# Benoit Mandelbrot

#165

Most Influential Person Now

Polish-born, French and American mathematician

## Benoit Mandelbrot's AcademicInfluence.com Rankings

Benoit Mandelbrotmathematics Degrees

Mathematics

#38

World Rank

#124

Historical Rank

Measure Theory

#5

World Rank

#16

Historical Rank

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Mathematics

## Benoit Mandelbrot's Degrees

- PhD Mathematical Sciences Université Paris Cité

## Why Is Benoit Mandelbrot Influential?

(Suggest an Edit or Addition)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

### Published Works

- Fractal Geometry of Nature (1984) (25641)
- Fractional Brownian Motions, Fractional Noises and Applications (1968) (7037)
- How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension (1967) (3287)
- The Variation of Certain Speculative Prices (1963) (3279)
- Fractals: Form, Chance and Dimension (1978) (3000)
- Fractal character of fracture surfaces of metals (1984) (1616)
- Fractals and Scaling in Finance (1997) (1155)
- Noah, Joseph, and Operational Hydrology (1968) (994)
- Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence (1969) (908)
- Some long‐run properties of geophysical records (1969) (898)
- Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier (1974) (859)
- Self-Affine Fractals and Fractal Dimension (1985) (815)
- Intermittent turbulence in self-similar cascades : divergence of high moments and dimension of the carrier (2004) (792)
- RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. (1964) (765)
- New Methods in Statistical Economics (1963) (662)
- THE PARETO-LEVY LAW AND THE DISTRIBUTION OF INCOME* (1960) (627)
- A Multifractal Model of Asset Returns (1997) (552)
- The Variation of Some Other Speculative Prices (1967) (519)
- On the Distribution of Stock Price Differences (1967) (517)
- Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis (1972) (492)
- Stochastic models for the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. (1975) (492)
- Computer Experiments With Fractional Gaussian Noises: Part 1, Averages and Variances (1969) (489)
- The Misbehavior of Markets: A Fractal View of Risk, Ruin, and Reward (2004) (488)
- When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models (1971) (466)
- Forecasts of Future Prices, Unbiased Markets, and "Martingale" Models (1966) (414)
- Fractals and Scaling In Finance: Discontinuity, Concentration, Risk (2010) (406)
- Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E (1997) (377)
- Multifractal measures, especially for the geophysicist (1989) (363)
- A Multifractal Walk down Wall Street (1999) (333)
- Some noises with I/f spectrum, a bridge between direct current and white noise (1967) (333)
- A Fast Fractional Gaussian Noise Generator (1971) (330)
- How Long Is the Coast of Britain ? (2002) (297)
- The fractal geometry of nature /Revised and enlarged edition/ (1983) (291)
- A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices: Comment (1973) (285)
- Computer Experiments with Fractional Gaussian Noises: Part 2, Rescaled Ranges and Spectra (1969) (282)
- Critical Phenomena on Fractal Lattices (1980) (276)
- Fractals and Chaos (2004) (267)
- Long-Run Linearity, Locally Gaussian Process, H-Spectra and Infinite Variances (1969) (264)
- Solvable Fractal Family, and Its Possible Relation to the Backbone at Percolation (1981) (262)
- Fractal properties of rain, and a fractal model (1985) (258)
- FRACTAL ASPECTS OF THE ITERATION OF z →Λz(1‐ z) FOR COMPLEX Λ AND z (1980) (252)
- On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars (1975) (245)
- Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence (1972) (234)
- Fractal geometry: what is it, and what does it do? (1989) (212)
- Geometric Implementation of Hypercubic Lattices with Noninteger Dimensionality by Use of Low Lacunarity Fractal Lattices (1983) (202)
- Multifractal products of cylindrical pulses (2002) (200)
- Multifractals And 1/F Noise (1999) (199)
- Phase transitions on fractals. III. Infinitely ramified lattices (1984) (198)
- Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity (1965) (194)
- Multifractals and 1/f noise : wild self-affinity in physics (1963-1976) : selecta volume N (1999) (158)
