Michael Barnsley

Q: What Schools Are Affiliated With Michael Barnsley

Michael Barnsley is affiliated with the following schools: University of Wisconsin–Madison, University of Georgia, Georgia Tech, Australian National University

Michael Barnsley's AcademicInfluence.com Rankings

Michael Barnsley

Mathematics

#896

World Rank

#1573

Historical Rank

#393

USA Rank

Measure Theory

#87

World Rank

#141

Historical Rank

#45

USA Rank

mathematics Degrees

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Mathematics

Why Is Michael Barnsley Influential?

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According to Wikipedia, Michael Fielding Barnsley is a British mathematician, researcher and an entrepreneur who has worked on fractal compression; he holds several patents on the technology. He received his Ph.D. in theoretical chemistry from University of Wisconsin–Madison in 1972 and BA in mathematics from Oxford in 1968. In 1987 he founded Iterated Systems Incorporated, and in 1988 he published a book entitled Fractals Everywhere and in 2006 SuperFractals.

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Michael Barnsley's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Fractals everywhere (1988) (4541)
The science of fractal images (2011) (1825)
Fractal image compression (1993) (1035)
Iterated function systems and the global construction of fractals (1985) (998)
Fractal functions and interpolation (1986) (692)
A better way to compress images (1988) (429)
Recurrent iterated function systems (1989) (355)
Solution of an inverse problem for fractals and other sets. (1986) (340)
Invariant measures for Markov processes arising from iterated function systems with place-dependent (1988) (248)
The calculus of fractal interpolation functions (1989) (236)
Hidden variable fractal interpolation functions (1989) (180)
Application Of Recurrent Iterated Function Systems To Images (1988) (141)
A new class of markov processes for image encoding (1988) (134)
Fractals everywhere, 2nd Edition (1993) (129)
Harnessing chaos for image synthesis (1988) (119)
V -variable fractals: Fractals with partial self similarity ✩ (2008) (87)
Bilinear fractal interpolation and box dimension (2012) (74)
The chaos game on a general iterated function system (2010) (72)
Fractal modelling of real world images (1988) (59)
A FRACTAL VALUED RANDOM ITERATION ALGORITHM AND FRACTAL HIERARCHY (2003) (58)
Orthogonal polynomials associated with invariant measures on Julia sets (1982) (52)
The bounding properties of the multipoint Padé approximant to a series of Stieltjes on the real line (1973) (47)
Developments in fractal geometry (2013) (43)
Measure-Valued Images, Associated Fractal Transforms, and the Affine Self-Similarity of Images (2009) (42)
THE CONLEY ATTRACTORS OF AN ITERATED FUNCTION SYSTEM (2012) (37)
Almost periodic Jacobi matrices associated with Julia sets for polynomials (1985) (35)
Shorter Notes: Erratum to "Infinite-Dimensional Jacobi Matrices Associated with Julia Sets" (1983) (34)
On the invariant sets of a family of quadratic maps (1983) (34)
Real Projective Iterated Function Systems (2010) (33)
Transformations between Self-Referential Sets (2009) (33)
A mandelbrot set for pairs of linear maps (1985) (32)
Fractal video compression (1992) (31)
Fractal Modeling of Biological Structures (1987) (30)
On a class of solutions of the Krook–Tjon–Wu model of the Boltzmann equation (1980) (28)
A Characterization of Hyperbolic Affine Iterated Function Systems (2009) (27)
Fractals Everywhere: New Edition (2012) (27)
How to Transform and Filter Images Using Iterated Function Systems (2011) (26)
A variational approach to the theory of multipoint Padé approximants (1973) (26)
The entropy of a special overlapping dynamical system (2011) (26)
Numerics and Fractals (2013) (24)
Chaos game for IFSs on topological spaces (2014) (23)
The Chaos Game on a General Iterated Function System from a Topological Point of View (2010) (23)
Fractal Tilings from Iterated Function Systems (2014) (23)
Geometry, electrostatic measure and orthogonal polynomials on Julia sets for polynomials (1983) (22)
The Diophantine moment problem and the analytic structure in the activity of the ferromagnetic Ising model (1979) (22)
Some Recent Progress Concerning Topology of Fractals (2014) (22)
Moments of balanced measures on Julia sets (1984) (20)
Chapter V – Fractal Dimension (1993) (19)
Fractal Continuation (2012) (19)
On the Abel transformation and the nonlinear Boltzmann equation (1979) (19)
Lower bounds for quantum mechanical energy levels (1978) (18)
Theory and Applications of Fractal Tops (2005) (17)
On the Continuity of the Hutchinson Operator (2012) (17)
Fractal homeomorphism for bi-affine iterated function systems (2011) (15)
V-variable fractals and superfractals (2003) (15)
