 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Journal of Dynamics and Differential Equations 3 Experimental Mathematics 3 Potential Analysis ...and 229 more Serials all top 5 Cited in 59 Fields 662 Measure and integration (28-XX) 413 Dynamical systems and ergodic theory (37-XX) 174 Numerical analysis (65-XX) 170 Approximations and expansions (41-XX) 139 Computer science (68-XX) 136 Probability theory and stochastic processes (60-XX) 115 Operator theory (47-XX) 95 General topology (54-XX) 89 Real functions (26-XX) 76 Information and communication theory, circuits (94-XX) 75 Harmonic analysis on Euclidean spaces (42-XX) 46 Functions of a complex variable (30-XX) 43 Ordinary differential equations (34-XX) 40 Functional analysis (46-XX) 35 Statistics (62-XX) 34 Biology and other natural sciences (92-XX) 33 Partial differential equations (35-XX) 30 Difference and functional equations (39-XX) 30 Quantum theory (81-XX) 29 Number theory (11-XX) 27 Combinatorics (05-XX) 26 Convex and discrete geometry (52-XX) 26 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 24 Statistical mechanics, structure of matter (82-XX) 22 Linear and multilinear algebra; matrix theory (15-XX) 21 Operations research, mathematical programming (90-XX) 21 Systems theory; control (93-XX) 17 Global analysis, analysis on manifolds (58-XX) 17 Mechanics of deformable solids (74-XX) 16 Special functions (33-XX) 15 Potential theory (31-XX) 13 Integral equations (45-XX) 12 Group theory and generalizations (20-XX) 11 Mathematical logic and foundations (03-XX) 10 Fluid mechanics (76-XX) 7 General and overarching topics; collections (00-XX) 7 Geometry (51-XX) 6 Topological groups, Lie groups (22-XX) 6 Manifolds and cell complexes (57-XX) 5 Algebraic geometry (14-XX) 5 Abstract harmonic analysis (43-XX) 5 Geophysics (86-XX) 4 Differential geometry (53-XX) 4 Algebraic topology (55-XX) 3 History and biography (01-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Relativity and gravitational theory (83-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Category theory; homological algebra (18-XX) 2 \(K\)-theory (19-XX) 2 Sequences, series, summability (40-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mechanics of particles and systems (70-XX) 2 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Mathematics education (97-XX) 1 Field theory and polynomials (12-XX) 1 Nonassociative rings and algebras (17-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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