- Limit Theorem on the Self-Normalized Range for Weakly and Strongly Dependent Process (1975) (155)
- Phase transitions on fractals. II. Sierpinski gaskets (1984) (155)
- THE (MIS)BEHAVIOR OF MARKETS (2004) (154)
- A New Model for Error Clustering in Telephone Circuits (1963) (147)
- Computer Experiments with Fractional Gaussian Noises: Part 3, Mathematical Appendix (1969) (147)
- Negative fractal dimensions and multifractals (1990) (132)
- Multifractality of Deutschemark / Us Dollar Exchange Rates (1997) (131)
- Limit theorems on the self-normalized range for weakly and strongly dependent processes (1975) (130)
- STABLE PARETIAN RANDOM FUNCTIONS AND THE MULTIPLICATIVE VARIATION OF INCOME (1961) (128)
- Phase transitions on fractals. I. Quasi-linear lattices (1983) (112)
- A CLASS OF MICROPULSES AND ANTIPERSISTENT FRACTIONAL BROWNIAN MOTION (1995) (111)
- Fractals in physics: Squig clusters, diffusions, fractal measures, and the unicity of fractal dimensionality (1984) (106)
- 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) (92)
- Fractals and chaos : the Mandelbrot set and beyond : selecta volume C (2004) (88)
- Is Nature Fractal? (1998) (88)
- Discovery Of Cosmic Fractals (2002) (86)
- A Note On a Class of Skew Distribution Functions: Analysis and Critique of a Paper by H. A. Simon (1959) (82)
- Scaling in financial prices: I. Tails and dependence (2001) (80)
- Fractals in Geophysics (1989) (79)
- The (mis)behavior of markets : a fractal view of financialturbulence (2004) (75)
- Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn (1994) (73)
- Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism (1991) (72)
- Renewal sets and random cutouts (1972) (71)
- THE STABLE PARETIAN INCOME DISTRIBUTION WHEN THE APPARENT EXPONENT IS NEAR TWO (1963) (67)
- The Role of Sufficiency and of Estimation in Thermodynamics (1962) (67)
- Diffusion on fractal lattices and the fractal Einstein relation (1983) (65)
- The potential distribution around growing fractal clusters (1990) (65)
- A Fractal’s Lacunarity, and how it can be Tuned and Measured (1994) (64)
- Fractal Analysis and Synthesis of Fracture Surface Roughness and Related Forms of Complexity and Disorder (2006) (64)
- A population birth-and-mutation process, I: explicit distributions for the number of mutants in an old culture of bacteria (1974) (63)
- Physical properties of a new fractal model of percolation clusters (1984) (62)
- Measures of Fractal Lacunarity: Minkowski Content and Alternatives (1995) (58)
- Temperature Fluctuation: A Well‐Defined and Unavoidable Notion (1989) (58)
- 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)
- An Introduction to Multifractal Distribution Functions (1988) (56)
- Fractal Nature of Software-Cache Interaction (1983) (55)
- Gaussian self-affinity and fractals : globality, the earth, 1/fnoise, and R/S (2001) (55)
- Scaling in financial prices: II. Multifractals and the star equation (2001) (53)
- Multifractal Formalism for Infinite Multinomial Measures (1995) (51)
- 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)
- On the quadratic mapping z→z2-μ for complex μ and z: The fractal structure of its M set, and scaling (1983) (48)
- On the Derivation of Statistical Thermodynamics from Purely Phenomenological Principles (1964) (47)
- Levy dusts, Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension (1997) (47)
- New “anomalous” multiplicative multifractals: Left sided ƒ(α) and the modelling of DLA (1990) (47)
- Angular gaps in radial diffusion-limited aggregation: two fractal dimensions and nontransient deviations from linear self-similarity. (2002) (46)
- An outline of a purely phenomenological theory of statistical thermodynamics-I: Canonical ensembles (1956) (44)
- A Class of Multinomial Multifractal Measures with Negative (Latent) Values for the “Dimension” f(α) (1989) (44)
- Directed recursion models for fractal growth (1989) (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)
- 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)
- Fractals and an art for the sake of science (1989) (41)
- The Canopy and Shortest Path in a Self-Contacting Fractal Tree (1999) (41)
- Scaling in financial prices: III. Cartoon Brownian motions in multifractal time (2001) (40)
- Convergence of complex multiplicative cascades (2008) (38)
