Benoit Mandelbrot | Academic Influence

Why Is Benoit Mandelbrot Influential?

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According to Wikipedia, Benoit B. Mandelbrot was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.

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Benoit Mandelbrot'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 Papers

Fractal Geometry of Nature (1984) (25197)
Fractional Brownian Motions, Fractional Noises and Applications (1968) (6903)
The Variation of Certain Speculative Prices (1963) (3291)
How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension (1967) (3220)
Fractals: Form, Chance and Dimension (1978) (2969)
Fractal character of fracture surfaces of metals (1984) (1593)
Fractals and Scaling in Finance (1997) (1154)
Noah, Joseph, and Operational Hydrology (1968) (991)
Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence (1969) (892)
Some long‐run properties of geophysical records (1969) (886)
Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier (1974) (850)
Self-Affine Fractals and Fractal Dimension (1985) (797)
Intermittent turbulence in self-similar cascades : divergence of high moments and dimension of the carrier (2004) (786)
RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. (1964) (759)
New Methods in Statistical Economics (1963) (654)
THE PARETO-LEVY LAW AND THE DISTRIBUTION OF INCOME* (1960) (620)
A Multifractal Model of Asset Returns (1997) (544)
On the Distribution of Stock Price Differences (1967) (516)
The Variation of Some Other Speculative Prices (1967) (510)
Computer Experiments With Fractional Gaussian Noises: Part 1, Averages and Variances (1969) (485)
Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis (1972) (480)
The Misbehavior of Markets: A Fractal View of Risk, Ruin, and Reward (2004) (479)
Stochastic models for the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. (1975) (473)
When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models (1971) (456)
Forecasts of Future Prices, Unbiased Markets, and "Martingale" Models (1966) (414)
Fractals and Scaling In Finance: Discontinuity, Concentration, Risk (2010) (399)
Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E (1997) (371)
Multifractal measures, especially for the geophysicist (1989) (359)
A Multifractal Walk down Wall Street (1999) (327)
A Fast Fractional Gaussian Noise Generator (1971) (326)
Some noises with I/f spectrum, a bridge between direct current and white noise (1967) (324)
The fractal geometry of nature /Revised and enlarged edition/ (1983) (292)
How Long Is the Coast of Britain ? (2002) (291)
Computer Experiments with Fractional Gaussian Noises: Part 2, Rescaled Ranges and Spectra (1969) (286)
A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices: Comment (1973) (285)
Critical Phenomena on Fractal Lattices (1980) (275)
Long-Run Linearity, Locally Gaussian Process, H-Spectra and Infinite Variances (1969) (263)
Solvable Fractal Family, and Its Possible Relation to the Backbone at Percolation (1981) (261)
Fractals and Chaos (2004) (261)
Fractal properties of rain, and a fractal model (1985) (261)
FRACTAL ASPECTS OF THE ITERATION OF z →Λz(1‐ z) FOR COMPLEX Λ AND z (1980) (249)
On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars (1975) (241)
Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence (1972) (231)
Fractal geometry: what is it, and what does it do? (1989) (210)
Multifractal products of cylindrical pulses (2002) (200)
Geometric Implementation of Hypercubic Lattices with Noninteger Dimensionality by Use of Low Lacunarity Fractal Lattices (1983) (198)
Phase transitions on fractals. III. Infinitely ramified lattices (1984) (196)
Multifractals And 1/F Noise (1999) (196)
Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity (1965) (193)
Multifractals and 1/f noise : wild self-affinity in physics (1963-1976) : selecta volume N (1999) (157)
THE (MIS)BEHAVIOR OF MARKETS (2004) (155)
Phase transitions on fractals. II. Sierpinski gaskets (1984) (155)
