Areas of expertise

• Dynamical Systems In Applications 010204

Research interests

Publications

• Barnsley, M & Vince, A 2020, 'Tilings from graph directed iterated function systems', Geometriae Dedicata, vol. 212, pp. 299â324.
• Barnsley, M & Mihalache, N 2019, 'Symmetric itinerary sets', Bulletin of the Australian Mathematical Society, vol. 100, no. 1, pp. 97-108.
• Barnsley, M, Lesniak, K & Rypka, M 2018, 'Basic topological structure of fast basins', Fractals. Complex Geometry, Patterns and Scaling in Nature and Society, vol. 26, no. 1, pp. 11pp.
• Vince, A & Barnsley, M 2018, 'Self-Similar Polygonal Tiling: extended abstract', Electronic Notes in Discrete Mathematics, vol. 68, pp. 5-10.
• Barnsley, M & Vince, A 2017, 'Self-Similar polygonal tiling', The American Mathematical Monthly, vol. 124, no. 10, pp. 905-921.
• Barnsley, M, Lesniak, K & Rypka, M 2016, 'Chaos game for IFSs on topological spaces', Journal of Mathematical Analysis and Applications, vol. 435, no. 2, pp. 1458-1466.
• Barnsley, M, Harding, B, Vince, A et al. 2016, 'Approximation of rough functions', Journal of Approximation Theory, vol. 209, no. -, pp. 23-43.
• Barnsley, M & Vince, A 2015, 'Fast basins and branched fractal manifolds of attractors of iterated function systems', Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), vol. 11, no. 084, pp. 1-21.
• Barnsley, M & Lesniak, K 2015, 'On the Continuity of the Hutchinson Operator', Symmetry, vol. 7, no. 4, pp. 1831-1840.
• Barnsley, M & Harding, B 2015, 'Three-Dimensional Fractal Homeomorphisms', in (ed.), Benoit Mandelbrot : a life in many dimensions, New Jersey World Scientific, New Jersey, pp. 117-142.
• Barnsley, M & Massopust, P 2015, 'Bilinear fractal interpolation and box dimension', Journal of Approximation Theory, vol. 192, pp. 362-378.
• Barnsley, M & Lesniak, K 2014, 'The Chaos game on a general iterated function system from a topological point of view', International Journal of Bifurcation and Chaos, vol. 24, no. 11, pp. 1-10pp.
• Barnsley, M & vince, A 2014, 'Fractal Tilings from Iterated Function Systems', Discrete and Computational Geometry, vol. 51, no. 3, pp. 729-752.
• Barnsley, M, Harding, B & Rypka, M 2014, 'Measure preserving fractal homeomorphisms', 1st International Conference and Workshop on Fractals and Wavelets, ICFW India, ed. C Bandt, M Barnsley, R Devaney, K Falconer, V Kannan, P B Vinod Kumar, Springer, India, pp. 79-102.
• Barnsley, M, Harding, T & vince, A 2012, 'The entropy of an overlapping dynamical system', Ergodic Theory and Dynamical Systems, available on CJO2012. doi:10.1017/etds.2012.140.
• Barnsley, M, Hegland, M & Massopust, P 2014, 'Numerics and Fractals', Bulletin of the Institute of Mathematics, Academia Sinica (New Series), vol. 9, no. 3, pp. 389-430.
• Barnsley, M, Steiner, W & Vince, A 2014, 'Critical itineraries of maps with constant slope and one discontinuity', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 157, no. 3, pp. 547-565.
• Barnsley, M, Wilson, D & Lesniak, K 2014, 'Some Recent Progress Concerning Topology of Fractals', in (ed.), Recent Progress in General Topology III, Atlantis Press, Paris, pp. 69-92.
• Barnsley, M & vince, A 2013, 'Fractal Continuation', Constructive Approximation, vol. 38, no. 2, pp. 311-337.
• Barnsley, M & Vince, A 2013, 'Fractal homeomorphism for bi-affine iterated function systems', International Journal of Applied Nonlinear Science, vol. 1, no. 1, pp. 3-19.
• Barnsley, M & Vince, A 2013, 'The Conley attractors of an iterated function system', Bulletin of the Australian Mathematical Society. doi:10.1017/S0004972713000348
• Barnsley, M and Vince, A , 2013 'Developments in fractal geometry', Bulletin of Mathematical Sciences,doi:10.1007/s13373-013-0041-3
• Barnsley, M, Freiberg, U & La Torre, D 2012, 'Optimization on fractals and stability', Journal of Nonlinear and Convex Analysis, vol. 13, no. 4, pp. 695-708.
• Barnsley, M & Frame, M 2012, 'The influence of Benoît B. Mandelbrot on mathematics', Notices of the American Mathematical Society, vol. 59, no. 9, pp. 1208-1221.
• Barnsley, M & Igudesman, K 2012, 'Overlapping iterated function systems on a segment', Russian Mathematics, vol. 56, no. 12, pp. 1-12.
