Why Is Benoit Mandelbrot Influential?
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.
Benoit Mandelbrot's Published Works
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1960 1970 1980 1990 2000 2010 0 2500 5000 7500 10000 12500 15000 17500 20000 22500 25000 Published Papers Fractal Geometry of Nature Fractional Brownian Motions, Fractional Noises and Applications Fractal Geometry of Nature The Variation of Certain Speculative Prices How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension Fractal character of fracture surfaces of metals Fractals: Form, Chance and Dimension Fractals: Form, Chance, and Dimension. Fractals and Scaling in Finance Noah, Joseph, and Operational Hydrology Some long‐run properties of geophysical records Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier Intermittent turbulence in self-similar cascades : divergence of high moments and dimension of the carrier Self-Affine Fractals and Fractal Dimension RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. THE PARETO-LEVY LAW AND THE DISTRIBUTION OF INCOME* New Methods in Statistical Economics A Multifractal Model of Asset Returns (523) On the Distribution of Stock Price Differences The Variation of Some Other Speculative Prices Computer Experiments With Fractional Gaussian Noises: Part 1, Averages and Variances When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis (460) Stochastic models for the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. The Misbehavior of Markets: A Fractal View of Risk, Ruin, and Reward Forecasts of Future Prices, Unbiased Markets, and "Martingale" Models Fractals and Scaling In Finance: Discontinuity, Concentration, Risk Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E Fractals: Form, Chance, and Dimension Computer Experiments with Fractional Gaussian Noises: Part 2, Rescaled Ranges and Spectra The fractal geometry of nature /Revised and enlarged edition/ (316) Some noises with I/f spectrum, a bridge between direct current and white noise A Fast Fractional Gaussian Noise Generator A Multifractal Walk down Wall Street Fractal properties of rain, and a fractal model Multifractal Measures, Especially for the Geophysicist Critical Phenomena on Fractal Lattices Fractals and Chaos Long-Run Linearity, Locally Gaussian Process, H-Spectra and Infinite Variances Solvable Fractal Family, and Its Possible Relation to the Backbone at Percolation How Long Is the Coast of Britain ? (260) A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices: Comment FRACTAL ASPECTS OF THE ITERATION OF z →Λz(1‐ z) FOR COMPLEX Λ AND z On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence THE (MIS)BEHAVIOR OF MARKETS (201) Multifractals And 1/F Noise (198) Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity Geometric Implementation of Hypercubic Lattices with Noninteger Dimensionality by Use of Low Lacunarity Fractal Lattices Fractal geometry: what is it, and what does it do? Phase transitions on fractals. III. Infinitely ramified lattices Multifractal products of cylindrical pulses Phase transitions on fractals. II. Sierpinski gaskets Limit Theorem on the Self-Normalized Range for Weakly and Strongly Dependent Process Multifractals and 1/f noise : wild self-affinity in physics (1963-1976) : selecta volume N A New Model for Error Clustering in Telephone Circuits Computer Experiments with Fractional Gaussian Noises: Part 3, Mathematical Appendix Multifractality of Deutschemark / Us Dollar Exchange Rates (131) STABLE PARETIAN RANDOM FUNCTIONS AND THE MULTIPLICATIVE VARIATION OF INCOME Negative fractal dimensions and multifractals Multifractal measures, especially for the geophysicist Limit theorems on the self-normalized range for weakly and strongly dependent processes A CLASS OF MICROPULSES AND ANTIPERSISTENT FRACTIONAL BROWNIAN MOTION Phase transitions on fractals. I. Quasi-linear lattices Fractals in physics: Squig clusters, diffusions, fractal measures, and the unicity of fractal dimensionality Paretian Distributions and Income Maximization SELF-AFFINE FRACTAL SETS, I: THE BASIC FRACTAL DIMENSIONS Large Deviations and the Distribution of Price Changes (91) Is Nature Fractal? A Note On a Class of Skew Distribution Functions: Analysis and Critique of a Paper by H. A. Simon Scaling in financial prices: I. Tails and dependence Discovery Of Cosmic Fractals Fractals in Geophysics Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism The (mis)behavior of markets : a fractal view of financialturbulence (68) Renewal sets and random cutouts THE STABLE PARETIAN INCOME DISTRIBUTION WHEN THE APPARENT EXPONENT IS NEAR TWO The Role of Sufficiency and