Limit Theorem on the Self-Normalized Range for Weakly and Strongly Dependent Process (1975) (154)
Computer Experiments with Fractional Gaussian Noises: Part 3, Mathematical Appendix (1969) (147)
A New Model for Error Clustering in Telephone Circuits (1963) (145)
Negative fractal dimensions and multifractals (1990) (132)
Multifractality of Deutschemark / Us Dollar Exchange Rates (1997) (130)
STABLE PARETIAN RANDOM FUNCTIONS AND THE MULTIPLICATIVE VARIATION OF INCOME (1961) (127)
Limit theorems on the self-normalized range for weakly and strongly dependent processes (1975) (127)
A CLASS OF MICROPULSES AND ANTIPERSISTENT FRACTIONAL BROWNIAN MOTION (1995) (111)
Phase transitions on fractals. I. Quasi-linear lattices (1983) (111)
Fractals in physics: Squig clusters, diffusions, fractal measures, and the unicity of fractal dimensionality (1984) (105)
Large Deviations and the Distribution of Price Changes (1997) (97)
Paretian Distributions and Income Maximization (1962) (93)
SELF-AFFINE FRACTAL SETS, I: THE BASIC FRACTAL DIMENSIONS (1986) (91)
Is Nature Fractal? (1998) (88)
Discovery Of Cosmic Fractals (2002) (86)
Fractals and chaos : the Mandelbrot set and beyond : selecta volume C (2004) (84)
A Note On a Class of Skew Distribution Functions: Analysis and Critique of a Paper by H. A. Simon (1959) (81)
Scaling in financial prices: I. Tails and dependence (2001) (79)
Fractals in Geophysics (1989) (77)
The (mis)behavior of markets : a fractal view of financialturbulence (2004) (74)
Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism (1991) (72)
Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn (1994) (71)
Renewal sets and random cutouts (1972) (69)
THE STABLE PARETIAN INCOME DISTRIBUTION WHEN THE APPARENT EXPONENT IS NEAR TWO (1963) (67)
The Role of Sufficiency and of Estimation in Thermodynamics (1962) (66)
The potential distribution around growing fractal clusters (1990) (64)
Diffusion on fractal lattices and the fractal Einstein relation (1983) (64)
A Fractal’s Lacunarity, and how it can be Tuned and Measured (1994) (63)
Physical properties of a new fractal model of percolation clusters (1984) (62)
Fractal Analysis and Synthesis of Fracture Surface Roughness and Related Forms of Complexity and Disorder (2006) (61)
A population birth-and-mutation process, I: explicit distributions for the number of mutants in an old culture of bacteria (1974) (61)
Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selecta (Old or New), Volume H) (2001) (57)
Multifractals and 1/{hookl}f Noise : Wild Self-Affinity in Physics (1963-1976) (1998) (56)
Measures of Fractal Lacunarity: Minkowski Content and Alternatives (1995) (56)
An Introduction to Multifractal Distribution Functions (1988) (56)
Fractal Nature of Software-Cache Interaction (1983) (55)
Temperature Fluctuation: A Well‐Defined and Unavoidable Notion (1989) (55)
Gaussian self-affinity and fractals : globality, the earth, 1/fnoise, and R/S (2001) (54)
Scaling in financial prices: II. Multifractals and the star equation (2001) (53)
Plane DLA is not self-similar; is it a fractal that becomes increasingly compact as it grows? (1992) (51)
Towards a Second Stage of Indeterminism in Science (1987) (50)
Multifractal Formalism for Infinite Multinomial Measures (1995) (49)
On the quadratic mapping z→z2-μ for complex μ and z: The fractal structure of its M set, and scaling (1983) (48)
New “anomalous” multiplicative multifractals: Left sided ƒ(α) and the modelling of DLA (1990) (47)
Levy dusts, Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension (1997) (46)
Angular gaps in radial diffusion-limited aggregation: two fractal dimensions and nontransient deviations from linear self-similarity. (2002) (46)
On the Derivation of Statistical Thermodynamics from Purely Phenomenological Principles (1964) (46)
A Class of Multinomial Multifractal Measures with Negative (Latent) Values for the “Dimension” f(α) (1989) (44)
An outline of a purely phenomenological theory of statistical thermodynamics-I: Canonical ensembles (1956) (44)
