4524 Carol Alexander/Ian Giblin/David Newton: Symmetry groups of fractals. Math. Intell. 14/2 (1992), 32-38. Matthias Arbeiter/Norbert Patzschke: Random self-similar multifractals. Math. Nachr. 181 (1996), 5-42. 19407 James Baish/Rakesh Jain: Fractals and cancer. Cancer Res. 60 (2000), 3683-3688. 8708 C. Bandt: Besprechung der zweiten Auflage von Barnsleys Buch "Fractals everywhere". Jber. DMV 98 (1996), B 24-25. C. Bandt/J. Flachsmeyer/H. Haase (ed.): Topology, measures, and fractals. Akademie-Verlag 1992, 220p. 3-05-501554-1. DM 84. 5712 Massimo Banzi: Meraviglie del caos. Applicando Novembre 1993, 52-55. 19432 Albert-Laszlo Barabasi/H. Stanley: Fractal concepts in surface growth. Cambridge UP 1995, 360p. Eur 31. 713 Michael Barnsley: Fractals everywhere. Academic Press 1988. Michael Barnsley: Superfractals. Cambridge UP 2006, 450p. Eur 40. A. Beardon: Iteration of rational functions. Springer 2000, 280p. DM 90. T. Bedford: Dimensions and dynamics for fractal recurrent sets. J. London Math. Soc. 33 (1986), 89-100. 17950 Marcel Berger: Dynamiser la geometrie elementaire - introduction a des travaux de Richard Schwartz. Rend. Mat. 25 (2005), 127-153. Abram Besicovitch: The Kakeya problem. Am. Math. Monthly 70 (1963), 697-706. C. Bovill: Fractal geometry in architecture and design. Birkhaeuser 1995, 200p. 3-7643-3795-8. DM 78. 12052 Jürgen Brickmann: Fraktale Dimension in der Chemie. In 4019 Gerok/, 229-247. 12339 Sergei Buldyrev a.o.: Fractals in biology and medicine - from DNA to the heartbeat. In 12338 Bunde/, 49-87. Armin Bunde/Shlomo Havlin (ed.): Fractals and disordered systems. Springer 1991. 12338 Armin Bunde/Shlomo Havlin (ed.): Fractals in science. Springer 1994, 300p. Macintosh-Version 3-540-56221-4, MS-DOS-Version 3-540-56220-6. DM 94. "We strongly recommend the text for introductory graduate seminars." (P. Dixon/A. Hobday/G. Sugihara) 2577 Dane Camp: A fractal excursion. Math. Teacher 1991/4, 265-275. [3015] 2527 Giulio Casati (ed.): Il caos. Le Scienze 1991. 2559 D. Chalice: A characterization of the Cantor function. Am. Math. Monthly 98 (1991), 255-258. 2583 G. Cherbit (ed.): Fractals. Wiley 1990. F. Cramer: Chaos and order. VCH 1993, 310p. 3-527-29067-2. DM 48. K. Culik/S. Dube: Methods for generating deterministic fractals and image processing. Springer LN Computer Science 464 (1990), 2-28. F. Cunningham: The Kakeya problem for simply connected and for star-shaped sets. Am. Math. Monthly 78 (1971), 114-129. F. Cunningham: Three Kakeya problems. Am. Math. Monthly 81 (1974), 582-592. Richard Darst/Judith Palagallo/Thomas Price: Curious curves. World Scientific 2009, 230p. F. Dekking: Recurrent sets. Adv. Math. 44 (1982), 78-104. 2584 F. Dekking: Construction of fractals and dimension problems. In 2583 Cherbit, 83-97. [3015] F. Dekking/M. Mendes-France: Uniform distribution modulo one - geometric point of view. J. reine u. angew. Math. 329 (1981), 143-153. 2528 Robert Devaney: Caos e frattali. Addison-Wesley 1990. Robert Devaney: Cantor and Sierpinski, Julia and Fatou - complex topology meets complex dynamics. Notices AMS January 2004, ... Thomas Gregory Dewey: Fractals in molecular biophysics. Oxford UP 1997. 0-19508447-0. Robert Dixon: Mathographics. Dover 1987, 210p. 0-486-26639-7. R. Dobrushin/S. Kusuoka: Statistical mechanics and fractals. SLN Math. 1567 (1993), 100p. 3-540-57516-2. 335 M. Dodson/J. Vickers (ed.): Number theory and dynamical systems. Cambridge UP 1989. Vladimir Drobot/John Turner: Hausdorff dimension and Perron-Frobenius theory. Ill. J. Math. 33 (1989), 1-9. 2452 Richard Durrett: Crabgrass, measles, and gypsy moths: An introduction to interacting particle systems. Math. Intell. 