- Fractals, their transfer matrices and their eigen-dimensional sequences (1985) (37)
- Stochastic volatility, power laws and long memory (2001) (37)
- Inverse Measures, the Inversion Formula, and Discontinuous Multifractals (1997) (37)
- Exceptions to the multifractal formalism for discontinuous measures (1998) (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) (33)
- Correction of an Error in "The Variation of Certain Speculative Prices" (1963) (1972) (31)
- Multifractality of the harmonic measure on fractal aggregates, and extended self-similarity (1991) (31)
- The variation of the prices of cotton, wheat, and railroad stocks, and of some financial rates (1997) (31)
- 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) (31)
- Fractals, Graphics, and Mathematics Education (2002) (31)
- Simpie games of strategy occurring in communication through natural languages (1954) (31)
- Scaling in financial prices: IV. Multifractal concentration (2001) (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)
- Harmonic measure around a linearly self-similar tree (1992) (30)
- Mild vs. Wild Randomness: Focusing on those Risks that Matter (2007) (29)
- Inversion Formula for Continuous Multifractals (1997) (29)
- Fractal geometry of critical Potts clusters (2002) (28)
- 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)
- Fractal landscapes without creases and with rivers (1988) (26)
- Broken line process derived as an approximation to fractional noise (1972) (26)
- On Dvoretzky coverings for the circle (1972) (26)
- Fractals and the Rebirth of Iteration Theory (1986) (26)
- Crosscut Analysis of Large Radial DLA: Departures from Self-Similarity and Lacunarity Effects (1995) (25)
- Local Regularity of Nonsmooth Wavelet Expansions and Application to the Polya Function (1996) (25)
- Self-similarity of harmonic measure on DLA (1992) (24)
- Horton-Strahler ordering of random binary trees (1994) (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)
- The Fractalist: Memoir of a Scientific Maverick (2012) (22)
- Comments on:''A subordinated stochastic process model with finite variance for speculative prices (1973) (21)
- Intermittent turbulence and fractal dimension: Kurtosis and the spectral exponent 5/3+B (1999) (21)
- Uniform convergence for complex [0, 1]-martingales (2008) (21)
- The Variation of Certain Speculative Prices Author ( s ) : (2007) (20)
- Renormalization and fixed points in finance, since 1962 (1999) (20)
- The inescapable need for fractal tools in finance (2005) (20)
- Post Scriptum to "Final Note" (1961) (20)
- The Fractal Geometry of Trees and Other Natural Phenomena (1978) (19)
- 10 Exactly self-similar left-sided multifractals (1991) (17)
- The colours of infinity - the beauty and power of fractals (2010) (17)
- Fractional multiplicative processes (2009) (17)
- The Statistics of Natural Resources and the Law of Pareto (1995) (17)
- Deviations from Self-Similarity in Plane DLA and the “Infinite Drift” Scenario (1995) (17)
- Self-affine fractal sets, II: Length and surface dimensions (1986) (17)
- Fractal geometry and analysis : the Mandelbrot festschrift, Curaçao 1995 (1996) (16)
- “New Methods of Statistical Economics,” revisited: Short versus long tails and Gaussian versus power-law distributions (2009) (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)
- Introduction to fractal sums of pulses (1995) (14)
- Note on the definition and the stationarity of fractional Gaussian noise (1976) (14)
- BEHAVIOUR OF THE HARMONIC MEASURE AT THE BOTTOM OF FJORDS (1991) (14)
- Multifractals and Fractals (1986) (12)
- Multiperiodic multifractal martingale measures (2003) (12)
- Lecture V Fractals and turbulence: Attractors and dispersion (1977) (11)
- "New Methods of Statistical Economics, " revisited: Short versus long tails and Gaussian versus power-law distributions (2009) (11)
- Fractals: An Animated Discussion (1997) (11)
- Self-similarity of the branching structure in very large DLA clusters and other branching fractals (1994) (10)
- Linear Regression With Non-Normal Error Terms: A Comment (1971) (10)
- Self-similarity and covered neighborhoods of fractals: A random walk test (1993) (10)
- Multifractal Formalism for In nite Multinomial Measures (10)