Responses to: A. Jaffe and F. Quinn, “Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics” [Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 1–13; MR1202292 (94h:00007)] (1994) (43)
Alternative micropulses and fractional Brownian motion (1996) (43)
Multifractal Power Law Distributions: Negative and Critical Dimensions and Other “Anomalies,” Explained by a Simple Example (2003) (43)
Directed recursion models for fractal growth (1989) (42)
The Canopy and Shortest Path in a Self-Contacting Fractal Tree (1999) (40)
Fractals and an art for the sake of science (1989) (40)
Scaling in financial prices: III. Cartoon Brownian motions in multifractal time (2001) (40)
Convergence of complex multiplicative cascades (2008) (38)
Inverse Measures, the Inversion Formula, and Discontinuous Multifractals (1997) (37)
Fractals, their transfer matrices and their eigen-dimensional sequences (1985) (37)
Exceptions to the multifractal formalism for discontinuous measures (1998) (36)
Stochastic volatility, power laws and long memory (2001) (36)
Final Note on a Class of Skew Distribution Functions: Analysis and Critique of a Mode Due to H. A. Simon (1961) (35)
Random Walks, Fire Damage Amount and Other Paretian Risk Phenomena (1964) (33)
On the secular pole motion and the Chandler wobble. (1970) (32)
Fractals, Graphics, and Mathematics Education (2002) (31)
The variation of the prices of cotton, wheat, and railroad stocks, and of some financial rates (1997) (31)
Multifractality of the harmonic measure on fractal aggregates, and extended self-similarity (1991) (31)
Simpie games of strategy occurring in communication through natural languages (1954) (31)
Harmonic measure around a linearly self-similar tree (1992) (30)
Fractals : a geometry of nature : fractal goemetry is the key to understanding chaos. It is also the geometry of mountains, clouds and galaxies (1990) (30)
Scaling in financial prices: IV. Multifractal concentration (2001) (30)
Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (Ingram Olkin, Sudhist G. Ghurye, Wassily Hoeffding, William G. Madow, and Henry B. Mann, eds.) (1961) (29)
Mild vs. Wild Randomness: Focusing on those Risks that Matter (2007) (29)
Inversion Formula for Continuous Multifractals (1997) (29)
Fractals in physics : essays in honour of Benoit B. Mandelbrot : proceedings of the international conference honouring Benoit B. Mandelbrot on his 65th birthday, Vence, France, 1-4 October, 1989 (1990) (28)
Correction of an Error in "The Variation of Certain Speculative Prices" (1963) (1972) (28)
Fractal geometry of critical Potts clusters (2002) (27)
Fractal landscapes without creases and with rivers (1988) (26)
Fractals and the Rebirth of Iteration Theory (1986) (26)
Broken line process derived as an approximation to fractional noise (1972) (26)
Local Regularity of Nonsmooth Wavelet Expansions and Application to the Polya Function (1996) (25)
On Dvoretzky coverings for the circle (1972) (25)
Crosscut Analysis of Large Radial DLA: Departures from Self-Similarity and Lacunarity Effects (1995) (25)
Horton-Strahler ordering of random binary trees (1994) (24)
Self-similarity of harmonic measure on DLA (1992) (24)
HEAVY TAILS IN FINANCE FOR INDEPENDENT OR MULTIFRACTAL PRICE INCREMENTS (2003) (23)
Recent Advances in Probability Theory, in Some Aspects of Analysis and Probability, I. Kaplansky, E. Hewitt, M. Hall, R. Fortet, in: Surveys in Applied Mathematics, Vol. IV. John Wiley, New York (1958), 169, $9.00 (1960) (22)
Comments on:''A subordinated stochastic process model with finite variance for speculative prices (1973) (21)
The Fractalist: Memoir of a Scientific Maverick (2012) (21)
Uniform convergence for complex [0, 1]-martingales (2008) (21)
The inescapable need for fractal tools in finance (2005) (20)
The Variation of Certain Speculative Prices Author ( s ) : (2007) (20)
Post Scriptum to "Final Note" (1961) (20)
Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3+B (1999) (20)
The Fractal Geometry of Trees and Other Natural Phenomena (1978) (19)
Renormalization and fixed points in finance, since 1962 (1999) (19)