10/2 (1988), 37-47. 5755 Richard Dyce: Nature trails. Mac User (UK) 12 november 1993, 101-103. 2154 Gerald Edgar: Measure, topology, and fractal geometry. Springer 1990. 5539 Gerald Edgar: A fractal puzzle. Math. Intell. 13/3 (1991), 44-50. Gerald Edgar: Integral, probability, and fractal measures. Springer 1998, 290p. 3-540-98205-1. DM 69. Gerald Edgar/R. Mauldin: Multifractal decompositions of digraph recursive fractals. Proc. London Math. Soc. 65 (1992), 604-628. Pal Erdös: The dimension of the rational points in Hilbert space. Annals of Math. 41 (1940), 734-736. L. Evans/R. Gariepy: Measure theory and fine properties of functions. CRC Press, Boca Raton, 1988. Should be a very good text on Hausdorff dimension, but CRC books are often incredibly expensive. I don't know the price in this case. Kenneth Falconer: Sections of sets of zero Lebesgue measure. Mathematika 27 (1980), 90-96. 576 Kenneth Falconer: The geometry of fractal sets. Cambridge UP 1987. 4841 Kenneth Falconer: The integral geometry of fractals. 335 Dodson/Vickers, 103-115. 17814 Kenneth Falconer: Techniques in fractal geometry. Wiley 1997, 260p. Eur 55. "... contains methods for studying dimensions and other parameters of fractal sets and measures, and also more sophisticated techniques such as the thermodynamic formalism and tangent measures. Many examples and applica- tions are described, for instance in differential equations and harmonic analysis. Also main results of probabilistic analysis are presented: the ergodic theorem, the renewal theorem and the martingale convergence theorem, including applications to average densities of fractals and box-counting numbers of self-similar sets." (F. Haslinger) 17827 Kenneth Falconer: Fractal geometry. Wiley 2005, 340p. Eur 50. 5951 Jens Feder: Fractals. Plenum Press 1988. C. Fefferman: The multiplier problem for the ball. Annals of Math. 94 (1971), 330-336. 8392 Henning Fernau: Iterierte Funktionen, Sprachen und Fraktale. Bibl. Inst. 1994, 290p. 3-411-17011-5. DM 58. 6392 Henning Genz: Besprechung des Buches "Denkt Gott symmetrisch? Das Ebenmass in Mathematik und Natur" von Ian Stewart und Martin Golubitsky. Spektrum 1995/1, 112-113. C. Giustozzi: Il biomorfoscopio. MC Microcomputer 94 (1990), 150-153. D. Goffinet: Number systems with a complex base: A fractal tool for teaching topology. Am. Math. Monthly 98 (1991), 249-255. 6632 Ary Goldberg/David Rigney/Bruce West: Caos e frattali in fisiologia umana. 6626 Israel, 45-50. Horst Halling/Rolf Moeller: Mathematik fuers Auge. Spektrum 1995, 144p. 3-86025-427-8. DM 48. 8488 Keith Hannabuss: Forgotten fractals. Math. Intell. 18/3 (1996), 28-31. Henry Smith had (around 1875) examples of discontinous sets, similar to the Sierpinski gasket. 4842 J. Harrison: Geometry of algebraic continued fractals. In 335 Dodson/Vickers, 117-136. Harold Hastings/George Sugihara: Fractals. A user's guide for the natural sciences. Oxford UP 1993, 320p. $20 (pb). "... it is an excellent book from which even those that have been working in this area for a long time have something to learn. I strongly recommend it for anyone interested in how to apply these new and exciting techniques to the understanding of natural phenomena." (Bruce West) Felix Hausdorff: Dimension und aeusseres Mass. Math. Annalen 79 (1918), 157-179. 912 F. Hunt/F. Sullivan: Methods of computing fractal dimensions. Gill/Zachary, 83-93. J. Hutchinson: Fractals and self-similarity. Indiana Univ. Math. J. 30 (1981), 713-747. Phillip Iannacone/Mustafa Khokha (ed.): Fractal geometry in biological systems - an analytical approach. CRC 1996, 370p. $70. 