- Stable fractal sums of pulses: the cylindrical case (1995) (10)
- Squig sheets and some other squig fractal constructions (1984) (10)
- Comment on ‘Stochastic Models in Hydrology’ by Adrian E. Scheidegger (1970) (9)
- Some “Facts” That Evaporate Upon Examination (1989) (9)
- Peano-pólya motions, when time is intrinsic or binomial (uniform or multifractal) (1997) (9)
- Nonlinear forecasts, rational bubbles, and martingales (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)
- People and events behind the “Science of Fractal Images” (1988) (9)
- Fractal Measures (Their Infinite Moment Sequences and Dimensions) and Multiplicative Chaos: Early Works and Open Problems (1986) (8)
- Survey of Multifractality in Finance (1999) (8)
- 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)
- Gibbs Distributions—I (2006) (8)
- Comment on the equivalence between fracton/spectral dimensionality, and the dimensionality of recurrence (1984) (8)
- TESTS OF THE DEGREE OF WORD CLUSTERING IN SAMPLES OF WRITTEN ENGLISH (1973) (8)
- Fractal aggregates, and the current lines of their electrostatic potentials (1991) (7)
- Reply [to “Comments on ‘Noah, Joseph, and Operational Hydrology’ by Benoit B. Mandelbrot and James R. Wallis”] (1969) (7)
- Limitations of efficiency and of martingale models (1997) (7)
- Fractal aspects of materials : disordered systems, November 29-December 2, 1988 (1988) (7)
- A case against the lognormal distribution (1997) (7)
- SOME ASPECTS OF THE RANDOM WALK MODEL OF STOCK MARKET PRICES: COMMENT* (1968) (7)
- Harold Edwin Hurst (2001) (7)
- The Fractal Range of the Distribution of Galaxies; Crossover to Homogeneity, and Multifractals (1989) (7)
- Scalebound or Scaling shapes: A Useful Distinction in the Visual Arts and in the Natural Sciences (2017) (7)
- Intermittent free turbulence (1999) (6)
- A Geometry Able to Include Mountains and Clouds (2010) (6)
- SELF-AFFINE FRACTAL SETS, III: HAUSDORFF DIMENSION ANOMALIES AND THEIR IMPLICATIONS (1986) (6)
- States of randomness from mild to wild, and concentration from the short to the long run (1997) (6)
- Fractional Brownian Motions and Fractional Gaussian Noises (2014) (6)
- Large Deviation Theory and the Distribution of Price Changes (2011) (6)
- Some Reasons for the Effectiveness of Fractals in Mathematics Education (2002) (5)
- Iterated random multiplications and invariance under randomly weighted averaging (1999) (5)
- 4. The Many Faces of Scaling: Fractals, Geometry of Nature, and Economics (1982) (5)
- Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups (1983) (5)
- Easy and Natural Generation of Multifractals: Multiplying Harmonics of Periodic Functions (1999) (4)
- Fractal Geometry in Physics (1993) (4)
- Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence (1999) (4)
- Mandelbrot on price variation (1997) (4)
- Steady-State Noises in Diffusion-Limited Fractal Growth (1991) (3)
- Leo Szilard and unique decipherability (Corresp.) (1965) (3)
- Benoît Mandelbrot (2011) (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)
- SELECTED TOPICS IN MATHEMATICS, PHYSICS, AND FINANCE ORIGINATING IN FRACTAL GEOMETRY (2004) (3)
- Documents in Mycenaean Greek, John Chadwick, Michael Ventris. Cambridge University Press (1956), 452, $15.00 (1960) (3)
- The Theory of Probability, 2nd ed., B.V. Gnedenko. Chelsea, New York (1962), 459, $8.75 (1962) (2)
- Parallel diff usion-limited aggregation (1995) (2)
- Visual Language (2005) (2)
- Rank-size plots, Zipf’s law, and scaling (1997) (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)
- Comment on transport processes on fractal structures (1984) (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)
- Sporadic random functions and conditional spectra; self-similar examples and limits (1999) (2)
- Fractal structure of the galaxy universe (2002) (2)
- FRACTIONAL BROWNIAN MOTION, SELF-SIMILAR PROCESSES, AND APPLICATIONS, (1966) (2)
- Correlations and texture in a new model hierarchical universe, based upon trema sets. (1979) (2)
- ON THE AGGREGATIVE FRACTALS CALLED “SQUIGS”, WHICH INCLUDE RECURSIVE MODELS OF POLYMERS AND OF PERCOLATION CLUSTERS (1984) (2)
- Cartoons of the Variation of Financial Prices and of Brownian Motions in Multifractal Time (2000) (2)
- TOWARDS A REVIVAL OF THE STATISTICAL LAW OF PARETO (1962) (2)
- A Note on a Law of Berry and on Insistence Stress (1957) (2)
- Some Mathematical Questions Arising in Fractal Geometry (2000) (2)
- The Geometry of Dla: Different Aspects of the Departure from Self-Similarity (1994) (2)
- New model for the clustering of errors on telephone circuits (Berger & M 1963) (1999) (1)
- Comment on Dr. Herdan's letter (1961) (1)
- Percolation, critical phenomena and fractals (1981) (1)
- Multifractals, probability and statistical mechanics, applications (2004) (1)
- Self-inverse fractals, Apollonian nets, and soap (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)
- The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems (2004) (1)
- Fractal Landscapes: from the Real World (1994) (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)
- New model for the clustering of errors on telephone circuits (Berger & M 1963) (1999) (1)
- Introduction to papers on quadratic dynamics: a progression from seeing to discovering (2004) (1)
- Harmonic Analysis and the Theory of Probability, S. Bochner. University of California Press (1955), 176, $4.50 (1960) (1)
- Continuous Interpolation of the Complex Discrete Map z → λz(1 - z), and Related Topics. On the dynamics of iterated maps IX (1985) (1)
- Self-similarity and panorama of self-affinity (1997) (1)
- Gibbs and Mandelbrot at Yale (1989) (1)
- Bilateral Canonical Cascades: Multiplicative Refinement Paths to Wiener's and Variant Fractional Brownian Limits (2007) (1)
- Radial DLA: two fractal dimensions and deviations from self-similarity (2001) (1)
- Hurst Coefficient (Rescaled Range Analysis) (2004) (1)
- A Class of Pulse Processes (1994) (1)
- Self-similarity and conditional stationarity (1999) (1)
- Statistical macro-linguistics (1959) (1)
- Editorial introduction: Heavy tails and stable Paretian distributions in empirical finance☆ (2010) (1)
- Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski (2004) (1)
- 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)
- Recent Soviet Contributions to Mathematics, Joseph P. La Salle, Solomon Lefschetz (Eds.). Macmillan (1962), 324 (1963) (0)
- SYMMETRY: A SPECIAL FOCUS ON FRACTALS (2012) (0)
- Information and Decision Processes (Robert E. Machol, ed.) (1961) (0)
- Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs (2004) (0)
- Gravity – the enigmatic creator of order (2002) (0)
- Integrating the Outliers (2003) (0)
- Self-inverse fractals osculated by sigma-discs: the limit sets of (“Kleinian”) inversion groups (2004) (0)
- “On certain martingales of Benoit Mandelbrot” Guest contribution (Kahane & Peyrière 1976) (1999) (0)
- Two nonquadratic rational maps devised from Weierstrass doubling formulas (2004) (0)
- The “normalized radical” of the ℳ-set (2004) (0)
- A new model of percolation clusters (1984) (0)
- 1987 Conference on Dynamic Patterns in Complex Systems (1988) (0)
- Sources of inspiration and historical background (1997) (0)
- Factal aspects of materials: Metal and catalyst surfaces, powders and aggregates. Extended abstracts (1984) (0)
- The map z → λ (z+1/z) and roughening of chaos, from linear to planar (computer-assisted homage to K. Hokusai) (2004) (0)
- Some potential problems arising in the theory of axial turbomachines (1949) (0)
- The triumph of uniformity in cosmology (2002) (0)
- The charm of self-similarity (2002) (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)
- Letter from Benoit B. Mandelbrot to Joshua Lederberg (1974) (0)
- Book reviewviii + 210 pp., $5.00 Finite Markov Chains, John G. Kemeny, J. Laurie Snell, van Nostrand, New York (1960) (1960) (0)
- Comments by P. H. Cootner, E. Parzen, and W. S. Morris (1960s) and responses (1997) (0)
- L-stability and multiplicative variation of income (1997) (0)
- The Origins of Megafractals (2002) (0)
- Fractal dimension, dispersion, and singularities of fluid motion (1999) (0)
- Random sets of multiplicity for trigonometric series (Kahane & M 1965) (1999) (0)
- Computation of the L-stable distributions (1997) (0)
- Fractal and chaos: planets, stardust, dark haloes (2002) (0)
- The boundary of the ℳ-set is of dimension 2 (2004) (0)
- Chapter 2 Unsolved Problems and Still-Emerging Concepts in Fractal Geometry (2002) (0)
- A discussion of Benoit Mandelbrot ’ s T he ( Mis ) Behavior of Markets by Nassim (2005) (0)
- Expansion and curvature of space (2002) (0)
- The inexhaustible function z squared plus c (2004) (0)
- The dream of a hierarchical world: protofractals (2002) (0)
- Designers need consistent interface to CAD tools (2006) (0)
- Introduction to papers on chaos in nonquadratic dynamics: rational functions devised from doubling formulas (2004) (0)
- The birth of cosmological principles (2002) (0)
- 1/ƒ noises and the infrared catastrophe (1999) (0)
- Additional Perspectives on Fractals (2018) (0)
- Dark matter – the grey eminence (2002) (0)
- Discontinuity and scaling: their scope and likely limitations (1997) (0)
- Fractal financial fluctuations ; do they threaten sustainability ? (2003) (0)
- The law of redshift in the kingdom of galaxies (2002) (0)
- Dimension, Symmetrie, Divergenz (1987) (0)
- Critical Phenomena and Fractals with Dimensionality Near 1 (1981) (0)
- Landscapes on an Imaginary Planet (1988) (0)
- The gate into cosmic order (2002) (0)
- L-stable model for the distribution of income (1997) (0)
- Foreword by Benoit Mandelbrot (2007) (0)
- A crisis of intuition as viewed by Felix Klein and Hans Hahn and its resolution by fractal geometry (2003) (0)
- Dark energy – the new emperor (2002) (0)
- Analysis, number theory, and dynamical systems (2004) (0)
- Filtering and specification of self-affinity (1999) (0)
- Multifractal Products of Cylindrical Pulses By Julien Barral and (0)
- Fractal Financial Fluctuations (2010) (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 new world of relativity and quantum forces (2002) (0)
- Bifurcation points and the “n-squared” approximation and conjecture, illustrated by M.L Frame and K Mitchell (2004) (0)
- The molecular concept of law (2011) (0)
- A Branching Process Analysis of the Stack Algorithm for Variable Channel Conditions (1992) (0)
- The complex quadratic map and its ℳ-set (2004) (0)
- Fe b 20 09 CONSTRUCTION OF SIGNED MULTIPLICATIVE CASCADES (2009) (0)
- Cosmic hierarchies: from dream to science (2002) (0)
- Scaling, invariants and fixed points (1999) (0)
- INTERVEIW WITH PROFESSOR BENOIT B. MANDELBROT (2005) (0)
- Fractals: an animated discussion (videotape) (1990) (0)
- Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991) (2004) (0)
- Co-indicator functions and related 1/ƒ noises (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)
- Short excerpts (1964–1984) (1999) (0)
- Chapter 3 Fractals , Graphics , and Mathematics Education 1 (2002) (0)
- Acknowledgments related to quadratic dynamics (2004) (0)
- Vita and Publications (1992) (0)
- The mysterious singularity (2002) (0)
- The fractal cosmos: New shapes in the sciences and arts (1984) (0)
- Synergetics and the Images of Future (2000) (0)
- Scaling distributions and income maximization (1997) (0)
- Sketches of prehistory and history (1999) (0)
- Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets (2004) (0)
- Certain Julia sets include smooth components (2004) (0)
- Scaling, invariants and fixed points (1999) (0)
- The Fatou and Julia stories (2004) (0)
- Panorama of grid-bound self-affine variability (1999) (0)
- Industrial concentration and scaling (1997) (0)
- Cantor and Fatou dusts; self-squared dragons (2004) (0)
- Proportional growth with or without diffusion, and other explanations of scaling (1997) (0)
- Book-Review - Fractals - Form Chance and Dimension (1980) (0)
- Symmetry with respect to several circles: dilation/reduction, fractals, and roughness (2004) (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)
- 8. Fractal Geometry (0)
- The Paradoxal Universe of Sir Isaac (2002) (0)
- The nature of roughness in mathematics, science, and art (2005) (0)
- Mathematical analysis while in the wilderness (2004) (0)
- ON TELEPHONE ERROR CLUSTERING CONSIDERED AS AN ILLUSION (1962) (0)
- Fractal Lacunarity and Scenarios for the Near-Isotropic Distribution of Galaxies (2001) (0)
- Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments (2004) (0)
- Redshift – the quiet cosmographer (2002) (0)

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## Other Resources About Benoit Mandelbrot

## What Schools Are Affiliated With Benoit Mandelbrot?

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