10 Exactly self-similar left-sided multifractals (1991) (17)
The colours of infinity - the beauty and power of fractals (2010) (17)
Deviations from Self-Similarity in Plane DLA and the “Infinite Drift” Scenario (1995) (17)
The Statistics of Natural Resources and the Law of Pareto (1995) (17)
Scalebound or Scaling Shapes: A Useful Distinction in the Visual Arts and in the Natural Sciences (1981) (17)
Self-affine fractal sets, II: Length and surface dimensions (1986) (17)
“New Methods of Statistical Economics,” revisited: Short versus long tails and Gaussian versus power-law distributions (2009) (16)
Fractional multiplicative processes (2009) (16)
Fractal geometry and analysis : the Mandelbrot festschrift, Curaçao 1995 (1996) (16)
Parallel cartoons of fractal models of finance (2005) (16)
The Fractal Geometry of Percolation, Polymers and Almost Everything Else (1977) (15)
Sporadic random functions and conditional spectral analysis: self-similar examples and limits (1967) (15)
Note on the definition and the stationarity of fractional Gaussian noise (1976) (14)
Introduction to fractal sums of pulses (1995) (14)
BEHAVIOUR OF THE HARMONIC MEASURE AT THE BOTTOM OF FJORDS (1991) (13)
Multiperiodic multifractal martingale measures (2003) (12)
Multifractals and Fractals (1986) (12)
Lecture V Fractals and turbulence: Attractors and dispersion (1977) (11)
Fractals: An Animated Discussion (1997) (11)
"New Methods of Statistical Economics, " revisited: Short versus long tails and Gaussian versus power-law distributions (2009) (11)
Self-similarity of the branching structure in very large DLA clusters and other branching fractals (1994) (10)
Squig sheets and some other squig fractal constructions (1984) (10)
Linear Regression With Non-Normal Error Terms: A Comment (1971) (10)
Multifractal Formalism for In nite Multinomial Measures (10)
Stable fractal sums of pulses: the cylindrical case (1995) (10)
Self-similarity and covered neighborhoods of fractals: A random walk test (1993) (10)
Peano-pólya motions, when time is intrinsic or binomial (uniform or multifractal) (1997) (9)
The art of fractal landscapes (1991) (9)
Mathematical Methods in the Social Sciences, 1959, Proceedings of the First Stanford Symposium (Kenneth J. Arrow, Samuel Karlin, and Patrick Suppes, eds.) (1961) (9)
Some “Facts” That Evaporate Upon Examination (1989) (9)
Comment on ‘Stochastic Models in Hydrology’ by Adrian E. Scheidegger (1970) (9)
People and events behind the “Science of Fractal Images” (1988) (9)
On an eigenfunction expansion and on fractional Brownian motions (1982) (8)
A PRIMER OF NEGATIVE TEST DIMENSIONS AND DEGREES OF EMPTINESS FOR LATENT SETS (2009) (8)
TESTS OF THE DEGREE OF WORD CLUSTERING IN SAMPLES OF WRITTEN ENGLISH (1973) (8)
Survey of Multifractality in Finance (1999) (8)
Gibbs Distributions—I (2006) (8)
Nonlinear forecasts, rational bubbles, and martingales (1997) (8)
Fractal Measures (Their Infinite Moment Sequences and Dimensions) and Multiplicative Chaos: Early Works and Open Problems (1986) (8)
Comment on the equivalence between fracton/spectral dimensionality, and the dimensionality of recurrence (1984) (7)
A case against the lognormal distribution (1997) (7)
Reply [to “Comments on ‘Noah, Joseph, and Operational Hydrology’ by Benoit B. Mandelbrot and James R. Wallis”] (1969) (7)
SOME ASPECTS OF THE RANDOM WALK MODEL OF STOCK MARKET PRICES: COMMENT* (1968) (7)
Fractal aspects of materials : disordered systems, November 29-December 2, 1988 (1988) (7)
Limitations of efficiency and of martingale models (1997) (7)
Fractal aggregates, and the current lines of their electrostatic potentials (1991) (7)
The Fractal Range of the Distribution of Galaxies; Crossover to Homogeneity, and Multifractals (1989) (7)
Harold Edwin Hurst (2001) (7)
Scalebound or Scaling shapes: A Useful Distinction in the Visual Arts and in the Natural Sciences (2017) (6)
Large Deviation Theory and the Distribution of Price Changes (2011) (6)
States of randomness from mild to wild, and concentration from the short to the long run (1997) (6)