26013 Maria Infusino: Successioni uniformemente distribuite su insiemi frattali. Tesi Univ. Calabria 2007, 126p. Gaston Julia: Memoire sur l'iteration des fonctions rationelles. J. Math. 8 (1918), 47-245. J. Kaandorp: Fractal modelling. Growth and form in biology. Springer 1994, 240p. 3-540-56685-6. DM 78. B. Kaye: Chaos and complexity. VCH 1993, 612p. 3-527-29007-9. DM 78. B. Kaye: A random walk through fractal dimensions. VCH 1989, 420p. DM 64 (pbk). 24716 Marc Kesseböhmer/Bernd Stratmann: A multifractal analysis for Stern-Brocot intervals, continued fractions and diophantine growth rates. J. reine angew. Math. 605 (2007), 133-163. Bern Kieninger: Iterated function systems on compact Hausdorff spaces. Shaker 2002, 210p. Eur 49. K. Kiesswetter: Ein einfaches Beispiel einer Funktion, welche ueberall stetig und nicht differenzierbar ist. Math.-phys. Semesterberichte 13 (1966), 216-221. Helge von Koch: Sur une courbe continue sans tangente, obtenue par une construction geometrique elementaire. Archiv fuer Mat. 1 (1904), 681-704. Helge von Koch: Une methode geometrique elementaire pour l'etude de certaines questions de la theorie des courbes planes. Acta Math. 30 (1906), 145-174. 24715 Ljubisa Kocic/Liljana Stefanovska: Fractals from the Stern-Brocot tree. Internet 2008, 2p. 881 Steven Krantz: Fractal geometry. Math. Intell. 11/4 (1989), 12-16, 19. D. Larman: A compact set of disjoint line segments in E^3 whose end set has positive measure. Mathematika 18 (1971), 112-125. 5936 Alain Le Mehaute: Fractal geometries. Penton Press 1990, 180p. 1-85718-001-1. Roger Lewin: Complexity. Life at the edge of chaos. 1992. 19507 Gabriele Losa/Danilo Merlini/Theo Nonnenmacher/Ewald Weibel (ed.): Fractals in biology and medicine IV. Birkhäuser 2005, 310p. 8300 Evelyne Lutton a.o.: Mixed IFS - resolution of the inverse problem using genetic programming. INRIA Rapport 2631 (1995), 17p. 1174 Benoit Mandelbrot: Die fraktale Geometrie der Natur. Birkhaeuser 1987. 2500 Benoit Mandelbrot: Gli oggetti frattali. Einaudi 1987. 19514 Benoit Mandelbrot/Richard Hudson: Fraktale und Finanzen. Piper 2007, 440p. Eur 13. 17574 Yuri Manin: The notion of dimension in geometry and algebra. Bull. AMS ... (2006), ... 24637 Albert Marden: Review of the book "Indra's pearls" by Mumford/Series/Wright. Notices AMS January 2003, 38-44. 10224 Michael Marder: Roughing it. Science 1 August 1997, 647. Fractals in material science. 7069 Mario Markus: Ljapunow-Diagramme. Spektrum 1995/4, 66-73. J. Marstrand: Packing smooth curves in R^q. Mathematika 26 (1979), 1-12. 17811 Pertti Mattila: Geometry of sets and measures in euclidean spaces. Fractals and rectifiability. Cambridge UP 2004, 340p. Eur 46. 24545 R. Mauldin: Infinite iterated function systems - theory and applications. Progress Probability 37 (1995), 91-110. R. Mauldin/S. Williams: Hausdorff dimension in graph directed constructions. Trans. AMS 309 (1988), 811-829. 4538 Michel Mendes-France: Chaos implies confusion. In 335 Dodson/Vickers, 137-152. 22112 David Mumford/Caroline Series/David Wright: Indra's pearls. Cambridge UP 2008, 390p. Eur 51. 2541 Roberta Nibbi: Topologia dei frattali. Tesi, Ferrara 1991. K. Oldham/J. Spanier: The fractional calculus. Academic Press 1974. Dick Oliver/Daniel Hoviss: Frattali. Jackson 1994, 480p. Con dischetto e CD-ROM. 88-256-0625-7. Lire 79.000. Programmi per PC. 15269 Alfonso Ortega/Marina de la Cruz/Manuel Alfonseca: Parametric 2-dimensional L-systems and recursive fractal images - Mandelbrot set, Julia sets and biomorphs. Computers and Graphics 26 (2002), 143-149. David Peak/Michael Frame: Chaos under control. Freeman 1994. 