• Barnsley, M 2012, Fractals Everywhere: New Edition, Dover Publications, USA.
• Barnsley, M & Frame, M 2012, 'Glimpses of Benoît B. Mandelbrot (1924-2010)', Notices of the American Mathematical Society, vol. 59, no. 8, pp. 1056-1063.
• Barnsley, M & vince, A 2011, 'The chaos game on a general iterated function system', Ergodic Theory and Dynamical Systems, vol. 31, no. 4, pp. 1073-1079.
• Barnsley, M, Hutchinson, J & Stenflo, O 2012, 'V-variable fractals: dimension results', Forum Mathematicum, vol. 24, no. 3, pp. 445-470.
• Barnsley, M & Vince, A 2011, 'The eigenvalue problem for linear and affine iterated function systems', Linear Algebra and its Applications, vol. 435, pp. 3124-3138.
• Barnsley, M & Vince, A 2011, 'Real Projective Iterated Function Systems', Journal of Geometric Analysis, vol. Online, pp. 1-36.
• Barnsley, M & Igudesman, K 2011, 'Topological Contractive Systems', Lobachevskii Journal of Mathematics, vol. 32, no. 3, pp. 220-223.
• Barnsley, M, Harding, B & Igudesman, K 2011, 'How to Transform and Filter Images Using Iterated Function Systems', SIAM Journal of Imaging Sciences, vol. 4, no. 4, pp. 1001-1028.
• Atkins, R, Barnsley, M, Vince, A et al 2010, 'A CHARACTERIZATION OF HYPERBOLIC AFFINE ITERATED FUNCTION SYSTEMS', Topology proceedings, vol. 36, pp. 189-211.
• Barnsley, M 2010, 'The life and survival of mathematical ideas', Notices of the American Mathematical Society, vol. 57, no. 1, pp. 10-22.
• Barnsley, M 2009, 'Transformations between Self-Referential Sets', The American Mathematical Monthly, vol. 116, no. 4, pp. 291-304.
• Barnsley, M, La Torre, D, Vrscay, E et al 2009, 'Measure-Valued Images, Associated Fractal Transforms and the Affine Self-Similarity of Images', SIAM Journal of Imaging Sciences, vol. 2, no. 2, pp. 470-507.
• Barnsley, M 2009, 'Transformations Between Fractals', in Christoph Bandt, Peter Morters, Martina Zahle (ed.), Fractal Geometry and Stochastics IV, Birkhauser Verlag, Basel, pp. 227-250.
• Barnsley, M, Hutchinson, J & Stenflo, O 2008, 'V-variable fractals: Fractals with partial self similarity', Advances in Mathematics, vol. 218, pp. 2051-2088.
• Barnsley, M 2007, 'Book Review: Differential Equations on Fractals: A Tutorial', SIAM Review, vol. 49, no. 4, pp. 695-732.
• Barnsley, M & Freiberg, U 2007, 'Fractal transformations of harmonic functions', Complexity and Nonlinear Dynamics Conference 2006, ed. Axel Bender, SPIE - The International Society for Optical Engineering, Washington USA, pp. 64170C.
• Barnsley, M 2006, Superfractals, Cambridge University Press, New York, USA.
• Barnsley, M & Hutchinson, J 2006, 'New Methods in Fractal Imaging', International Conference on Computer Graphics, Imaging and Visualisation 2006, ed. Conference Program Committee, Institute of Electrical and Electronics Engineers (IEEE Inc), Piscataway USA, pp. 296-301.
• Barnsley, M 2005, 'Theory and Applications of Fractal Tops', in Jacques Levy-Veheland Evelyne Lutton (ed.), Fractals in Engineering: new trends in theory and applications, Springer, London UK, pp. 3-20.
• Barnsley, M, Hutchinson, J & Stenflo, O 2005, 'A fractal valued random iteration algorithm and fractal hierachy', Fractals. Complex Geometry, Patterns and Scaling in Nature and Society, vol. 13, no. 2, pp. 111-146.
• Barnsley, M & Barnsley, L 2004, 'Fractal Transformations', in Nigel Lesmoir-Gordon (ed.), The Colours of Infinity: The Beauty, The Power and the Sense of Fractals, Clear Books, London, pp. 66-81.
• Barnsley, M 2002, 'Iterated function systems for lossless data compression', in Michael F Barnsley, Dietmar Saupe, Edward R Vrscay (ed.), Fractals in Multimedia, Springer, New York, pp. 33-63.
• Barnsley, M, Vrscay, E & Saupe, D 2002, 'Fractals in Multimedia', IMA Journal of Applied mathematics, vol. 132, p. 259.
• Barnsley, M 2002, 'Introduction to IMA fractal proceedings', in Michael F Barnsley, Dietmar Saupe, Edward R Vrscay (ed.), Fractals in Multimedia, Springer, New York, pp. 1-12.

Projects and Grants

Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.

• Theory and Applications of Three Dimensional Fractal Transformations (Primary Investigator)

Related websites

• http://www.superfractals.com