A Geometry Able to Include Mountains and Clouds (2010) (6)
Intermittent free turbulence (1999) (6)
Fractional Brownian Motions and Fractional Gaussian Noises (2014) (6)
SELF-AFFINE FRACTAL SETS, III: HAUSDORFF DIMENSION ANOMALIES AND THEIR IMPLICATIONS (1986) (6)
Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups (1983) (5)
Some Reasons for the Effectiveness of Fractals in Mathematics Education (2002) (5)
4. The Many Faces of Scaling: Fractals, Geometry of Nature, and Economics (1982) (5)
Iterated random multiplications and invariance under randomly weighted averaging (1999) (5)
Fractal Geometry in Physics (1993) (4)
Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence (1999) (4)
Partial dimensional sequences and percolation (1984) (4)
DISCUSSION PAPER: FRACTALS, ATTRACTORS, AND THE FRACTAL DIMENSION (1979) (4)
Mandelbrot on price variation (1997) (4)
Easy and Natural Generation of Multifractals: Multiplying Harmonics of Periodic Functions (1999) (4)
SELECTED TOPICS IN MATHEMATICS, PHYSICS, AND FINANCE ORIGINATING IN FRACTAL GEOMETRY (2004) (3)
TOPICS ON FRACTALS IN MATHEMATICS AND PHYSICS (2001) (3)
On the Dynamics of Iterated Maps VIII: The Map z→λ(z+1/z), from Linear to Planar Chaos, and the Measurement of Chaos (1984) (3)
Fractal Sums of Pulses and a Practical Challenge to the Distinction Between Local and Global Dependence (2003) (3)
Steady-State Noises in Diffusion-Limited Fractal Growth (1991) (3)
Documents in Mycenaean Greek, John Chadwick, Michael Ventris. Cambridge University Press (1956), 452, $15.00 (1960) (3)
Benoît Mandelbrot (2011) (3)
Cartoons of the Variation of Financial Prices and of Brownian Motions in Multifractal Time (2000) (2)
A Note on a Law of Berry and on Insistence Stress (1957) (2)
Correlations and texture in a new model hierarchical universe, based upon trema sets. (1979) (2)
The Theory of Probability, 2nd ed., B.V. Gnedenko. Chelsea, New York (1962), 459, $8.75 (1962) (2)
Visual Language (2005) (2)
ON THE AGGREGATIVE FRACTALS CALLED “SQUIGS”, WHICH INCLUDE RECURSIVE MODELS OF POLYMERS AND OF PERCOLATION CLUSTERS (1984) (2)
The Geometry of Dla: Different Aspects of the Departure from Self-Similarity (1994) (2)
Fractal structure of the galaxy universe (2002) (2)
Fractality, Lacunarity, and the Near-Isotropic Distribution of Galaxies (1998) (2)
Sporadic random functions and conditional spectra; self-similar examples and limits (1999) (2)
Some Mathematical Questions Arising in Fractal Geometry (2000) (2)
Leo Szilard and unique decipherability (Corresp.) (1965) (2)
Party Legislative Representative as a Function of Election Results-James G. March Games Decisions and Industrial Organization-Martin Shubik Theories of the General Interest, and the Logical Problem of Aggregation- (2016) (2)
Rank-size plots, Zipf’s law, and scaling (1997) (2)
FRACTIONAL BROWNIAN MOTION, SELF-SIMILAR PROCESSES, AND APPLICATIONS, (1966) (2)
Sporadic random functions and conditional spectra; self-similar examples and limits (1999) (2)
TOWARDS A REVIVAL OF THE STATISTICAL LAW OF PARETO (1962) (2)
Comment on transport processes on fractal structures (1984) (2)
Self-inverse fractals, Apollonian nets, and soap (2004) (1)
Self-similarity and panorama of self-affinity (1997) (1)
Introduction to papers on quadratic dynamics: a progression from seeing to discovering (2004) (1)
Bilateral Canonical Cascades: Multiplicative Refinement Paths to Wiener's and Variant Fractional Brownian Limits (2007) (1)
Parallel diff usion-limited aggregation (1995) (1)
The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems (2004) (1)
A Class of Pulse Processes (1994) (1)
Harmonic Analysis and the Theory of Probability, S. Bochner. University of California Press (1955), 176, $4.50 (1960) (1)
Self-similarity and conditional stationarity (1999) (1)
Continuous Interpolation of the Complex Discrete Map z → λz(1 - z), and Related Topics. On the dynamics of iterated maps IX (1985) (1)
Percolation, critical phenomena and fractals (1981) (1)
Gibbs and Mandelbrot at Yale (1989) (1)