908 Heinz-Otto Peitgen/Peter Richter: The beauty of fractals. Springer 1986. 12054 Heinz-Otto Peitgen/Hartmut Ju''rgens: Fraktale Computerexperimente (ent)zaubern komplexe Strukturen. In 4019 Gerok/, 123-153. Heinz-Otto Peitgen/H. Ju''rgens/D. Saupe: Fractals for the classroom II. Complex systems and Mandelbrot sets. Springer 1992, 500p. 3-540-97722-8. DM 54. Carefully written. Mathematical aspects with relations to natural phenomena. Heinz-Otto Peitgen/H. Ju''rgens/D. Saupe: Chaos. Bausteine der Ordnung. Klett-Cotta, 700p. 3-608-95435-x. DM 78. Heinz-Otto Peitgen/H. Ju''rgens/D. Saupe: Bausteine des Chaos. Fraktale. Klett-Cotta, 510p. 3-608-95888-6. DM 68. 907 Heinz-Otto Peitgen/Dietmar Saupe (ed.): The science of fractal images. Springer 1988. 20838 Washek Pfeffer: A devil's platform. Am. Math. Monthly 115/10, 943-947. 4711 Clifford Pickover: Mit den Augen des Computers. Markt & Technik 1992. 12142 Christoph Po''ppe: Gefa''s''- und Entladungsba''ume - eine fruchtbare Analogie. Spektrum 1998/10, 12-13. 14727 Christoph Po''ppe: Fraktal zum Anfassen. Spektrum 2001/3, 96. Geometrie-Wochenende an der Uni Mu''nchen. 18900 Christoph Pöppe: Jos Leys - Meister der fraktalen Kunst. Spektrum 2007/2, 105-107. Feliks Przytycki/Mariusz Urbanski: Conformal fractals - ergodic theory methods. Cambridge UP 2010, 350p. Eur 57. 22379 Clifford Reiter: Fractals, visualization and J. Lulu 2007, 244p. Eur 83. Ignacio Rodrigues-Iturbe/Andrea Rinaldo: Fractal river basins. Cambridge UP 1997, 550p. 0-521-47398-5. $100. B. Ross: Fractional calculus and its applications. Springer 1974. Hans Sagan: Space-filling curves. Springer 1994, 220p. 3-540-94265-3. DM 54. B. Sapoval: Les fractales. Aditech 1989. M. Saunder: L'accrescimento dei frattali. Le Scienze 223 (1987), 68-77. 11173 Christoph Scha''ftner: Fraktale Bildkompression. Internet ca. 1995, 2p. 6353 Dierk Schleicher: Wann kann man ein nichtlineares dynamisches System geradebiegen. Spektrum 1994/12, 96-99. Der Fields-Preistraeger Jean-Christophe Yoccoz hat in einem Spezialfall das Problem der kleinen Nenner vollstaendig geloest. 5954 Manfred Schroeder: Fractals, chaos, power laws. Minutes from an infinite paradise. Freeman 1991, 420p. 0-7167-2357-3 (pb). DM 69. One of the best books on chaos and fractals. 2426 Heinz Georg Schuster: Deterministic chaos. VCH 1988. A. Semmes: Some novel types of fractal geometry. Oxford UP 2001, 160p. Pds 50. B. Sendov: Hausdorff approximations. Kluwer 1990, 360p. HFL 230. Approximation of functions with respect to the Hausdorff metric is an important topic in many applications. Essentially a translation from the Bulgarian original (1979), the book is still very valuable, according to H. Feichtinger. 3361 Caroline Series: The geometry of Markoff numbers. Math. Intell. 7/3 (1985), 20-29. 15094 Manfred Sernetz: Die fraktale Geometrie des Lebendigen. Spektrum 2000/7, 72-79. Waclaw Sierpinski: Sur une courbe dont tout point est un point de ramification. Compt. Rendus Acad. Sci. Paris 160 (1915), 302-305. Waclaw Sierpinski: Un example elementaire d'une fonction croissante qui a presque partout une derivee nulle. Giornale Mat. Battaglini 6 (1916), 314-334. 24123 Jonathan Smith: Quasigroup permutation representations. Quasigroups Rel. Syst. 10 (2003), 115-134. 16170 I. Sokolov: Ein Ritt auf Sierpinskis Teppich und eine Kreuzfahrt entlang einer unendlichen Küstenlinie. Int. Math. Nachr. 194 (2003), 1-12. Julien Sprott: Strange attractors. Creating patterns in chaos. M & T 1993. 1-55851-298-5. 14933 Wilhelm Sternemann: Neue Fraktale aus platonischen Ko''rpern. Spektrum 2000/11, 116-119. R. Stevens: Learning C with fractals. Academic Press 1993, 340p. Pds. 33. 