of Estimation in Thermodynamics The potential distribution around growing fractal clusters Fractals and chaos : the Mandelbrot set and beyond : selecta volume C (62) Diffusion on fractal lattices and the fractal Einstein relation Physical properties of a new fractal model of percolation clusters A population birth-and-mutation process, I: explicit distributions for the number of mutants in an old culture of bacteria A Fractal’s Lacunarity, and how it can be Tuned and Measured Fractal Nature of Software-Cache Interaction Scaling in financial prices: II. Multifractals and the star equation Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selecta (Old or New), Volume H) (56) Multifractals and 1/{hookl}f Noise : Wild Self-Affinity in Physics (1963-1976) (56) Gaussian self-affinity and fractals : globality, the earth, 1/fnoise, and R/S (54) Measures of Fractal Lacunarity: Minkowski Content and Alternatives An Introduction to Multifractal Distribution Functions Plane DLA is not self-similar; is it a fractal that becomes increasingly compact as it grows? Temperature Fluctuation: A Well‐Defined and Unavoidable Notion Towards a Second Stage of Indeterminism in Science Fractal Analysis and Synthesis of Fracture Surface Roughness and Related Forms of Complexity and Disorder New Methods in Statistical Economics On the quadratic mapping z→z2-μ for complex μ and z: The fractal structure of its M set, and scaling New “anomalous” multiplicative multifractals: Left sided ƒ(α) and the modelling of DLA Levy dusts, Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension A Class of Multinomial Multifractal Measures with Negative (Latent) Values for the “Dimension” f(α) Alternative micropulses and fractional Brownian motion Angular gaps in radial diffusion-limited aggregation: two fractal dimensions and nontransient deviations from linear self-similarity. Scaling in financial prices: III. Cartoon Brownian motions in multifractal time On the Derivation of Statistical Thermodynamics from Purely Phenomenological Principles Multifractal Power Law Distributions: Negative and Critical Dimensions and Other “Anomalies,” Explained by a Simple Example An outline of a purely phenomenological theory of statistical thermodynamics-I: Canonical ensembles 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)] Directed recursion models for fractal growth Fractals and an art for the sake of science The Canopy and Shortest Path in a Self-Contacting Fractal Tree Inverse Measures, the Inversion Formula, and Discontinuous Multifractals Stochastic volatility, power laws and long memory Fractals, their transfer matrices and their eigen-dimensional sequences Exceptions to the Multifractal Formalism for Discontinuous Measures Final Note on a Class of Skew Distribution Functions: Analysis and Critique of a Mode Due to H. A. Simon Scaling in financial prices: IV. Multifractal concentration Random Walks, Fire Damage Amount and Other Paretian Risk Phenomena On the secular pole motion and the Chandler wobble. Multifractality of the harmonic measure on fractal aggregates, and extended self-similarity Simpie games of strategy occurring in communication through natural languages The variation of the prices of cotton, wheat, and railroad stocks, and of some financial rates Mild vs. Wild Randomness: Focusing on those Risks that Matter The Fractal Geometry of Nature Inversion Formula for Continuous Multifractals Fractals : a geometry of nature : fractal goemetry is the key to understanding chaos. It is also the geometry of mountains, clouds and galaxies (29) Invariant multifractal measures in chaotic Hamiltonian systems, and related structures. 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 (28) Harmonic measure around a linearly self-similar tree Fractal geometry of critical Potts clusters Broken line process derived as an approximation to fractional noise Correction of an Error in "The Variation of Certain Speculative Prices" (1963) Fractals, Graphics, and Mathematics Education Fractals and the Rebirth of Iteration Theory On Dvoretzky coverings for the circle 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.) HEAVY TAILS IN FINANCE FOR INDEPENDENT OR MULTIFRACTAL PRICE INCREMENTS Crosscut Analysis of Large Radial DLA: Departures from Self-Similarity and Lacunarity Effects The Fractalist: Memoir of a Scientific Maverick Horton-Strahler ordering of random binary trees Fractal landscapes without creases and with rivers (23) Local Regularity of Nonsmooth Wavelet Expansions and Application to the Polya Function Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3+B Self-similarity of harmonic measure on DLA 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 Post Scriptum to "Final Note" Renormalization and fixed points in finance, since 1962 The Fractal Geometry of Trees and Other Natural Phenomena The Fractal Geometry of Percolation, Polymers and Almost Everything Else The inescapable need for fractal tools in finance Scalebound or Scaling Shapes: A Useful Distinction in the Visual Arts and in the Natural Sciences 10 Exactly self-similar left-sided multifractals The Variation of Certain Speculative Prices Author ( s ) : (17) Parallel cartoons of fractal models of finance Fractal geometry and analysis : the Mandelbrot festschrift, Curaçao 1995 (16) Self-affine fractal sets, II: Length and surface dimensions “New Methods of Statistical Economics,” revisited: Short versus long tails and Gaussian versus power-law distributions Deviations from Self-Similarity in Plane DLA and the “Infinite Drift” Scenario The Statistics of Natural Resources and the Law of Pareto Note on the definition and the stationarity of fractional Gaussian noise Sporadic random functions and conditional spectral analysis: self-similar examples and limits (14) Fractional multiplicative processes Multiperiodic multifractal martingale measures BEHAVIOUR OF THE HARMONIC MEASURE AT THE BOTTOM OF FJORDS The colours of infinity - the beauty and power of fractals (12) Multifractals and Fractals Introduction to fractal sums of pulses Fractals: An Animated Discussion (11) Lecture V Fractals and turbulence: Attractors and dispersion Fractal analysis and synthesis of fracture surface roughness and related forms of complexity and disorder Squig sheets and some other squig fractal constructions Self-similarity of the branching structure in very large DLA clusters and other branching fractals Multifractal Formalism for In nite Multinomial Measures (10) Stable fractal sums of pulses: the cylindrical case Comment on ‘Stochastic Models in Hydrology’ by Adrian E. Scheidegger Some “Facts” That Evaporate Upon Examination Mathematical Methods in the Social Sciences, 1959, Proceedings of the First Stanford Symposium (Kenneth J. Arrow, Samuel Karlin, and Patrick Suppes, eds.) The art of fractal landscapes People and events behind the “Science of Fractal Images” (9) TESTS OF THE DEGREE OF WORD CLUSTERING IN SAMPLES OF WRITTEN ENGLISH Fractal Measures (Their Infinite Moment Sequences and Dimensions) and Multiplicative Chaos: Early Works and Open Problems On an eigenfunction expansion and on fractional Brownian motions Linear Regression With Non-Normal Error Terms: A Comment Survey of Multifractality in Finance (8) Self-similarity and covered neighborhoods of fractals: A random walk test Nonlinear forecasts, rational bubbles, and martingales "New Methods of Statistical Economics, " revisited: Short versus long tails and Gaussian versus power-law distributions Peano-pólya motions, when time is intrinsic or binomial (uniform or multifractal) The fractals book (7) Fractal aspects of materials : disordered systems, November 29-December 2, 1988 (7) Harold Edwin Hurst A case against the lognormal distribution Fractional Brownian Motions and Fractional Gaussian Noises A PRIMER OF NEGATIVE TEST DIMENSIONS AND DEGREES OF EMPTINESS FOR LATENT SETS Reply [to “Comments on ‘Noah, Joseph, and Operational Hydrology’ by Benoit B. Mandelbrot and James R. Wallis”] Comment on the equivalence between fracton/spectral dimensionality, and the dimensionality of recurrence Limitations of efficiency and of martingale models Fractal aggregates, and the current lines of their electrostatic potentials States of randomness from mild to wild, and concentration from the short to the long run The Fractal Range of the Distribution of Galaxies; Crossover to Homogeneity, and Multifractals SELF-AFFINE FRACTAL SETS, III: HAUSDORFF DIMENSION ANOMALIES AND THEIR IMPLICATIONS A Geometry Able to Include Mountains and Clouds Gibbs Distributions—I Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups SOME ASPECTS OF THE RANDOM WALK MODEL OF STOCK MARKET PRICES: COMMENT* Intermittent free turbulence Some Reasons for the Effectiveness of Fractals in Mathematics Education (5) 4. The Many Faces of Scaling: Fractals, Geometry of Nature, and Economics Iterated random multiplications and invariance under randomly weighted averaging Large Deviation Theory and the Distribution of Price Changes (5) Scalebound or Scaling shapes: A Useful Distinction in the Visual Arts and in the Natural Sciences Mandelbrot on price variation Radial DLA: two fractal dimensions and deviations from self-similarity Easy and Natural Generation of Multifractals: Multiplying Harmonics of Periodic Functions Fractal Geometry in Physics Partial dimensional sequences and percolation DISCUSSION PAPER: FRACTALS, ATTRACTORS, AND THE FRACTAL DIMENSION On the Dynamics of Iterated Maps VIII: The Map z→λ(z+1/z), from Linear to Planar Chaos, and the Measurement of Chaos SELECTED TOPICS IN MATHEMATICS, PHYSICS, AND FINANCE ORIGINATING IN FRACTAL GEOMETRY Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence Fractal Sums of Pulses and a Practical Challenge to the Distinction Between Local and Global Dependence Steady-State Noises in Diffusion-Limited Fractal Growth Documents in Mycenaean Greek, John Chadwick, Michael Ventris. Cambridge University Press (1956), 452, $15.00 Benoît Mandelbrot New model for the clustering of errors on telephone circuits (Berger & M 1963) New model for the clustering of errors on telephone circuits (Berger & M 1963) Cartoons of the Variation of Financial Prices and of Brownian Motions in Multifractal Time (2) The Theory of Probability, 2nd ed., B.V. Gnedenko. Chelsea, New York (1962), 459, $8.75 Harmonic Analysis and the Theory of Probability, S. Bochner. University of California Press (1955), 176, $4.50 1/ƒ noises and the infrared catastrophe Fractality, Lacunarity, and the Near-Isotropic Distribution of Galaxies Fractal structure of the galaxy universe Correlations and texture in a new model hierarchical universe, based upon trema sets. (2) ON THE AGGREGATIVE FRACTALS CALLED “SQUIGS”, WHICH INCLUDE RECURSIVE MODELS OF POLYMERS AND OF PERCOLATION CLUSTERS The Geometry of Dla: Different Aspects of the Departure from Self-Similarity FRACTIONAL BROWNIAN MOTION, SELF-SIMILAR PROCESSES, AND APPLICATIONS, (2) Rank-size plots, Zipf’s law, and scaling TOPICS ON FRACTALS IN MATHEMATICS AND PHYSICS TOWARDS A REVIVAL OF THE STATISTICAL LAW OF PARETO A Note on a Law of Berry and on Insistence Stress Some Mathematical Questions Arising in Fractal Geometry 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) Sporadic random functions and conditional spectra; self-similar examples and limits Sporadic random functions and conditional spectra; self-similar examples and limits Hurst Coefficient (Rescaled Range Analysis) 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- (1) Continuous Interpolation of the Complex Discrete Map z → λz(1 - z), and Related Topics. On the dynamics of iterated maps IX Leo Szilard and unique decipherability (Corresp.) Multifractal Products of Cylindrical Pulses By Julien Barral and (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 Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski Self-similarity and panorama of self-affinity Fractal Landscapes: from the Real World (1) Self-similarity and conditional stationarity Editorial introduction: Heavy tails and stable Paretian distributions in empirical finance☆ (1) The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems Self-inverse fractals, Apollonian nets, and soap Bilateral Canonical Cascades: Multiplicative Refinement Paths to Wiener's and Variant Fractional Brownian Limits (1) Gibbs and Mandelbrot at Yale Comment on Dr. Herdan's letter Comment on transport processes on fractal structures Introduction to papers on quadratic dynamics: a progression from seeing to discovering Visual Language Parallel diff usion-limited aggregation (1) A Class of Pulse Processes (1) Percolation, critical phenomena and fractals Designers need consistent interface to CAD tools (0) Letter from Benoit B. Mandelbrot to Joshua Lederberg (0) A Collection of Mathematical Problems, S.M. Ulam. Interscience, New York (1960), 150, $5.00 Self-inverse fractals osculated by sigma-discs: the limit sets of (“Kleinian”) inversion groups The law of redshift in the kingdom of galaxies The map z → λ (z+1/z) and roughening of chaos, from linear to planar (computer-assisted homage to K. Hokusai) The “normalized radical” of the ℳ-set The molecular concept of law (0) Bifurcation points and the “n-squared” approximation and conjecture, illustrated by M.L Frame and K Mitchell Integrating the Outliers (0) 1987 Conference on Dynamic Patterns in Complex Systems Critical Phenomena and Fractals with Dimensionality Near 1 Book reviewviii + 210 pp., $5.00 Finite Markov Chains, John G. Kemeny, J. Laurie Snell, van Nostrand, New York (1960) Dark matter – the grey eminence “On certain martingales of Benoit Mandelbrot” Guest contribution (Kahane & Peyrière 1976) Annual Report for Contract N00014-90-J-1026 (Yale University, Mathematics Dept.) Random sets of multiplicity for trigonometric series (Kahane & M 1965) Discussion Panel: Fractal Large Scale Structures and Crossover to Homogeneity: the Mass-Radius