Fractal Landscapes: from the Real World (1994) (1)
New model for the clustering of errors on telephone circuits (Berger & M 1963) (1999) (1)
New model for the clustering of errors on telephone circuits (Berger & M 1963) (1999) (1)
Radial DLA: two fractal dimensions and deviations from self-similarity (2001) (1)
Comment on Dr. Herdan's letter (1961) (1)
Multifractals, probability and statistical mechanics, applications (2004) (1)
Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski (2004) (1)
Book review(from a series of mathematics texts under the general editorship of C. B. Allendoerfer) Introduction to Mathematical Statistics, Robert V. Hogg, Allen B. Craig, x + 245 pp., $6.75 , Macmillan, New York (1959) (1960) (1)
Hurst Coefficient (Rescaled Range Analysis) (2004) (1)
Editorial introduction: Heavy tails and stable Paretian distributions in empirical finance☆ (2010) (1)
Type Token Mathematics, Gustav Herdan, in: A Textbook of Mathematical Linguistics. Mouton & Cie, The Hague (1960), 338, (+ 110 pp. of indices and tables of functions). 54 Dutch GL, approx. $14.00 (1961) (1)
Letter from Benoit B. Mandelbrot to Joshua Lederberg (1974) (0)
Computation of the L-stable distributions (1997) (0)
The inexhaustible function z squared plus c (2004) (0)
The molecular concept of law (2011) (0)
The charm of self-similarity (2002) (0)
Sources of inspiration and historical background (1997) (0)
Fractal dimension, dispersion, and singularities of fluid motion (1999) (0)
Information and Decision Processes (Robert E. Machol, ed.) (1961) (0)
Scaling distributions and income maximization (1997) (0)
Introduction to papers on chaos in nonquadratic dynamics: rational functions devised from doubling formulas (2004) (0)
Book-Review - Fractals - Form Chance and Dimension (1980) (0)
Self-inverse fractals osculated by sigma-discs: the limit sets of (“Kleinian”) inversion groups (2004) (0)
Statistical macro-linguistics (1959) (0)
A crisis of intuition as viewed by Felix Klein and Hans Hahn and its resolution by fractal geometry (2003) (0)
L-stability and multiplicative variation of income (1997) (0)
The Paradoxal Universe of Sir Isaac (2002) (0)
Discontinuity and scaling: their scope and likely limitations (1997) (0)
Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs (2004) (0)
8. Fractal Geometry (0)
The law of redshift in the kingdom of galaxies (2002) (0)
Fractal financial fluctuations ; do they threaten sustainability ? (2003) (0)
Vita and Publications (1992) (0)
Redshift – the quiet cosmographer (2002) (0)
Additional Perspectives on Fractals (2018) (0)
Some potential problems arising in the theory of axial turbomachines (1949) (0)
Fractal Lacunarity and Scenarios for the Near-Isotropic Distribution of Galaxies (2001) (0)
“On certain martingales of Benoit Mandelbrot” Guest contribution (Kahane & Peyrière 1976) (1999) (0)
Sketches of prehistory and history (1999) (0)
Certain Julia sets include smooth components (2004) (0)
Acknowledgments related to quadratic dynamics (2004) (0)
Extended Abstracts. Fractal Aspects of Materials. Metal and Catalyst Surfaces, Powders and Aggregates. Proceedings of Symposium P 1984 Fall Meeting of the Materials Research Society Held on 26-27 November 1984 at Boston, Massachusetts, (1984) (0)
The “normalized radical” of the ℳ-set (2004) (0)
Panorama of grid-bound self-affine variability (1999) (0)
Cosmic hierarchies: from dream to science (2002) (0)
Symmetry with respect to several circles: dilation/reduction, fractals, and roughness (2004) (0)
Chapter 2 Unsolved Problems and Still-Emerging Concepts in Fractal Geometry (2002) (0)
Expansion and curvature of space (2002) (0)
Short excerpts (1964–1984) (1999) (0)
Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991) (2004) (0)
Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets (2004) (0)
A new model of percolation clusters (1984) (0)
Fractal Financial Fluctuations (2010) (0)
1/ƒ noises and the infrared catastrophe (1999) (0)
The Fatou and Julia stories (2004) (0)
Gravity – the enigmatic creator of order (2002) (0)