6624 Ian Stewart: Four encounters with Sierpinski's gasket. Math. Intelligencer 17/1 (1995), 52-64. 12969 Ian Stewart: Die Allgegenwart des Sierpinski-Dreiecks. Spektrum 2000/2, 106-107. Ian Stewart/Martin Golubitsky: Denkt Gott symmetrisch? Das Ebenmass in Mathematik und Natur. Birkhaeuser 1993, 300p. DM 78. [ = "Fearful symmetry".] "Wie die vielen anderen Buecher dazu auf dem Markt behandelt auch dieses die Symmetrie zusammen mit der Symmetriebrechung. Dabei treten die Autoren auf, als haetten sie beides gerade neu erfunden. ... In der englischsprachigen populaerwissenschaftlichen Literatur ist die Unart verbreitet, ohne Quellenangaben zu zitieren. Das sollte verboten sein. Aber mein Hauptvorwurf gegen das Buch ist ein anderer: Es setzt sich auf das hohe Ross Mathematik und urteilt von dort herab ueber die Einzelwissenschaften, insbesondere die Physik. ... Der fuer die Anwendungen von Symmetrie und Symmetriebrechung in der Physik grundlegende Unterschied zwischen der Symmetrie von Objekten und der von Naturgesetzen kommt nicht vor. ... Allgemein wirft das Buch die spontane Symmetriebrechung der Physik mit der normalen und alltaeglichen Asymmetrien, die aus Anfangsbedingungen folgen, in einen Topf. Das ist voellig falsch. Von spontaner Symmetriebrechung kann nur bei Systemen gesprochen werden, die Zustaende niedrigster Energie - Grundzustaende - haben. ... Die abermals andere explizite Symmetriebrechung spielt in dem Buch keine Rolle. ... Ausser den grundsaetzlichen Diskussionen, die mich nicht ueberzeugt haben, enthaelt das Buch zahlreiche interessante Fallstudien. Sie reichen von Kornkreisen ueber die Vererbung der Haendigkeit von Schneckenhaeusern und die Gangarten von Tieren bis zur Physik der Elementarteilchen. Besonderen Wert legen die Autoren auf die Symmetriebrechung durch chaotische Stoerungen. ... Ich kann nicht allen Aussagen in den Fallstudien zustimmen. Aber sie sind in jedem Fall anregend zu lesen. Ihretwegen empfehle ich das Buch." (6392 Henning Genz). Robert Strichartz: Analysis on fractals. Notices AMS November 1999, 1199-1208. Robert Strichartz: Differential equations on fractals. Princeton UP 2006, 190p. Eur 19. 14617 Volkhard Stu''rzbecher: Bilder, die sich selber malen. Spektrum 2001/4, 78-85. 17756 Terence Tao: From rotating needles to stability of waves - emerging connections between combinatorics, analysis, and PDE. Notices AMS March 2001, 294-303. 18902 Norbert Treitz: Die Vielseitigkeit der Rollkurven. Spektrum 2007/4, 104-107. Claude Tricot: Curves and fractal dimension. Springer 1994, 320p. 3-540-94095-2. DM 74. Hans Triebel: Fractals and spectra related to Fourier analysis and function spaces. Birkhäuser 1997, 270p. Eur 152. 12037 Tamas Vicsek: Fractal growth phenomena. World Scientific 1989. Herbert Voss: Chaos und Fraktale selbst programmieren. Franzis 1994, 320p. mit CD-ROM. 3-7723-7003-9. DM 89. Hans Walser: Der goldene Schnitt. Teubner 1993, 140p. 3-8154-2070-9. DM 17. 5939 D. Welsh: Complexity: Knots, colourings and countings. Cambridge UP 1993. 0-521-45740-8. 3743 Bruce West: Fractal physiology and chaos in medicine. World Scientific 1990. 8118 Bruce West: Review of the book "Fractals" by H. Hastings and G. Sugihara. Bull. Math. Biol. 57 (1995), 169-171. 10149 Geoffrey West/James Brown/Brian Enquist: A general model for the origin of allometric scaling laws in biology. Science 4 April 1997, 122-126. 3964 Keith Wicks: Fractals and hyperspaces. Springer LN Math. 1492 (1991). 2429 Stephen Wolfram: Geometry of binomial coefficients. Am. Math. Monthly 91 (1984), 566-570. [3015]