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Contents
Contributors ix
Preface by Michael Frame xv
Preface by Nathan Cohen xix
Chapter 1 Watching Benoit at work 1
Aliette Mandelbrot
Chapter 2 Benoit Mandelbrot: nor does lightning travel
in a straight line 5
Michael Frame
Chapter 3 Irregularities and scaling in signal and image
processing: multifractal analysis 31
Patrice Abry, Stephane Jajfard, Herwig Wendt
Chapter 4 Three-dimensional fractal homeomorphisms 117
Michael F. Barnsley and Brendan Harding
Chapter 5 Mandelbrot's cascades: a legendary destiny 143
Julien Barral and Jacques Peyriere
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vi Contents
Chapter 6 Benoit Mandelbrot and art 173
Javier Barrallo
Chapter 7 The nature of fractal music 181
Harlan J. Brothers
Chapter 8 Fractal antenna and fractal resonator primer 207
Nathan Cohen
Chapter 9 Fractal-based wideband invisibility cloak 229
Nathan Cohen, Obinna Okoro, Dan Earle,
Phil Salkind, Barry linger, Sean Yen,
Daniel McHugh, Stefan Polterzycki and
A. J. Shelman-Cohen
Chapter 10 From fractional Brownian motion to
multifractional and multistable motion 239
Kenneth Falconer
Chapter 11 Watching the markets misbehave 257
Richard L. Hudson
Chapter 12 Partition zeta functions, multifractal spectra,
and tapestries of complex dimensions 267
Kate E. Ellis, Michel L. Lapidus,
Michael C. Mackenzie and John A. Rock
Chapter 13 Benoit Mandelbrot, films, and me: a tribute 323
Nigel Lesmoir-Gordon
Chapter 14 Fractals and humor 337
Demetri Martin
Chapter 15 Multifractal measures of time series: curvature
surfaces of f(a) curves 339
William Martino and Michael Frame
Chapter 16 Benoit Mandelbrot, educator 367
Nial Neger and Harlan J. Brothers
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Contents vii
Chapter 17 The art of roughness 381
Emer O'Daly
Chapter 18 Long-range dependence of the two-dimensional
Ising model at critical temperature 399
Vladas Pipiras and Murad S. Taqqu
Chapter 19 Benoit Mandelbrot, W. H. Freeman,
and the launch of The Fractal Geometry of Nature 441
Peter Renz
Chapter 20 Math and physics: Levy flights and drives 449
Michael Shlesinger
Chapter 21 Benoit Mandelbrot in finance 459
Christian Walter
Chapter 22 How Benoit Mandelbrot changed my thinking
about biological form 471
Ewald R. Weibel
Chapter 23 Entropic origin of allometry relations 489
Bruce J. West and Damien West
Chapter 24 Music and fractals 501
Charles Wuorinen
Chapter 25 Stories about Benoit 507
Chapter 26 Some final thoughts 543
Michael Frame
Index 547