Chapter 3 Fractals , Graphics , and Mathematics Education 1 (2002) (0)
Fractals: an animated discussion (videotape) (1990) (0)
Mathematical analysis while in the wilderness (2004) (0)
Scaling, invariants and fixed points (1999) (0)
Dark energy – the new emperor (2002) (0)
Scaling, invariants and fixed points (1999) (0)
Integrating the Outliers (2003) (0)
The birth of cosmological principles (2002) (0)
Bifurcation points and the “n-squared” approximation and conjecture, illustrated by M.L Frame and K Mitchell (2004) (0)
1987 Conference on Dynamic Patterns in Complex Systems (1988) (0)
Recent Soviet Contributions to Mathematics, Joseph P. La Salle, Solomon Lefschetz (Eds.). Macmillan (1962), 324 (1963) (0)
The gate into cosmic order (2002) (0)
Fe b 20 09 CONSTRUCTION OF SIGNED MULTIPLICATIVE CASCADES (2009) (0)
INTERVEIW WITH PROFESSOR BENOIT B. MANDELBROT (2005) (0)
Proportional growth with or without diffusion, and other explanations of scaling (1997) (0)
Landscapes on an Imaginary Planet (1988) (0)
The Origins of Megafractals (2002) (0)
A discussion of Benoit Mandelbrot ’ s T he ( Mis ) Behavior of Markets by Nassim (2005) (0)
The boundary of the ℳ-set is of dimension 2 (2004) (0)
Analysis, number theory, and dynamical systems (2004) (0)
The complex quadratic map and its ℳ-set (2004) (0)
Comments by P. H. Cootner, E. Parzen, and W. S. Morris (1960s) and responses (1997) (0)
Industrial concentration and scaling (1997) (0)
Synergetics and the Images of Future (2000) (0)
Foreword by Benoit Mandelbrot (2007) (0)
SYMMETRY: A SPECIAL FOCUS ON FRACTALS (2012) (0)
Critical Phenomena and Fractals with Dimensionality Near 1 (1981) (0)
Factal aspects of materials: Metal and catalyst surfaces, powders and aggregates. Extended abstracts (1984) (0)
Filtering and specification of self-affinity (1999) (0)
Cantor and Fatou dusts; self-squared dragons (2004) (0)
The mysterious singularity (2002) (0)
Fractal and chaos: planets, stardust, dark haloes (2002) (0)
Random sets of multiplicity for trigonometric series (Kahane & M 1965) (1999) (0)
The geometry that describes the shape of coastlines and the patterns of galaxies also elucidates how stock prices soar and plummet by (2007) (0)
L-stable model for the distribution of income (1997) (0)
Dimension, Symmetrie, Divergenz (1987) (0)
Co-indicator functions and related 1/ƒ noises (1999) (0)
What is fractal, and why fractals should matter to the petroleum geologist. [The use of fractal geometry to determine the occurrence and movement of hydrocarbons] (1991) (0)
Multifractality of US Dollar/Deutsche Mark Exchange Rates (2011) (0)
Discussion Panel: Fractal Large Scale Structures and Crossover to Homogeneity: the Mass-Radius Function versus the Correlations, and the Measurement of the Corrrelation Range (1988) (0)
Two nonquadratic rational maps devised from Weierstrass doubling formulas (2004) (0)
The fractal cosmos: New shapes in the sciences and arts (1984) (0)
The triumph of uniformity in cosmology (2002) (0)
Book reviewviii + 210 pp., $5.00 Finite Markov Chains, John G. Kemeny, J. Laurie Snell, van Nostrand, New York (1960) (1960) (0)
Designers need consistent interface to CAD tools (2006) (0)
A Branching Process Analysis of the Stack Algorithm for Variable Channel Conditions (1992) (0)
The dream of a hierarchical world: protofractals (2002) (0)
ON TELEPHONE ERROR CLUSTERING CONSIDERED AS AN ILLUSION (1962) (0)
Dark matter – the grey eminence (2002) (0)
Annual Report for Contract N00014-90-J-1026 (Yale University, Mathematics Dept.) (1994) (0)
Chapter 4 Mathematics and Society in the 20 th Century 1 (2002) (0)
The map z → λ (z+1/z) and roughening of chaos, from linear to planar (computer-assisted homage to K. Hokusai) (2004) (0)
The new world of relativity and quantum forces (2002) (0)
The nature of roughness in mathematics, science, and art (2005) (0)
Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments (2004) (0)
Multifractal Products of Cylindrical Pulses By Julien Barral and (0)

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