General solution of a Boltzmann equation, and the formation of Maxwellian tails (1981) (14)
Iterated Function Systems for Lossless Data Compression (2002) (13)
Old wine in fractal bottles I: Orthogonal expansions on self-referential spaces via fractal transformations (2016) (13)
Mixing Markov Chains and Their Images (1988) (13)
-variable fractals: dimension results (2012) (12)
Correction terms for Padé approximants (1975) (12)
Condensed Julia sets, with an application to a fractal lattice model Hamiltonian (1985) (12)
Fractals in Multimedia (2002) (11)
Erratum to: Nonlinear Boltzmann equations and kinetic stochastic equations (1981) (11)
The Eigenvalue Problem for Linear and Affine Iterated Function Systems (2010) (11)
Critical itineraries of maps with constant slope and one discontinuity (2014) (11)
The life and survival of mathematical ideas (2010) (11)
Pointwise Bivariational Bounds on Solutions of Fredholm Integral Equations (1979) (11)
MAKING CHAOTIC DYNAMICAL SYSTEMS TO ORDER (1986) (10)
The Tjon-Wu equation in Banach space settings (1981) (10)
Rendering and magnification of fractals using iterated function systems (1987) (10)
Self-Similar Polygonal Tiling (2016) (10)
Bivariational Bounds for Non-linear Problems (1977) (10)
Iterated Function Systems (2015) (10)
9.—Bivariational Bounds associated with Non-self-adjoint Linear Operators (1976) (10)
New Methods in Fractal Imaging (2006) (10)
Fractal Continuation of Analytic (Fractal) Functions (2012) (9)
Generalized Padé resummation of the solution of a nonlinear Boltzmann equation (1979) (9)
Calculation of some solutions of the Bobylev-Krook-Wu and Tjon-Wu equations (1981) (9)
Basic Topological Structure of Fast Basins (2013) (9)
New Results on the Nonlinear Boltzmann Equation (1980) (9)
The Influence of Benoît B. Mandelbrot on mathematics (2012) (9)
Dual Variational Principles and Padé-type Approximants (1974) (9)
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems (2013) (9)
Existence and Uniqueness of Orbital Measures (2005) (8)
Some tree-like Julia sets and Padé approximants (1983) (8)
Topological contractive systems (2011) (8)
Iterated networks and the spectra of renormalizable electromechanical systems (1985) (8)
Approximation of rough functions (2014) (8)
A Better Way to Compress Images Mathematics is providing a novel technique forachieving compression ratios of 10 , 000 to 1-and higher (2002) (7)
Bivariational bounds in a complex Hilbert space, and correction terms for Padé approximants (1976) (7)
Rational approximation of fractals (1984) (7)
Stationary Stochastic Processes and Fractal Data Compression (1997) (7)
A Mandelbrot set whose boundary is piecewise smooth (1989) (7)
Geometry and combinatorics of Julia sets of real quadratic maps (1984) (7)
A study of Boltzmann energy equations (1985) (6)
SUM RULE FUNCTIONS. (1971) (6)
Transformations Between Fractals (2009) (6)
SYMMETRIC ITINERARY SETS (2011) (6)
Self-similar tilings of fractal blow-ups (2017) (6)
ERGODIC THEORY , FRACTAL TOPS AND COLOUR (2003) (5)
Symbolic Iterated Function Systems, Fast Basins and Fractal Manifolds (2013) (5)
Measure Preserving Fractal Homeomorphisms (2014) (5)
Energy and Laplacian on Hanoi-type fractal quantum graphs (2016) (5)
On the approximation of potential-energy functions for two-center systems (1978) (5)
Padé approximant bounds for the difference of two series of Stieltjes (1976) (5)
Fractal transformations of harmonic functions (2006) (5)
Pointwise bounds for eigenfunctions of one-electron systems (1975) (5)
Variational bounds on overlaps (in Hilbert space) (1975) (5)
Transformations between attractors of hyperbolic iterated function systems (2007) (5)
Three-dimensional fractal homeomorphisms (2015) (4)
Tiling iterated function systems and Anderson-Putnam theory (2018) (4)
Erratum to “Infinite-dimensional Jacobi matrices associated with Julia sets” [Proc. Amer. Math. Soc. 88\ (1983), no. 4, 625–630; MR0702288 (85a:30040)] (1984) (4)
Rational Approximant Bounds for a Class of Two-Variable Stieltjes Functions (1978) (4)
Padé-approximant Bounds and Approximate Solutions for Kirkwood-Riseman Integral Equations (1974) (4)
Fractal Transformations in 2 and 3 Dimensions (2013) (4)
Some operators which commute in a nonlinear Boltzmann equation (1981) (4)
Self-referential Functions (2016) (4)
Overlapping iterated function systems on a segment (2012) (4)
Tilings from graph directed iterated function systems (2019) (4)
Bivariational bounds (1974) (4)
A Combinatorial Characterization of the Critical Itineraries of a Uniform Dynamical System (2012) (3)
Fractals for Everyone (1989) (3)
Bounding methods in nuclear physics (1981) (3)
Bivariational bounds on solutions of two-point boundary-value problems (1976) (3)
Homeomorphisms generated from overlapping affine iterated function systems (2011) (3)