Function versus the Correlations, and the Measurement of the Corrrelation Range (0) Acknowledgments related to quadratic dynamics Cantor and Fatou dusts; self-squared dragons The charm of self-similarity Certain Julia sets include smooth components A crisis of intuition as viewed by Felix Klein and Hans Hahn and its resolution by fractal geometry (0) Expansion and curvature of space The fractal cosmos: New shapes in the sciences and arts Symmetry with respect to several circles: dilation/reduction, fractals, and roughness Co-indicator functions and related 1/ƒ noises Introduction to papers on chaos in nonquadratic dynamics: rational functions devised from doubling formulas The new world of relativity and quantum forces Filtering and specification of self-affinity Multifractals, probability and statistical mechanics, applications (0) 8. Fractal Geometry (0) The Origins of Megafractals Fractals: an animated discussion (videotape) (0) Fractals: Form, Chance, and Dimension Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991) The boundary of the ℳ-set is of dimension 2 The dream of a hierarchical world: protofractals The mysterious singularity Additional Perspectives on Fractals The inexhaustible function z squared plus c The nature of roughness in mathematics, science, and art (0) Two nonquadratic rational maps devised from Weierstrass doubling formulas Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets Panorama of grid-bound self-affine variability ON TELEPHONE ERROR CLUSTERING CONSIDERED AS AN ILLUSION (0) Chapter 3 Fractals , Graphics , and Mathematics Education 1 (0) Vita and Publications (0) A Branching Process Analysis of the Stack Algorithm for Variable Channel Conditions (0) Cosmic hierarchies: from dream to science Redshift – the quiet cosmographer The gate into cosmic order The Paradoxal Universe of Sir Isaac Proportional growth with or without diffusion, and other explanations of scaling Industrial concentration and scaling Sources of inspiration and historical background INTERVEIW WITH PROFESSOR BENOIT B. MANDELBROT Book-Review - Fractals - Form Chance and Dimension (0) Scaling, invariants and fixed points 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] (0) Fe b 20 09 CONSTRUCTION OF SIGNED MULTIPLICATIVE CASCADES (0) Mathematical analysis while in the wilderness Analysis, number theory, and dynamical systems (0) Gravity – the enigmatic creator of order The complex quadratic map and its ℳ-set Chapter 4 Mathematics and Society in the 20 th Century 1 (0) Discontinuity and scaling: their scope and likely limitations A new model of percolation clusters The Fatou and Julia stories Fractal financial fluctuations ; do they threaten sustainability ? (0) Chapter 2 Unsolved Problems and Still-Emerging Concepts in Fractal Geometry (0) Sketches of prehistory and history Fractal dimension, dispersion, and singularities of fluid motion Factal aspects of materials: Metal and catalyst surfaces, powders and aggregates. Extended abstracts (0) Multifractality of US Dollar/Deutsche Mark Exchange Rates (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, (0) Scaling distributions and income maximization Fe b 20 09 CONVERGENCE OF SIGNED MULTIPLICATIVE CASCADES (0) Scaling, invariants and fixed points L-stable model for the distribution of income Fractal Lacunarity and Scenarios for the Near-Isotropic Distribution of Galaxies Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments Dark energy – the new emperor The birth of cosmological principles The triumph of uniformity in cosmology The geometry that describes the shape of coastlines and the patterns of galaxies also elucidates how stock prices soar and plummet by (0) Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs Computation of the L-stable distributions Dimension, Symmetrie, Divergenz A discussion of Benoit Mandelbrot ’ s T he ( Mis ) Behavior of Markets by Nassim (0) L-stability and multiplicative variation of income Fractal Financial Fluctuations Some potential problems arising in the theory of axial turbomachines (0) Statistical macro-linguistics SYMMETRY: A SPECIAL FOCUS ON FRACTALS (0) Short excerpts (1964–1984) Fractal and chaos: planets, stardust, dark haloes Information and Decision Processes (Robert E. Machol, ed.) Foreword by Benoit Mandelbrot (0) Landscapes on an Imaginary Planet Comments by P. H. Cootner, E. Parzen, and W. S. Morris (1960s) and responses Recent Soviet Contributions to Mathematics, Joseph P. La Salle, Solomon Lefschetz (Eds.). Macmillan (1962), 324 More Papers This paper list is powered by the following services:
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