Fractals, Wavelets, and their Applications (2014) (3)
Chaotic Dynamics on Fractals (1993) (3)
Variational bounds on transition probabilities (1975) (3)
Fractal Tiling (2013) (3)
Introduction to IMA Fractal Proceedings (2002) (2)
Projection method for Boltzmann energy equations (1982) (2)
A method of fractal coding for measure-valued images (2006) (2)
Padé approximant bounds on the positive solutions of some nonlinear elliptic equations (1978) (2)
Conjugacies provided by fractal transformations I : Conjugate measures, Hilbert spaces, orthogonal expansions, and flows, on self-referential spaces (2014) (2)
Analysis of Boltzmann Equations in Hilbert Space by Means of a Non-Linear Eigenvalue Property (1981) (2)
System for guaranteed high-quality video compression (1998) (1)
Approximation Theory on a Snowflake (1982) (1)
Chaotic Dynamics and Fractals. Volume 2. Notes and Reports in Mathematics in Science and Engineering. (1986) (1)
Fractal Tilings from Iterated Function Systems (2014) (1)
Fractal Image Encoding (1988) (1)
Bounds for the Linearly Perturbed Eigenvalue Problem (1981) (1)
Transformations on Metric Spaces; Contraction Mappings; and the Construction of Fractals (1993) (1)
Bounds on dynamical polarizabilities at high frequencies (1975) (1)
Metric Spaces; Equivalent Spaces; Classification of Subsets; and the Space of Fractals (1993) (1)
Measures on Fractals (1993) (1)
Rigorous bounds for charge densities from form factor data (1979) (1)
Discontinuous Fractal Functions and Fractal Histopolation (2015) (1)
Tiling Iterated Function Systems (2020) (1)
Constructive methods based on analytic characterizations and their application to nonlinear elliptic and parabolic differential equations (1979) (1)
Chapter VI – Fractal Interpolation (1993) (1)
A method and apparatus for processing numeric data (1990) (1)
Fractal Image Filters for Specialized Image Recognition Tasks (2010) (0)
The Desktop Fractal Design Handbook (2014) (0)
Codes, metrics and topologies (2006) (0)
Your letters [Opinion Feedback] (2013) (0)
The Boltzmann energy equations (1984) (0)
Semigroups on sets, measures and pictures (2006) (0)
Fractal Continuation (2013) (0)
Julia Sets and Autonomous Differential Equations (1984) (0)
Parameter Spaces and Mandelbrot Sets (1993) (0)
Fractals, Wavelets, and their Applications : Contributions from the International Conference and Workshop on Fractals and Wavelets (2014) (0)
Superfractals: Transformations of points, sets, pictures and measures (2006) (0)
Erratum to: Nonlinear Boltzmann equations and kinetic stochastic equations (1981) (0)
CENTRAL OPEN SETS TILINGS (2021) (0)
Bivariational bounds on 〈g,φ〉 for non-linear problems Fφ=O (1976) (0)
Distortion Reversal in Aperiodic Tilings (2021) (0)
ESTIMATES AND BOUNDS FOR THE DOUBLY PERTURBED EIGENVALUE PROBLEM (1982) (0)
Optimization on fractals and stability (2012) (0)
New variational bounds on expectation values (in quantum mechanics) (1975) (0)
The Desktop Fractal Design System Handbook (1989) (0)
where the y,'s and k are finite positive integers and the a,'s are complex numbers. If (2016) (0)
Texture Synthesis using Super Fractal (2004) (0)
Hyperbolic IFSs, attractors and fractal tops (2006) (0)
Installation and Operation of Your Desktop Fractal Design System (1989) (0)
Self-Similar Polygonal Tiling: extended abstract (2018) (0)
Chapter VII – Julia Sets (1993) (0)
COMPRESSION AND DECOMPRESSION OF DIGITAL MAGE DATA (2017) (0)
PR ] 1 6 D ec 2 00 3 V-variable fractals and superfractals (2003) (0)
Introduction: Products of the Desktop Fractal Design System (1989) (0)
Parameter dependence of solutions of classes of quasi-linear elliptic and parabolic differential equations (1980) (0)
Chapter X – Recurrent Iterated Function Systems (1993) (0)
New variational bounds on expectation values (1975) (0)
Blowups and Tops of Overlapping Iterated Function Systems (2023) (0)
Tilings from graph directed iterated function systems (2020) (0)
How to Use the Desktop Fractal Design System (1989) (0)
Histopolating fractal functions (2023) (0)
Bivariational bounds on 〈ϕ,g〉, when Aϕ=f (1974) (0)
Overlapping iterated function systems on a segment (2012) (0)
The desktop fractal design system handbook : Macintosh version 2.0 (1992) (0)
Special issue on fractal geometry, dynamical systems, and their applications (2019) (0)
The desktop fractal design system handbook : IBM PC version 2.0 (1992) (0)
Real Projective Iterated Function Systems (2011) (0)
The Desktop Fractal Design System/Macintosh/Handbook and Floppy Disk (1990) (0)
Foreword to the Second Edition (1993) (0)
Harmonizable Fractional Stable Fields : Local Nondeterminism and Joint Continuity of the Local Times (2014) (0)

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What Schools Are Affiliated With Michael Barnsley?

Michael Barnsley is affiliated with the following schools: