Abstract
In comparison with the six chapters of the Programming volume [767] of the GuideBooks, this chapter is very long—almost one and a half times longer than the average chapter text, without the plots. The reason for this is threefold:
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The reader is now familiar with the structure of Mathematica expressions, and we can make full use of this knowledge to write larger programs. Often, one of the simplest ways to check whether a calculation produces the desired result is to look at it graphically for special values of parameters or/and limiting cases.
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Originally, it was not my intention to discuss a lot of graphical methods and examples. However, because of numerous requests by the students who listened to the original lectures that resulted in this book, I have now included, in my opinion, a sufficient amount of graphics. Apparently many students and colleagues wanted to use Mathematica not only for symbolic calculations, but also (sometimes, unfortunately, only) to produce plots of measured data or sets of data produced by other programs.
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Visualization of mathematical knowledge is very important for teaching and “understanding” mathematics [94], [835], [597], [228], [364], [438], [649], [361], [45], [446], [428], [269], [226].
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References
S. J. Abas in C. A. Pickover (ed.). The Pattern Book, World Scientific, Singapore, 1995.
S.J. Abas, A. S. Salman. Symmetries of Islamic Geometrical Patterns, World Scientific, Singapore, 1995.
P. Abbott. The Mathematica Journal 4, n2, 25 (1994).
P. Abbott. The Mathematica Journal 4, n2, 26 (1994).
L. Acedo, S. B. Yuste. arXiv:cond-mat/0003445 (2000).
J. A. Adam. Phys. Rep. 356, 229 (2002).
A. Adamatzky. Comput. Graphics 21, 519 (1997).
M. Adahl, I. Melbourne, M. Nicol. Nonlinearity 16, 977 (2003).
A. Adamatzky. Int. J. Mod. Phys. C 11, 47 (2000).
B. M. Adcock, K. C. Jones, C. A. Reiter, L. M. Vislocky. Comput. Graphics 24, 791 (2000).
G. Agoston. Color Theory and Its Application in Art and Design, Springer-Verlag, Berlin, 1987.
O. Aichholzer, C. Cortes, E. D. Demaine, V. Dujmovic, J. Erickson, H. Meijer, M. Overmars, B. Palop, S. Ramaswami, G. T. Toussaint. arXiv. cs.CG/0008010 (2000).
M. Aigner, J. Pein, T. Stechmiiller. Math. Semesterber. 38, 242 (1991).
S. Akiyama in S. Kanemitsu, K. Gyory (eds.). Number Theory and Its Applications, Kluwer, Dordrecht, 1999.
S. Akiyama. J. Math. Soc. Jap. 54, 283 (2002).
D. V. Alekseevskij, A. S. Solodovnikov in E. B. Vinberg (ed.). Geometry II, Springer-Verlag, Berlin, 1993.
M. Alexa, D. Cohen-Or, D. Levin. Comput. Graphics Proc. SIGGRAPH 2000 157 (2000).
P. S. Alexandrov. Vvedenie v teoriju mnoschestv i obschuju topologiju, Nauka, Moscow, 1977.
T. T. Allen. Am. Math. Monthly 94, 98 (1986).
T. J. Allen, J. R. Schmidt. Can. J. Phys. 76, 965 (1999).
N. W. Allis, J. P. Dumont, C. A. Reiter. Comput. Graphics 25, 519 (2001).
S. L. Altmann. Band Theory of Solids: An Introduction from the View of Symmetry, Clarendon Press, Oxford, 1994.
I. Amidror. The Theory of the Moire Phenomenon, Kluwer, Dordrecht, 2000.
M. Andrecut. Int. J. Mod. Phys. B 14, 53 (2000).
M. Aono, T. L. Kunii. IEEE Comput. Graphics Appl. 3, n5, 10 (1983).
S. Arimoto. J. Math. Chem. 27, 213 (2000).
P. Arnoux, V. Berthe, H. Ei, S. Ito. Discr. Math. Theor. Comput. S.i. Proc. AA DM-CCG 059 (2001). http://www.emis.ams.org/journals/DMTCS/proceedings/html/dmAAO104.abs.html
I.I. Artobolevskii. Mechanism for the Generation of Plane Curves, MacMillan, New York, 1964.
E. J. Austin, M. Wilkinson. Nonlinearity 5, 1137 (1992).
K. Azukawa, T. Yuzawa. Math. J. Toyama Univ. 13, 165 (1990).
M. Baake. Z. Naturf. 49a, 445 (1994).
M. Baake, U. Grimm, D. H. Harrington. J. Phys. A 27, 2669 (1994).
M. Baake. arXiv:math-ph/9901014 (1999).
M. Baake, R. V. Moody, P. A. Pleasants. arXivimath.MG/9906132 (1999).
M. Baake, U. Grimm, R. V. Moody. arXiv:math.HO/0203252 (2002).
B. Bagchi, S. Mallik, C. Quesne. arXiv:physics/0201096 (2002).
B. Bagchi, A. Ganguly. arXiv.math-ph/0302040 (2003).
S. Bahar. Solitons, Fractals 5, 1001 (1995).
S. Bahar. Chaos, Solitons, Fractals 7, 41 (1996).
P. Bak, K. Sneppen. Phys. Rev. Lett. 71, 4083 (1993).
P. Bak. How Nature Works, Springer-Verlag, New York, 1996.
C. P. Baliarda, C. B. Borau, M. N. Rodro, J. R. Robert. IEEE Trans. Antenn. Prop. 48, 713 (2003).
W. W. R. Ball, H. S. M. Coxeter. Mathematical Recreations and Essays, Toronto University Press, Toronto, 1974.
T. Banchoff, P. Giblin. Am. Math. Monthly 101, 403 (1994).
T. F. Banchoff in A. M. Cohen, X.-S. Gao, N. Takayama (eds.). Mathematical Software, World Scientific, Singapore, 2003.
C. Bandt, P. Gummelt. Aeq. Math. 53, 295 (1997).
L. Bang-He. J. Sys. Sci. Math. Sci. 6, 263 (1986).
A.-L. Barabasi, H. E. Stanley. Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995.
D. Barache, B. Champagne, J.-P. Gazeau in J. Patera (ed.). Quasicrystals and Discrete Geometry, American Mathematical Society, Providence, 1998.
K. Baranski. Ann. Acad. Sci. Fennicce 27, 325 (2002).
M. Barnsley. Fractals Everywhere, Academic Press, San Diego, 1988.
M. F. Barnsley in G. Turchetti (ed.). Nonlinear Physics, World Scientific, Singapore, 1889.
M. F. Barnsley, C. P. Hurd. Fractal Image Compression, AK Peters, Wellesley, 1993.
L. Bartholdi, R. Grigorchuk, V. Nekrashevych. arXiv.math.GR/0202001 (2002).
W. Bartky. Rev. Mod. Phys. 10, 264 (1938).
M. Batty in A. J. Crilly, R. A. Earnshaw, H. Jones (eds.). Fractals and Chaos, Springer-Verlag, New York, 1991.
G. Baumann. Mathematica in der Theoretischen Physik, Springer-Verlag, Berlin, 1993.
C. Baxa, J. SchoiBengeier. Monatsh. Math. 135, 265 (2002).
A. F. Beardon in T. Bedford, M. Keane, C. Series (eds.). Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces, Oxford University Press, Oxford, 1991.
K. G. Beauchamp. Walsh Functions and Their Applications, Academic Press, London, 1975.
O. Beaver, T. Garrity. arXiv: math. NT/02104S0 (2002).
T. Bedford, F. M. Dekking, M. S. Keave. Nieuw Archief Wiskunde 10, 185 (1993).
L. H. Bennett. The Centroid Circles and Their Geometric Significance, Belt Printing, Modesto, 1973.
C. D. Bennett. Math. Intell. 23, n3, 39 (2000).
S. Berczi in B. Gruber, J. H. Yopp (eds.). Symmetries in Science, Plenum Press, New York, 1990.
M. Berger, P. Pansu, J.-P. Berry, X. Saint-Raymond. Problems in Geometry, Springer-Verlag, New York, 1984.
M. A. Berger. An Introduction to Probability and Stochastic Processes, Springer-Verlag, New York, 1993.
W. Bergweiler. Bull. Am. Math. Soc. 29, 151 (1993).
S. Berman, R. V. Moody. J. Phys. A 27, 115 (1994).
M. V. Berry, J. Goldberg. Nonlinearity 61, 1 (1988).
M. V. Berry, S. Klein. J. Mod. Opt. 43, 2139 (1996).
M. V. Berry. J. Phys. A 29, 6617 (1996).
M. V. Berry. Phil. Trans. R. Soc. Lond. 360, 1023 (2002).
D. Bessis, J. S. Geronimo, P. Moussa. J. Stat. Phys. 34, 75 (1984).
W. A. Beyer, R. G. Schrandt in A. R. Benarek, F. Ulam, S. M. Ulam (eds.). Analogies between Analogies, University of California Press, Berkeley, 1990.
L. Bieberbach. Monatshefte Math. Physik. 48, 509 (1939).
H.-G. Bigalke, H. Wippermann. Regulare Parkettierungen (Mit Anwendungen in Kristallographie, Industrie, Baugewerbe, Design undKunst), BI, Mannheim, 1994.
M. Bill. Retrospektive, Skulpturen, Gemdlde, Graphik 1928–1987, ABC-Verlag, Zurich, 1987.
R. W. Billings. The Power of Form Applied to Geometric Tracery, William Blackwood and Sons, Edinburgh, 1851.
K. S. Birdi. Fractals in Chemistry, Geochemistry and Biophysics, Plenum Press, New York, 1977.
N. Blachman. Mathematica—A Practical Approach, Prentice-Hall, New York, 1992.
J. F. Blinn. IEEE Comput. Graphics Appl., n5, 78 (1989).
J. F. Blinn. IEEE Compu. Graphics Appl., n1l, 70 (1989).
J. F. Blinn. IEEE Comput. Graphics Appl. n2, 85 (2000).
K. Bobek. Einleitung in die Theorie der elliptischen Funktionen, Teubner, Leipzig, 1884.
A. I. Bobenko, T. Hoffmann. arXiv:math.CV/0005245 (2000).
F. P. Boca, C. Cobeli, A. Zaharescu. Commun. Math. Phys. 213, 433 (2000).
S. Boettcher, M. Paczuski. Phys. Rev. Lett. 84, 2144 (2000).
E. Bogomolny, C. Schmitt. Phys. Rev. Lett. 88, 114102 (2002).
C. F. Bohrer. Clouds in a Glass of Beer, Wiley, Chichester, 1987.
C. Boldrighini, M. Keane, F. Marchetti. Ann. Prob. 6, 532 (1978).
J. P. Boon. J. Stat. Phys., 102, 355 (2001).
V. A. Borovikov, B. Y. Kinber. Geometrical Theory of Diffraction, Institute of Electrical Engineering, London, 1994.
J. Borwein, M. H. Morales, K. Polthier, J. F. Rodrigues (eds.). Multimedia Tools for Communicating Mathematics, Springer-Verlag, Berlin, 2002.
R. A. Bosch. SIAM Rev. 41, 594 (1999).
U. Bottazzini in L. Tatsien (ed.). Proceedings of the International Congress of Mathematicians v. 3, Higher Education Press, Beijing, 2002.
H. Bottger. Principles of the Theory of Lattice Dynamics, Akademie-Verlag, Berlin, 1983.
N. Bourbaki. Elements de Mathematique IV Functions d’une variable reelle, Herman, Paris, 1960.
J. Bourgoin. Arabic Geometrical Pattern and Design, Dover, New York, 1973.
C. J. Bouwekamp, A. J. W. Duijvestijn. Perfect Squared Squares, EUT Report 92-WSK-03, Eindhoven, 1992.
A. Bovier, P. Picco. Ann. Prob. 21, 168 (1993).
R. L. Bowman. Comput. & Graphics 19, 157 (1995).
C. B. Boyer. The Rainbow: From Myth to Mathematics, Princeton University Press, Princeton, 1987.
C. Bracher. arXiv:cond-mat/0304241 (2003).
D. A. Brannan, M. E. Esplen, J. J. Gray. Geometry, Cambridge University Press, Cambridge, 1999.
O. Bratteli, P. E. T. Jorgensen. Iterated Function Systems and Permutation Representations of the Cuntz Algebra, American Mathematical Society, Providence, 1999.
E. Brieskorn, H. Knorrer. Plane Algebraic Curves, Birkhauser, Basel, 1986.
K. Briggs. Math. Comput. 57, 435 (1991).
S. Brodetsky. A First Course in Nomography, Bell and Sons, London, 1925.
S. A. Broughton, D. M. Haney, L. T. McKeough, B. S. Mayfield. New York J. Math. 6, 237 (2000).
S. A. Broughton. Am. Math. Monthly 107, 689, (2000).
J. W. Bruce, P. G. Giblin, C. G. Gibson. Am. Math. Monthly 88, 651 (1981).
J. W. Bruce, P. G. Giblin, C. G. Gibson. Topology 21, 179 (1982).
J. W. Bruce, P. G. Giblin, C. G. Gibson. Proc. Symposia Pure Math. 40 /1, 179 (1983).
J. W. Bruce, P. G. Giblin. Curves and Singularities, Cambridge University Press, Cambridge, 1984.
K. M. Brucks, J. Ringland, C. Tresser. arXiv:math.DS/9604230 (1996).
T. A. Brun, J. B. Hartle. arXiv:quant-ph/9905019 (1999).
L. Brutman, E. Passow. Constr. Approx. 13, 381 (1997).
P. Buchberger, H. Genz, H.-M. Staudenmaier. Fridericiana 47, 3 (1993).
H. Buchholz. Elektrische und magnetische Potentialfelder, Springer-Verlag, Berlin, 1957.
W. Burnside: Theory of Groups if Finite Order, Dover, New York, 1955.
A. M. Burns. Math. Mag 70, 196 (1996).
A. M. Burns. Coll. Math. J. 29, 230 (1998).
A. R. Butz. Comput. System Sci. 3, 128 (1969).
A. R. Butz. J. Math. Anal. Appl. 37, 351 (1972).
J. Caceres, A. Marquez. Comput. Geom. 23, 171 (2002).
J. W. Cannon, W. J. Floyd, R. Kenyon, W. R. Parry in S. Levy (eds.). Flavors of Geometry, Cambridge University Press, Cambridge, 1998.
F. Cap. Wie lost man Randwertprobleme in Physik und Technik, de Gruyter, Berlin, 1993.
J.-G. Caputo, J. Leon, A. Spire. arXivmlin.PS/0103009 (2001).
J. L. Casti. Reality Rules I, Wiley, New York, 1992.
R. Chacon, A. M. Garcfa-Hoz. Europhys. Lett. 57, 7 (2002).
F. Chamizo, A. Cordoba. Advances Math. 142, 335 (1999).
C. J. Chang, F. K. Hwang, P. E. Wright, J. R. Griggs. J. Combinat. Design 3, 169 (1995).
M. A. Chaudry, R. Schinzinger. Int. J. Comput. Math. Electr. Eng. II, 263 (1992).
D. Chavey. Comput. Math. Appl. 17, 147 (1989).
N. Chiba, K. Ohshida, K. Muraoka, M. Miura, N. Saito. Comput Graphics 18, 469 (1994).
D. V. Chistyakov. Theor. Math. Phys. 109, 1495 (1996).
D. V. Chistyakov. arXiv:math.DS/0302162 (2003).
B. Chopard, M. Droz. Cellular Automata Modeling of Physical Systems, Cambridge University Press, Cambridge, 1998.
W. G. Christian, A. G. Law, W. F. Martens, A. L. Mullikin, M. B. Sledd. Math. Phys. 17, 146 (1976).
A. H. Christie. Traditional Methods of Pattern Designing, Clarendon Press, Oxford, 1910.
K. W. Chung, H. S. Y. Chan. Comput. Graphics Forum 12, 33 (1993).
K. W. Chung, H. S. Y. Chan, B. N. Wang. Comput. Math. Appl. 31, n2, 33 (1996).
K. W. Chung, H. S. Y. Chan, B. N. Wang. Comput. Graphics 21, 523 (1997).
K. W. Chung, H. S. Y. Chan, B. N. Wang. Comput. Graphics 23, 527 (1998).
K. W. Chung, H. S. Y. Chan, B. N. Wang. Chaos, Solitons, Fractals 13, 1175 (2002).
B. Cipra, R. M. Hanson. A. Kolan. Phys. R.v. E 52, 2066 (1995).
D. S. Clark, E. R. Suryanarayan. Acta Cryst. A47, 498 (1991).
Comput. Math. Appl. 12, n. 1–2 (1986).
Comput. Math. Appl 17, n. 4–6 (1989).
J. P. Coleman, N. J. Myers. Math. Comput. 64, 181 (1995).
P. Collet, J.-P. Eckmann. Iterated Maps on the Interval as Dynamical Systems, Birkhauser, Basel, 1980.
J.-F. Colonna. Visual Comput. 11, 447 (1995).
J. L. Coolidge. A Treatise on Algebraic Plane Curves, Dover, New York, 1959.
S. N. Coppersmith. Am. J. Phys. 67, 52 (1999).
J. D. Corbit, D. J. Garbary. Comput. Graphics 17, 85 (1993).
S. Cornbleet. Microwave and Geometrical Optics, Academic Press, London, 1994.
Y. Couder in A. Carbone, M. Gromov, P. Prusinkiewicz (eds.). Pattern Formation in Biology, Vision and Dynamics, World Scientific, Singapore, 2000.
C. A. Coulson, A. Jeffrey. Waves: A Mathematical Approach to the Common Types of Wave Motion, Longman, London, 1977.
G. Cousineau. Theor. Comput. Sc. 281, 207 (2002).
H. S. M. Coxeter. Trans. Royal Soc. Can., LI, ser. III, 1 (1957).
H. S. M. Coxeter. Leonardo 12, 19 (1979).
H. S. M. Coxeter. Indag. Math. N. S. 4, 27 (1993).
A. Crisanti, G. Paladin, A. Vulpiani. Products of Random Matrices in Statistical Physics, Springer-Verlag, Berlin, 1992.
H. T. Croft, K. J. Falconer, R. K. Guy. Unsolved Problems in Geometry, Springer-Verlag, New York, 1991.
K. Culik H, S. Dube. Acta Inform. 30, 279 (1993).
M. R. Cullen. College J. Math. 21, 370 (1990).
H. M. Cundy, A. P. Rollett. Mathematical Models, Clarendon Press, Oxford, 1961.
F. Cunningham. Am. Math. Monthly 78, 114 (1971).
R. Dafner, D. Cohen-Or, Y. Matias. Comput. Graphics Forum 19, C-210 (2000).
A. Dalai, E. Schmutz. Electr. J. Combinatorics 9, R 26 (2002). http://www.combinatorics.org/Volume_9/Abstracts/v9ilr26.html
E. de Amo, I. Chitescu, M. D. Carillo, N. A. Secelean. J. Comput. Appl. Math. 151, 355 (2003).
L. Danzer, B. Griinbaum, G. C. Shepard. Am. Math. Monthly 89, 568 (1982).
L. R. da Silva, R. O. Vallejos, C. Tsallis, R. S. Mendes. Phys. R.v. E 64, 011104 (2001).
C. Da vies, B. Griinbaum, F. A. Sherk (eds.). The Geometric Vein: The Coxeter Festschrift, Springer-Verlag, Berlin, 1981.
P. J. Davies. Spirals: From Theodorus to Chaos, A K Peters, Wellesley, 1993.
P. J. Davis. Circulant Matrices, Wiley, New York, 1979.
M. Davison, C. Essex, C. Schulzky, A. Franz, K. H. Hoffmann. J. Phys. A 34, L289 (2001).
R. Dawkins. The Blind Watchmaker, Longman Scientific & Technical, Harlow, 1986.
L. F. Day. Pattern Design, Batsford, London, 1908.
C. De Boor, K. Hollig. Am. Math. Monthly 98, 793 (1991).
P. Diaconis, D. Freedman. SIAM Rev. 41, 3 (1999).
N. G. de Brujn. Math. Proc. A 84, 39 (1981).
N. G. de Bruijn. Indag. Math. N.S. 1, 291 (1990).
M. de Guzman. Differentiation of Integrals in IR, Springer-Verlag, Berlin, 1975.
M. de Guzman. Real Variable Methods in Fourier Analysis, North-Holland, Amsterdam, 1981.
M. de Guzman. L’Enseigm. Math. 29, 1 (1983).
P. Deift, T. Kriechbauer, S. Venakides. Pure Appl. Math. 48, 1187 (1995).
P. Deift, T. Kriechbauer, S. Venakides. Pure Appl. Math. 48, 1251 (1995).
F. M. Dekking. Nieuw Archief Wiskunde 28, 275 (1980).
J.-P. Delahaye. Geometric and Artistic Graphics Design Generation with Microcomputers, Macmillan, Houndsmills, 1986.
O. Delgado, D. Huson, E. Zamorzaeva. Geom. Dedicata 42, 43 (1992).
T. K. Delillo, A. R. Elcrat. J. Comput. Phys. 108, 199 (1993).
D. DeTemple, M. Hudelson. Am. Math. Monthly 108, 101 (2001).
K. Devlin. Mathematics: The Science of Patterns, Scientific American Library, New York, 1994.
L. Devroye. Methol. Comput. Appl. Prob. 3, 97 (2001).
A. K. Dewdney. Sci. Am., n6, 120 (1988).
A. K. Dewdney. Sci. Am., n2, 128 (1988).
A. K. Dewdney. The Magic Machine, Freeman, New York, 1990.
L. G. G. V. Dias da Silva, M. A. M. de Aguiar. Eur. J. Phys. B 16, 719 (2000).
R. Dickman, M. A. Munoz, A. Vespignani, S. Zapperi. arXiv:cond-mat/9910454 (1999).
R. Dixon. Mathographics, Basil Blackwell, Oxford, 1987.
M. d’Ocagne. Traite de Nomographic, Gauthier-Villars, Paris, 1921.
P. S. Dodds, D. H. Rothman. arXiv:physics/0005047 (2000).
P. S. Dodds, J. S. Weitz. arXiv:cond-mat/0111212 (2001).
S. Douady, Y. Couder. Phys. Rev. Lett. 68, 2098 (1992).
S. Douady, Y. Couder in J. M. Garcia-Ruiz, E. Louis, P. Meakin, L. M. Sander (eds.). Growth Patterns in Physical Sciences and Biology, Plenum Press, New York, 1993.
F. d’Ovidio, E. Mosekilde. Phys. Rev. E 61, 354 (2000).
W. Dreyer, M. Kunik. WIAS-Preprint 489 /1999 (1999). http://www.wias-berlin.de/wias_publ_preprints_nr489.AB
M. Drexler, M. J. Gander. SIAM Rev. 40, 315 (1998).
T. A. Driscoll, L. N. Trefethen. Schwarz-Christoffel Mapping, Cambridge University Press, Cambridge, 2002.
R. Drociuk. arXiv:math.GM/020125S (2002).
L. E. Dubins. Am. J. Math. 19, 497 (1957).
S. Dubuc in R. Liedl, L. Reich, G. Targonski (eds.). Iteration Theory and Its Functional Equations, Springer-Verlag, Berlin, 1985.
J. J. Duistermaat. Nieuw Archiv Wiskunde 9, 303 (1991).
D. Dunham in H. S. M. Coxeter, M. Emmer, R. Penrose, M. Teuber (eds.). M. C. Escher: Art and Science, North Holland, Amsterdam, 1986.
D. Dunham. Comput. Math. Appl. 12B, 139 (1986).
D. Dunham, J. Lindgram, D. Witte. ACM SIGGRAPH Comput. Graphics 15, 215 (1981).
D. Dunham. Notices Am. Math. Soc. 50, 452 (2003).
A. Edelman, E. Kostlan, M. Shub. J. Am. Math. Soc. 1, 247 (1994).
A. Edelman, E. Kostlan. Bull Am. Math. Soc. 32, 1 (1995).
H. Edelsbrunner. Algorithms in Combinatorical Geometry, Springer-Verlag, Berlin, 1987.
H. M. Edwards. Riemann’s Zeta Function, Academic Press, New York, 1974.
J. Ehlers, E. T. Newman. J. Math. Phys. 41, 3344 (2000).
U. Einmahl. Prob. Th. Relat. Fields 96, 97 (1993).
M. Eisenberg. Int. J. Comput. Math. Learning 7, 1 (2002).
P. Embrechts, C. M. Goldie in P. Mandl, M. Huskova (eds.). Asymptotic Statistics, Physica, Heidelberg, 1994.
A. Emch. Am. Math. Monthly, 34, 76 (1927).
Encyklopadie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Herausgegeben im Auftrage der Akademieen der Wissenschaften zu Gottingen, Leipzig, Miinchen und Wien, sowie unter Mitwirkung zahlreicher Fachgenossen, Teubner, Leipzig, 1898/1904–1904/35, v. 3.
J. Engelbrecht. Proc. Estonian Acad. Sci. Phys. Math. 42, 107 (1993).
N. Engheta. IEEE Antennas Prop. Mag. 39, n4, 35 (1997).
D. Eppstein. arXiv:cs.AI/0004003 (2000).
D. Epstein, C. Gunn. Not Knot, Jones and Bartlett, Boston, 1991.
J. M. Epstein, R. A. Hammond. Preprint Santa Fe Institute 01–08–043 (2001). http://www.santafe.edu/sfi/publications/Abstracts/01–08–043abs.html
J. M. Epstein, R. A. Hammond. Complexity 7, n4, 18 (2002).
J. G. Escudero. J. Phys. Soc. Jap. 65, 1977 (1996).
J. G. Escudero. Mod. Phys. Lett. B 11, 795 (1997).
J. G. Escudero, J. G. Garcia. Int. J. Mod. Phys. B 13, 363 (1999).
J. G. Escudero, J. G. Garcia. J. Phys. Soc. Jap. 70, 3511 (2001).
J. G. Escudero. Int. J. Mod. Phys. B 15, 1165 (2001).
J. G. Escudero, J. G. Garcia. Int. J. Mod. Phys. B 16, 1205 (2002).
M. D. Esposti, G. del Magno, M. Lend. Nonlinearity 13, 1275 (2000).
E. Esrafilian. Punjab Univ. J. Math. 28, 118 (1995).
K. Falconer. Fractal Geometry, Wiley, Chichester, 1990.
F. A. Farris. Math. Mag. 69, 185 (1996).
F. A. Farris, N. K. Rossing. Math. Mag. 72, 33 (1999).
R. W. Fathauer. Comput. Graphics 25, 323 (2001).
R. W. Fathauer. Comput. Graphics 26, 635 (2002).
T. H. Fay. Amer. Math. Monthly 96, 442 (1989).
R. P. Feinermann, D. J. Newman. Polynomial Approximation, Williams & Wilkins, Baltimore, 1974.
A. M. Ferenberg, D. P. Landau, Y. J. Wong. Phys. Rev. Lett. 69, 3382 (1992).
F. Fernandez. Coll Math. J. 29, 18 (1998).
P. Field. Am. J. Math. 27, 243 (1905).
M. Field, M. Golubitsky. Symmetry in Chaos, Oxford University Press, Oxford, 1992.
A. M. Filimonov, P. F. Kurchanov, A. D. Myshkis. Compt. Rend. 313, 961 (1991).
A. M. Filimonov, P. F. Kurchanov, A. D. Myshkis. Compt. Rend. 313, 961 (1992).
A. M. Filimonov, A. D. Myshkis in S. Elaydi, I. Gyori, G. Ladas (eds.). Advances in Difference Equations, Gordon and Breach, Australia, 1997.
P. A. Firby. IMA J. Appl. Math. 33, 303 (1984).
P. A. Firby. IMA J. Appl. Math. 45, 49 (1990).
B. Fisher. Am. Math. Monthly 80, 785 (1973).
J. Flachsmeyer, U. Feiste, K. Manteuffel. Mathematik und ornamentale Kunstformen, Teubner, Leipzig, 1990.
M. Fleury. Struct. Topol. n12, 20 (1986).
J. M. Floryan, C. Zemach. J. Comput. Phys. 72, 347 (1987).
J. D. Foley, A. van Dam, S. K. Feiner, J. F. Hughes. Computer Graphics: Principles and Practice, Addison Wesley, Reading, 1990.
G. Foltin. arXiv.nlin.CD/0302049 (2003).
P. J. Forrester, G. Honner. arXiv:cond-mat/9812388 (1998).
D. R. Fowler, P. Prusinkiewicz, J. Battjes. Comput. Graphics 26, 361 (1992).
M. Frame, T. Cogevina. Comput. Graphics 24, 797 (2000).
M. Frame, B. B. Mandelbrot. Fractals, Graphics, and Mathematical Education, Mathematical Association of America, Washington, 2002.
B. J. O. Franco, F. W. O. da Silva, E. C. Inacio. phys. stat. sol. (b) 195, 3 (1996).
A. B. Fraser. J. Opt. Soc. Am. 73, 1626 (1983).
R. Fricke. Lehrbuch der Algebra, v. II, Vieweg, Braunschweig, 1926.
A. Friedman, W. M. Miller, Jr. (eds.). Mathematics for Industrial Problems, v. 5, Springer-Verlag, New York, 1992.
H. Frisk, R. Arvieu. J. Phys. A 22, 1765 (1989).
K. Fuchigami in A. Wyzkowski, T. Dyduch, R. Gorska, L. Piekarski, L. Zakowska (eds.). Proc. 7th Int. Conf. Eng. Computer Graph. Desc. GeomCracow, 1996.
A. Fuchs, A. Joffe, J. Teugels. Th. Prob. Appl. 46, 243 (2002).
G. Gagliotti. The Dynamics of Ambiguity, Springer-Verlag, Berlin, 1992.
A. Gajardo, A. Moreira, E. Goles. Disc. Appl. Math. 117, 41 (2002).
D. Gale. Math. Intell. 15, n2, 55 (1993).
D. Gale, J. Propp, S. Sutherland, S. Troubetzkoy. Math. Intell 17, n3, 48 (1995).
P. K. Galenko, N. A. Zhuravlev. Physics of Dendrites, World Scientific, Singapore, 1994.
S. Gallot, D. Hulin, J. Lafontaine. Riemannian Geometry, Springer-Verlag, Berlin, 1990.
J. Garcia-Escudero, P. Kramer. J. P.ys. A 26, L 1029 (1993).
J. M. Garcia-Ruiz, E. Louis, P. Meakin, L. M. Sander (eds.). Growth Patterns in Physical Sciences and Biology, Plenum Press, New York, 1993.
M. Gardner. Wheels, Life and Other Mathematical Amusements, Freeman, New York, 1983.
M. Gardner. Mathematical Circus, Mathematical Association of America, Washington, 1992.
T. M. Garoni, N. E. Frankel. J. Math. Phys. 43, 5090 (2002).
D. Gaier. Konstruktive Methoden der konformen Abbildung, Springer-Verlag, Berlin, 1964.
X.-S. Gao, K. Jiang, C.-C. Zhu. Comput.-AidedDesign 34, 421 (2002).
P. Gaspard. Chaotic Scattering and Statistical Mechanics, Cambridge University Press, Cambridge, 1999.
E. GauBin, A. Beutelspacher, N. Henze, U. Kulisch, H. WuBing. Uberblicke Mathematik 1998, Vieweg, Braunschweig, 1998.
R. J. Gaylord, P. R. Wellin. Computer Simulations with Mathematica, Springer-Verlag, TELOS, Santa Clara, 1994.
M. J. Gazale. Gnonom, Princeton University Press, Princeton, 1999.
J.-P. Gazeau in R. V. Moody (ed.). The Mathematics of Long-Range Aperiodic Order, Kluwer, Dordrecht, 1997.
G. Gelbrich. Geom. Dedicata 51, 235 (1994).
J. E. Gentle. Random Number Generation and Monte Carlo Methods, Springer-Verlag, New York, 1998.
B. Georgeot, D. L. Shepelyansky. arXiv:quant-ph/0101004 (2001).
C. Georgiou, T. Hasanis, D. Koutroufiotis. Geom. Dedicata 28, 153 (1988).
J. Gerver. Am. J. Math. 92, 33 (1970).
P. J. Giblin, J. G. Kingston. Quart. J. Math Oxford 37, 17 (1986).
J. Gielis. Am. J. Botany 90, 333 (2003).
H. Giger. Comput. & Maths. Appl. 128, 329 (1986).
T. Gilbert, J. R. Dorfman, P. Gaspard. arXiv:nlin.CD/000700S (2000).
W. J. Gilbert. Canad. Math. Bull. 29, 495 (1986).
J. Gill. J. Comput. Appl. Math. 105, 299 (1999).
M. Giona in M. Dekking, J. L. Vehel, E. Lutton, C. Tricot (eds.). Fractals: Theory and Applications in Engineering, Springer-Verlag, London, 1999.
R. Girgensohn. Aequationes Mathematicae 46, 201 (1993).
R. Girgensohn. J. Math. Anal Appl 203, 127 (1996).
A. Glassner. IEEE Comput. Graphic. Appl. n6, 97 1997.
A. Glassner. IEEE Comput. Graphics Appl n4, p. 78 (1998).
A. Glassner. IEEE Comput. Graphics Appl 22, n6, 108 (2002).
A. Glassner. IEEE Comput. Graphics Appl 23, n1, 77 (2003).
A. Glassner. IEEE Comput. Graphics Appl 23, n2, 80 (2003).
S. Gluzman, D. Sornette. arXiv:cond-mat/0106316 (2001).
C. Godreche. J. Phys. A 22, L 1163 (1989).
C. Goderche. Phase Transitions 32, 45 (1991).
B. Goertzel. Appl Math. Lett. 12, 133 (1999).
D. Goffinet. Am. Math. Monthly 98, 249 (1991).
C. M. Goldie, R. Griibel. Adv. Appl Prob. 28, 252 (1996).
C. Goodman-Strauss. Am. Math. Monthly 108, 38 (2001).
P. J. Grabner, P. Kirschenhofer, H. Prodinger. J. Lond. Math. Soc. 57, 20 (1998).
P. Grassberger. Phys. Lett. A 181, 43 (1993).
T. Gray, J. Glynn. Exploring Mathematics with Mathematica, Addison-Wesley, Reading, 1990.
D. G. Green in T. R. J. Bossomaier, D. G. Green (eds.). Complex Systems, Cambridge University Press, Cambridge, 1994.
M. J. Greenberg. Euclidean and Non-Euclidean Geometry, Freeman, New York, 1993.
R. Greenler. Rainbows, Halos, and Glories, Cambridge University Press, Cambridge, 1980.
W. Greiner. Theoretische Physik, Bd: Mechanik 2, Harri Deutsch, Frankfurt am Main, 1982.
C. A. Griffith, M. L. Lapidus in S. I. Andersson, M. L. Lapidus (eds.). Progress in Inverse Spectral Geometry, Birkhauser, Basel, 1997.
H. B. Griffith, A. Oldknow. Mathematics of Models, Ellis Horwood, Chichester, 1993.
U. Grimm, M. Schreiber. arXiv:cond-mat/9903010 (1999).
G. Grimmett, D. Stirzaker. Probability and Random Processes, Clarendon Press, Oxford, 1982.
M. J. Groenberg. Euclidean and Non-Euclidean Geometries, Freeman, New York, 1993.
H. Groemer. Geometric Applications of Fourier Series, Cambridge University Press, Cambridge, 1996.
C. Grosche, F. Steiner. Handbook ofFeynman Path Integrals, Springer-Verlag, Heidelberg 1998.
E. Groller. Comput. Graphics 18, 739 (1994).
B. Griinbaum, G. C. Shepard. Tilings and Patterns, Freeman, New York, 1987.
B. Griinbaum, G. C. Shepard. Leonardo 25, 331 (1992).
B. Griinbaum. Geombinatorics 5, 24 (1995).
J. Guerreiro. Physica D 80, 356 (1995).
V. C. Gulyaev. arXiv.cond-mat/9903263 (1999).
C. Gunn in B. Falcidieno, I. Hermann, C. Pienori (eds.). Computer Graphics and Mathematics, Springer-Verlag, Berlin, 1992.
M. Gurgoze. Int. J. Math. Educ. Sci. Technol. 23, 493 (1992).
E. Gutkin. Physica D 19, 311 (1986).
E. Gutkin. J. Stat. Phys. 38, 7 (1996).
M. Gutowski. arXiv:math-ph/0106003 (2001).
F. A. Haight in J. C. Butcher (ed.). A Spectrum of Mathematics, Oxford University Press, Oxford, 1971.
E. Hairer, G. Wanner. Analysis by Its History, Springer-Verlag, New York, 1996.
L. Halbeisen, N. Hungerbuhler. SIAM Rev. 42, 657 (2000).
P. R. Halmos. Problems for Mathematicians-Young and Old, Mathematical Association of America, Washington, 1991.
K. G. Hamilton. Comput. Phys. Commun. 75, 105 (1993).
K. G. Hamilton. Comput. Phys. Commun. 78, 172 (1993).
K. G. Hamilton. Comput. Phys. Commun. 95, 127 (1995).
H. Hankin. Math. Gaz 18, 165 (1934).
R. Hanson in Workshop on Physics and Computation PhysComp 92, IEEE Computer Society Press, Los Alamitos, 1993.
L. Harthong. Adv. Appl. Math. 2, 24 (1981).
P. Hartman, F. A. Valentine. Duke Math. J. 26, 373 (1959).
M. Hasegawa in M. Tokuyama, H. E. Stanley (eds.). Statistical Physics, American Institute of Physics, Melville, 2000.
S. Hassani. Eur. J. Phys. 21, 41 (2000).
W. C. Hassenpflug. Comput. Math Appl. 33, 15, n12 (1997).
B. Hausmann, B. Slopianka, H.-P. Seidel in H.-C. Hege, K. Polthier (eds.). Visualization in Mathematics, Springer-Verlag, Berlin, 1997.
A. Hausner, D. P. Dobkin in J.-R. Sack, J. Urrutia (eds.). Handbook of Computational Geometry, Elsevier, Amsterdam, 2000.
D. A. Head. arXiv:cond-mat/9910201 (1999).
D. Hearn, M. P. Baker. Computer Graphics, Prentice-Hall, New York, 1994.
H.-C. Hege, K. Polthier (eds.). Visualization and Mathematics, Springer-Verlag, Berlin 1997.
W. D. Heiss, H. L. Harney. arXiv:quant-ph/0012093 (2000).
H. Hemme. Bild der Wissenschaft n5, 143 (1989).
D. Hennig, G. P. Tsironis. Phys. Rep. 307, 333 (1999).
K. Hentschel. Arch. Hist. Exact Sc. 4, 297 (2001).
E. Heppner. Annates Univ. Budapest 19, 41 (1976).
H. Herda. Fibon. Quart. 19, 437 (1981).
R. Herrmann, U. Preppernau. Elektronen im Kristall, Akademie-Verlag, Berlin, 1979.
F. Herzog, B. M. Stewart. Am. Math. Monthly 78, 487 (1972).
F. S. Hill, Jr. Computer Graphics, Macmillan, New York, 1990.
E. Hille. Analytic Function Theory, v. n, Chelsea, New York, 1973.
H. Hilton. Plane Algebraic Curves, Oxford University Press, London, 1932.
A. Hirose, K. E. Lonngren. Introduction to Wave Phenomena, Wiley, New York, 1985.
A. Hobson. J. Math. Phys. 16, 2210 (1975).
C. Holton, L. Q. Zamboni. Bull. Soc. Math. France 126, 149 (1998).
S. Homolya, C. F. Osborne, I. D. Svalbe. Phys. Rev. E 67, 026211 (2003).
K. Hormann, A. Agathos. Comput. Geom. 20, 131 (2001).
A. N. Horn in A. J. Crilly, R. A. Earnshaw, H. Jones (eds.). Fractals and Chaos, Springer-Verlag, New York, 1991.
T. Y. Hu, K. S. Lau. Trans. Am. Math. Soc. 35, 649 (1993).
I. Hueter, S. Bahar. SIAM J. Appl. Math. 60, 1824 (2000).
K. Hulek, C. Kahn, S. H. Weintraub. Moduli Spaces ofAbelian Surfaces: Compactification, Degenerations and Theta Functions, de Gruyter, Berlin, 1993.
J. Hungershofer, J.-M. Wierum in P. M. A. Sloot, C. J. K. Tan, J. J. Dongarra, A. G. Hoekstra (eds.). Computational Science—ICCS 2002, v. 3, Springer-Verlag, Berlin, 2002.
B. R. Hunt, T. Sauer, J. A. Yorke. Bull. Am. Math. Soc. 27, 217 (1992).
B. R. Hunt. Proc. Am. Math. Soc. 122, 711 (1994).
B. R. Hunt. Proc. Am. Math. Soc. 126, 791 (1998).
J. L. Hunt, B. G. Nickel, C. Gigault. Am. J. Phys. 68, 232 (2000).
K. H. Hunt. Kinematic Geometry of Mechanisms, Clarendon Press, Oxford, 1978.
J. E. Hutchinson in T. R. J. Bossomaier, D. G. Green (eds.). Complex Systems, Cambridge University Press, Cambridge, 2000.
E. Huttingerr (ed.). Max Bill, ABC, Zurich, 1978.
M. N. Huxley. Area, Lattics Points, and Exponential Sums, Clarendon Press, Oxford, 1996.
S. T. Hyde, S. Ramsden. Eur. J. Phys. B 31, 273 (2003).
A. J. Ijspeert in J.-C. Heudin (ed.). Virtual Worlds, Springer-Verlag, Berlin, 2000.
K. Ingersent, P. J. Steinhardt. Phys. Rev. Lett. 64, 2034 (1990).
K. Ingersent, J. E. S. Socolar in D.P. DiVincenzo, P. J. Steinhardt (eds.). Quasicrystals: The State of the Art, World Scientific, Singapore, 1991.
S. Ito. Tokyo J. Math. 12, 299 (1989).
S. Ito, M. Kimura. Jpn. J. Indust. Appl Math. 8, 461 (1991).
S. Ito, Y. Sano in C. Jia, K. Matsumoto (eds.). Analytic Number Theory, Kluwer, Dordrecht, 2002.
V. I. Ivanov, M. K. Trubetskov. Handbook ofConformal Mapping with Computer-Aided Visualization, CRC Press, Boca Raton, 1995.
D. Jackel, B. Walter. Comput. Graphics Forum 16, 201 (1997).
C. Jacob. Mathematica Edu. Res. 4, n3, 12 (1995).
J. D. Jackson. Phys. Rep. 320, 27 (1999).
S. Jaffard. Revista Math. Iberoamerican 12, 441 (1996).
D. L. Jaggard in J. L. Vehel, E. Lutton, C. Tricot (eds.). Fractals in Engineering, Springer-Verlag, London, 1997.
N. Jain, W. Pruitt. Z. Wahrscheinlichkeitsth. verw. Geb. 27, 141 (1973).
N. C. Jain, W. E. Pruitt. Ann. Prob. 3, 1046 (1975).
W. Jank. Mech. Mach. Th. 18, 237 (1983).
V. Jankovic. Mat. Vestnik 48, 47 (1996).
C. Janot. Quasicrystals: A Primer, Clarendon Press, Oxford, 1992.
V. Jarnfk. Math. Z. 24, 500 (1925).
R. V. Jean. Math. Biosc. 64, 1 (1983).
R. V. Jean. Phyllotaxis—A Systematic Study in Plant Morphogenesi, Cambridge University Press, Cambridge, 1994.
R. V. Jean, D. Barabe (eds.). Symmetry in Plants, World Scientific, Singapore, 1998.
R. J. Jeanin in I. Hargittai, C. A. Pickover (eds.). Spiral Symmetry, World Scientific, Singapore, 1992.
D. Jennings. Discrete Math. 138, 293 (1995).
C.-W. Joel. Berichte des Forschungszentrums Jülich 2570 (1992).
E. Johnson, C. R. Wylie. Am. Math. Monthly 68, 461 (1961).
G. A. Jones. Bull. London Math. Soc. 16, 241 (1984).
H. Jones. The Theory of Brillouin Zones and Electronic States in Crystals, North Holland, Amsterdam, 1975.
D. Jungnickel. Graphs, Networks and Algorithms, Springer-Verlag, Berlin, 1999.
B. Juraschek. Coll. J. Math. 25, 145 (1995).
J. Justicz, E. R. Scheinerman, P. M. Winkler. Am. Math. Monthly 97, 881 (1990).
J. A. Kaandorp. The Algorithmic Beauty of Seaweeds, Sponges, and Corals, Springer-Verlag, New York, 2001.
F. Kaderavek. Geometrie und Kunst infriiherere Zeit, Teubner, Stuttgart, 1992.
H. H. Kairies. Aeq. Math. 53, 207 (1997).
M. J. Kallaher (ed.). Revolutions in Differential Equations, Mathematical Association of America, New York, 1999.
A. Kameyama in Y. Takahashi (ed.). Algorithms, Fractal and Dynamics, Plenum Press, New York, 1995.
K. Kaneko, I. Tsuda. Complex Systems: Chaos and Beyond, Springer-Verlag, Berlin, 2001.
G. Kanizsa. Organization in Vision, Prageer, New York, 1979.
S. Kantor. Publicationes Math. 22, 7 (1975).
C. S. Kaplan, D. H. Salesin. Comput. Graphics Proc. SIGGRAPH 2000 499 (2000).
C. Kaplan. Visual Math. 2, n3, A4 (2000). http://members.tripod.com/vismath4/kaplan/index.html
J. Kappraff. Connections, McGraw-Hill, New York, 1991.
H. Katsuura. Am. Math. Monthly 98, 411 (1991).
A. Katz in M. Waldschmidt, P. Moussa, J.-M. Luck, C. Itzykson (eds.). From Number Theory to Physics, Springer-Verlag, Berlin, 1992.
H. Kautschitsch, W. Metzler (eds.). Anschauung als Anregung zum mathematischen Tun, Teubner, Stuttgart, 1984.
S. Kawamoto, T. Tsubata. J. Phys. Soc. Japan 66, 2209 (1997).
K. Keating, A. Vince. Discr. Comput. Geom. 21, 615 (1999).
H. Kern. Labyrinthe, Prestel, Munchen, 1983.
H. Kesten. d’ Anal. Math. 80, 183 (2000).
P. G. Kevrekidis, I. G. Kevrekidis, A. R. Bishop, E. S. Titi. Phys. Rev. E 65, 046613 (2002).
D. C. Khandakar, S. V. Lawande. Phys. Rep. 137, 115 (1986).
D. C. Khandakar, S. V. Lawande, K. V. Bhagwat. Path-Integral Methods and Their Applications, World Scientific, Singapore, 1993.
P. A. Kidwell in R. Calinger (ed.). Vita Mathematica, Mathematical Association of America, Washington, 1996.
H. G. Killingberg. normat 45, 167 (1997).
C. Kittel. Introduction to Solid State Physics, Wiley, New York, 1986.
A. Klarner (ed.). The Mathematical Gardner, Prindle, Weber & Schmidt, Boston, 1981.
F. Klein. Vorlesungen iiber die hypergeometrische Funktion, Springer-Verlag, Berlin, 1933.
F. Klein. Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree, Dover, New York, 1956, republished with commentaries by P. Slodowy, Birkhauser, Basel, 1993.
H. Kleinert. Path Integrals in Quantum Mechanics, Statistics and Polymer Physics, World Scientific, Singapore, 1990.
M. Klemm. Symmetrie von Ornamenten und Kristallen, Springer-Verlag, Berlin, 1982.
J. J. Kozak, V. Balakrishnan. Int. J. Bifurc. Chaos 12, 2379 (2002).
O. Knill. Elem. Math. 53, 89 (1998).
K. Knopp. Archiv Math. Physik 26, 103 (1917).
K. Knopp. Math. Z. 2, 1 (1918).
H. Kober. Dictionary of Conformal Representations, Dover, New York, 1952.
R. Kobes, H. Letkeman. arXiv.nlin.CD/0112010 (2001).
L. M. Kocic. FILOMAT 9, 207 (1995).
L. Kolasa, T. Wolff. Pacific J. Math. 190, 111 (1999).
V. S. Kolezkuk. J. Math. Sci. Ill, 3717 (2002).
D. G. Konig. Theory of Finite and Infinite Graphs, Birkhauser, Boston, 1990.
K. Kopitzki. Einftihrung in die Festkorperphysik, Teubner, Stuttgart, 1989.
P. Kramer, R. Neri. Acta Cryst. A 40, 580 (1984).
P. Kramer, Z. Papadopolos (eds.). Coverings of Discrete Quasiperiodic Sets, Springer-Verlag, Berlin, 2003.
K. W. Kratky. J. Phys. All, 1017 (1978).
A. Kreuzer, M. Kreuzer in A. Beutelspacher, N. Henze, U. Kulisch, H. WuBing (eds.). Uberblicke Mathematik 1996/97, Vieweg, Braunschweig, 1997.
S. Kreuzer in C. A. Pickover (ed.). The Pattern Book, World Scientific, Singapore, 1995.
H. N. Kritikos, D. L. Jaggard (eds.). Recent Advances in Electromagnetic Theory, Springer-Verlag, New York, 1992.
M. Krivelevich. arXiv:math-ph/0009032 (2000).
J. Kriz. Chaos und Struktur Systemtheorie, v. 1, Quitessenz-Verlag, Munchen, 1992.
H. Kroger. Phys. Rep. 323, 81 (2000).
M. Kucma. Functional Equations in a Single Variable, PWN, Warszawa, 1968.
E. Kuhnicke. Wave Motion 35, 1 (2002).
I. A. K. Kupka, M. M. Peixoto in M. W. Hirsch, J. E. Marsden, M. Shub (eds.). From Topology to Computation: Proceedings of the SMALEFEST, Springer-Verlag, Berlin, 1993.
P. K. Kythe. Computational Conformal Mapping, Birkhauser, Boston, 1998.
J. C. Lagarias, C. P. Tresser. IBM J. Res. Dev. 39, 283 (1995).
L. Lam, R. Pochy. Comput. Phys. 1, 534 (1993).
T. Lambert. Congressus Numerantium 38, 59 (1983).
R. H. Landau, M. J. Paez. Computational Physics, Wiley, New York, 1997.
H. Lang in H. Niedrig (ed.). Bergmann-Schafer Optik, de Gruyter, Berlin, 1993.
L. J. Lange in B. C. Berndt, F. Gesztesy (eds.). Continued Fractions: From Analytic Number Theory to Constructive Approximations, American Mathematical Society, Providence, 1999.
M. L. Lapidus, J. W. Neuberger, R. J. Renka, C. A. Griffith. Int. J. Bifurc. Chaos 6, 1185 (1996).
V. N. Lavrik, V. N. Savenkol. Sprabotschnik po konformnim otobraschenijam, Nauka, Kiev, 1900.
J. D. Lawrence. A Catalog of Special Plane Curves, Dover, New York, 1972.
P. Leath. Phys. Rev. B 14, 5056 (1976).
N. N. Lebedev, I. P. Skalskaya, Y. S. Uflyand. Worked Problems in Applied Mathematics, Dover, New York, 1965.
C. Le Caer, J. S. Ho. J. Phys. A 23, 3279 (1990).
C. Lee, X. Zhu, K. Gao. Nonlinearity 16, 25 (2003).
R. L. Lehany. Phys. Rev. E 52, 5610 (1995).
D. H. Lehmer, E. Lehmer. Am. Math. Monthly 86, 725 (1979).
J. Lehner. A Short Course in Automorphic Functions, Holt, Rinehart and Winston, New York, 1966.
D. S. Lemons, T. C. Lipscombe. Am. J. Phys. 70, 570 (2002).
A. Leutbecher. J. Reine Angew. Math. 228, 199 (1967).
D. Levine, P. J. Steinhardt. Phys. Rev. B 34, 596 (1986).
H. Levy, F. Lessman. Finite Difference Equations, Pitman, London, 1959.
S. Levy. Leonardo 25, 349 (1992).
S. Levy (ed.). The Eightfold Way, Cambridge University Press, Cambridge, 1999.
F. Leyvraz, M.-C. Firpo, S. Ruffo. arXiv:cond-mat/0204255 (2002).
W. Li, X. Cai. arXiv:cond-mat/9905239 (1999).
W. Li, X. Cai. arXiv:cond-mat/0005067 (2000).
S.-S. Liaw. Phys. Rev. E 57, 4589 (1998).
A. Lima-de-Faria. Evolution without Selection, Elsevier, Amsterdam, 1988.
A. Lindenmayer. Theor. Biol. 18, 280 (1968).
J. A. Lock. J. Opt. Soc. Am. A 5, 2032 (1988).
E. H. Lockwood. A Book of Curves, Cambridge University Press, Cambridge, 1963.
B. L. Loe, N. Beagley. Coll. Math. J. 28, 277 (1997).
A. L. Loeb. Concepts & Images, Birkhauser, Basel, 1993.
G. Loria. Spezielle algebraische und transzendente ebene Kurven, 2 vol., Teubner, Leipzig, 1910, 1911.
J. L. Louck. Am. J. Phys. 30, 585 (1962).
Z. Lucic, E. Molnar, M. Stojanovic. Period. Math. Hung. 29, 177 (1994).
J. M. Luck in H. van Beijeren, M. H. Ernst (eds.). Fundamental Problems in Statistical Mechanics VIII, Elsevier, Amsterdam, 1994.
P. Luckey. Nomography, Teubner, Stuttgart, 1954.
A. L. Mackay. Sov. Phys. Crystallogr. 26, 517 (1981).
A. L. Mackay. Physica A 114, 609 (1982).
J. Maeda. Maeda @ Media, Thames & Hudson, London, 2000.
R. Maeder. Programming in Mathematica, Addison-Wesley, Reading, 1991.
G. D. Mahan. Applied Mathematics, Kluwer, New York, 2002.
E. Mahovicky, M. Mahovicky. Jahrbuch Mineralogie, n2, 58 (1977).
E. Makovicky. Z. Kritallographie 150, 13 (1979).
K. S. Mamedov. Comput. & Math. Appl 12B, 511 (1986).
C. Mann. Am. Math. Monthly 109, 383 (2002).
D. E. Manolopoulos, M. S. Child. Phys. Rev. Lett. 82, 2223 (1999).
R. N. Mantegna. Phys. Rev. E 49, 4677 (1994).
G. Mantica, A. Sloan. Complex Systems 3, 37 (1989).
G. Mantica. Int. J. Int. Phys. C 4, 345 (1993).
A. I. Markushevich. Complex Numbers and Conformal Mappings, Pergamon Press, Oxford, 1962.
G. Martin. arXiv.math.NT/0206168 (2002).
G. E. Martin. Polyominoes, Mathematical Association of America, Washington, 1991.
E. N. Martinez. Am. J. Phys. 61, 1102 (1993).
Y. Martinez-Maure. Demonstratio Math. 34, 59 (2001).
S. Maslov. arXiv:adap-org/9601003 (1996).
P. R. Massopust. Z Anal. Anw. 12, 201 (1993).
P. R. Massopust. Fractal Functions, Fractal Surfaces, and Wavelets, Academic Press, San Diego, 1994.
W. H. Matthews. Mazes and Labyrinths, Longmans, Gree and Co., London, 1922.
R. D. Mauldin, M. Urbanski. Adv. Math. 136, 26, (1998).
M. W. McCall, A. Lakhtakia, W. S. Weiglhofer. Eur. J. Phys. 23, 353 (2002).
J. L. McCauley. Chaos, Dynamics and Fractals, Cambridge University Press, Cambridge, 1993.
J. McGregor, A. Watt. The Art of Graphics for the IBM PC, Addison-Wesley, Wokingham, 1986.
D. M. McKenna in R. K. Guy, R. E. Woodrow (eds.). The Lighter Side of Mathematics, Mathematical Association of America, Washington, 1991.
P. Meakin in C. Domb, J. L. Lebowitz (eds.). Phase Transitions and Phenomena, v. 12, Academic Press, New York, 1988.
P. Meakin. Phys. Rep. 235, 189 (1993).
P. Meakin, A. T. Skjeltop. Adv. Phys. 42, 1 (1993).
M. L. Mehta. Random Matrices, Academic Press, Boston, 1991.
R. Merks, A. Hoekstra, J. Kaandorp, P. Sloot in P. M. A. Sloot, C. J. K. Tan, J. J. Dongarra, A. G. Hoekstra (eds.). Computational Science—ICCS 2002, v. 1, Springer-Verlag, Berlin, 2002.
A. Messaoudi. Appl. Math. Lett. 15, 981 (2002).
W. Metzler. Math. Semesterberichte 40, 87 (1993).
K. O. Mikaelian. J. Phys. A 26, 1673 (1993).
T. Milliron, R. J. Jensen, R. Barzel. ACM Trans. Graphics 21, 20 (2002).
R. S. Millman, G. D. Parker. Geometry, Springer-Verlag, New York, 1991.
D. P. Minassian, J. W. Gaisser. Am. Math. Monthly 91, 254 (1984).
M. G. J. Minnaert. Light and Color in the Outdoor, Springer-Verlag, Berlin, 1993.
M. Y. Mitrofanov, O. A. Tarakanov. J. Math. Sc. 115, 2223 (2003).
U. Mohrlock, R. Liedl. Geol. Rundschau 85, 92 (1996).
D. M. Monro, F. Dudbridge. IEEE Comput. Graphics Appl n1, 32 (1995).
H. L. Montgomery. Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis, American Mathematical Society, Providence, 1994.
E. Montini. Nieuw Archief Wiskunde 14, 217 (1996).
R. V. Moody in B. Gruber (ed.). Symmetries in Science, Plenum Press, New York, 1995.
R. V. Moody in R. V. Moody (ed.). The Mathematics of Long-Range Aperiodic Order, Kluwer, Dordrecht, 1997.
A. Moreira, A. Gajardo, E. Goles. Complexity 6, n4, 46 (2001).
K. Morita in E. Goles, S. Martinez (ed.). Complex Systems, Kluwer, Dordrecht, 2001.
M. Mozes. J. Anal Math. 53, 139 (1989).
W. Mtiller. Publ I.R.M.A. Strasbourg, 413/S21, 91 (1990).
D. Mumford, C. Series, D. Wright. Indra’s Pearls, Cambridge University Press, Cambridge, 2002.
F. Munley. Am. J. Phys. 59, 1096 (1991).
S. Nagahiro, Y. Hayakawa. arXiv:cond-mat/0210314 (2002).
T. Nagatani. Phys. Rev. E 47, 63 (1993).
K. Nassau. The Physics and Chemistry of Color, Wiley, New York, 1993.
K. Nassau (eds.). Color for Science, Art and Technology, Elsevier, Amsterdam, 1998.
S. S. Negi, R. Ramaswamy. Pramana 56, 47 (2001).
Z. Nehari. Conformal Mapping, McGraw-Hill, New York, 1952.
J. Nelissen. Schriften zur Informatik und Angewandten Mathematik 150, Aachen, 1991.
E. Neumann, A. Pikovsky. Phys. Rev. E 64, 058201 (2001).
D. J. Newman. Mich. J. Math. 11, 11 (1964).
M. E. J. Newman, G. T. Barkema. Monte Carlo Methods in Statistical Physics, Clarendon Press, Oxford, 1999.
M. Newman. Computing in Science and Engineering. 2, n1, 80 (2000).
J. A. Nickel. Math. Comput. Model 21, 87 (1995).
Y. Nievergelt. Wavelets Made Easy, Birkhauser, Boston, 1999.
K.-P. Nischke, L. Danzer. Discr. Comput. Geom. 15, 221 (1996).
M. A. Nowak. Int. J. Bifurc. Chaos, 3, 35 (1993).
M. A. Nowak, R. M. May. Nature 359, 826 (1992).
T. Nowicki in J.-M. Gabaudo, P. Hubert, P. Tisseur, S. Vaienti (eds.). Dynamical Systems, World Scientific, Singapore, 2000.
H. M. Nussenzweig. Sci. Am. 236, 116 (1977).
H. M. Nussenzweig. J. Opt. Soc. Am. 69, 1068 (1979).
H. M. Nussenzveig. Diffraction Effects in Semiclassical Scattering, Cambridge University Press, Cambridge, 1992.
Y. Ohno, K. Ohyama. J. Recreat. Math. 23, 161 (1991).
Y. Ohno, K. Ohyama. J. Recreat. Math. 23, 247 (1991).
A. Okabe, B. Boots, K. Sugihara. Spatial Tessellations—Concepts and Applications ofVoronoi Diagrams, Wiley, Chichester, 1995.
T. Okada, T. Sekiguchi, Y. Shiota. J. Number Theory. 52, 256 (1995).
J. O’Rourke, O. Petrovici. Proceedings of the 13th Canadian Conference on Computational Geometry Waterloo, (2001). http://compgeo.math.uwaterloo.ca/~cccg01/proceedings/long/orourke-13443.ps.gz
J. A. L. Osborn. Leonardo 26, 289 (1993).
V. Ostromoukhov in R. D. Hersch, J. Andre, H. Brown (eds.). Electronic Publishing, Artistic Imaging, and Digital Typography, Springer-Verlag, Berlin, 1998.
E. Ott, T. Te’l. Chaos 3, 417 (1993).
M. Paczuski, S. Maslov, P. Bak. Phys. Rev. 53, 414 (1996).
M. Paczuski, P. Bak. arXiv:cond-mat/9906011 (1999).
R. S. Palais. Notices Am. Math. Soc. 46, 647 (1999).
R. Parades, J. L. Aragon, R. A. Barrio. Phys. R.v. B 58, 11990 (1998).
J. Paradis, P. Viader. J. Math. Anal Appl. 253, 107 (2001).
A. N. Pargellis. Physica D 98, 86 (1996).
A. N. Pargellis. Physica D 98, 111 (1996).
K. R. Parthasarathy. Math. Sci. 3, 137 (1978).
R. P. Patterson. Comput. Aided Geom. Design 5, 139 (1988).
D. Pedoe. The Gentle Art of Mathematics, MacMillan, New York, 1960.
H.-O. Peitgen, H. Jiirgens, D. Saupe. Fractals for the Classroom, Springer-Verlag, Berlin, 1992.
R. Penrose. The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics, Oxford University Press, Oxford, 1989.
R. Penrose in R. V. Moody (ed.). The Mathematics of Long-Range Aperiodic Order, Kluwer, Amsterdam, 1997.
E. Perstein. Math. Scientist 26, 13 (2001).
M. Peruggia. Discrete Iterated Function Systems, A. K. Peters, Wellesley, 1993.
C. S. Peskin, T. Schlick. Commun. Pure Appl Math. 42, 1001 (1989).
I. Peterson. Islands of Truth, Freeman, New York, 1990.
P. Pfeifer, M. Obert in D. Avair (ed.). The Fractal Approach to Heterogeneous Chemistry, Wiley, Chichester, 1992.
E. C. Phillips. Am. Math. Monthly 33, 361 (1926).
C. A. Pickover. J. Recreational Math. 21, 256 (1989).
C. A. Pickover. Visual Comput. 11, 309 (1995).
C. A. Pickover (ed.). The Pattern Book, World Scientific, Singapore, 1995.
C. A. Pickover, L. Rudolph. Comput. Graphics Forum 12, 41 (1993).
C. A. Pickover. Visual Comput. 13, 127 (1997).
C. A. Pickover. Chaos and Fractals, Elsevier, Amsterdam, 1998.
T. A. Pierce. Am. Math. Monthly. 36, 523 (1929).
S. N. Pnevmatikos in S. N. Pnevmatikos (ed.). Singularities and Dynamical Systems, Elsevier, Amsterdam, 1986.
A. L. Pokrovsky, A. L. Efros. arXiv:cond-mat/0207534 (2002).
G. Polya, G. Szego. Aufgaben und Lehrsatze aus der Analysis, Springer-Verlag, Berlin, 1970.
I. R. Porteous. Geometric Differentiation for the Intelligence of Curves and Surfaces, Cambridge University Press, Cambridge, 1994.
T. Poston, I. Stewart. Catastrophe Theory and Its Application, Pitman, London, 1978.
E. J. F. Primrose. Plane Algebraic Curves, MacMillan, New York, 1955.
P. Prusinkiewicz, A. Lindenmayer. The Algorithmic Beauty of Plants, Springer-Verlag, New York, 1990.
P. Prusinkiewicz, A. Lindenmayer, D. Fracchia in H.-O. Peitgen, J. M. Henriques, L. F. Penedo (eds.). Fractals in the Fundamental and Applied Sciences, Elsevier, Amsterdam, 1991.
P. Prusinkiewicz. Commun. ACM 43, n7, 85 (2000).
P. Prusinkiewicz, L. Mundermann, R. Karwowski, B. Lane. Comput. Graphics Proc. SIGGRAPH 2001 289 (2001).
J. E. Pulsifer, C. A. Reiter. Comput. & Graphics 20, 457 (1996).
E. Quaisser. Diskrete Geometrie, Spektrum Akademischer Verlag, Heidelberg, 1994.
C. Radin. Ann. Math. 130, 661 (1994).
C. Radin. Notices Am. Math. Soc. 42, 26 (1995).
C. Radin. Geom. Dedicata 55, 257 (1995).
O. Radulescu, T. Janssen. J. Math. Phys. 40, 1317 (1999).
T. Rage, V. Frette, G. Wagner, T. Walmann, K. Christensen, T. Sun. Eur. J. Phys. 17, 110 (1996).
F. Raidan, I. A. R. Moghrabi in D. Bainov (ed.). 9th Int. Coll. Diff. Equations, VSP, Utrecht, 1999.
A. Ramsay, R. D. Richtmeyer. Introduction to Hyperbolic Geometry, Springer-Verlag, New York, 1995.
J. Rangel-Mondragon, S. J. Abas. Comput. Graphics Forum 7, 29 (1988).
N. S. Rao, E. R. Suryanarayan. Physica B 193, 139 (1994).
V. Reiner. Quotients ofCoxeter Complexes and P-Partitions, American Mathematical Society, Providence, 1992.
J. G. Ratcliffe. Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, 1994.
S. Ree. J. Korean Phys. Soc. 41, L283 (2002).
K. Reinhardt. Jahresber. DMV, 44, 41 (1934).
M. W. Reinsch. arXiv:math-ph/9911024 (1999).
C. A. Reiter. Comput. & Graphics 5, 673 (1997).
C. A. Reiter. Chaos, Solitions Fractals 14, 937 (2002).
N. Richert. Am. Math. Monthly 99, 101 (1992).
M. Richter. Einfuhrung in die Farbmetrik, de Gruyter, Berlin, 1976.
R. Richter, C. A. Kruelle, A. Kittel, O. E. Rossler. Z. Naturf. a49, 871, (1994).
J. F. Rigby. Math. Intell. 20, 4 (1998).
F. Riesz, B. Sz.-Nagy. Functional Analysis, Dover, New York, 1990.
J. F. Rigby in M. Emmer (ed.). The Visual Mind: Art and Mathematics, MIT, Cambridge, 1993.
W. F. Rigge. Am. Math. Monthly 26, 332 (1919).
W. F. Rigge. Am. Math. Monthly 29, 6 (1922).
A. Robert. El. Math. 49, 111 (1994).
E. A. Robinson, Jr. Indag. Math. 10, 581 (1999).
R. M. Robinson. Inv. Math. 44, 259 (1978).
D. W. Robinson, G. T. Reid (eds.). Interferogram Analysis, Institute of Physics Publishing, Bristol, 1993.
R. A. Romer. arXiv:cond-mat/0106005 (2001).
G. Roepstorff. Pfadintegrale in der Quantenphysik, Vieweg, Wiebaden, 1992.
A. Roli, F. Zambonelli in S. Bandini, B. Chopard, M. Tomassini (eds.). Cellular Automata, Springer-Verlag, Berlin, 2002.
D. Romero. Bol. Soc. Mat. Mexicana 1, 87 (1995).
P. Rosenau. Phys. Rev. B 36, 5868 (1987).
F. Rothen, P. Pieranski, N. Rivier. Eur. J. Phys. 14, 227 (1993).
G. Rougeron, B. Peroche. Comput. Graphics Forum 17, 3 (1998).
D. R. Rowland, C. Pask. Am. J. Phys. 67, 378 (1999).
G. Rozenberg, A. Salomaa (eds.). Lindenmayer Sytems, Springer-Verlag, Berlin, 1992.
C. Runge. Graphical Methods, Columbia University Press, New York, 1912.
S. Russ, B. Sapoval. Phys. Rev. E 65, 036614 (2002).
P. J. Ryan. Euclidian and Non-euclidian Geometry: An Analytical Approach, Cambridge University Press, Cambridge, 1986.
G. Sadasiv, Y. Meng. Phys. Rev. E 027101 (2001).
J. F. Sadoc, J. Charvolin. Coll. de Phys. C7, n23, 319 (1990).
L. Sadun. arXiv.math.CG 9712263 (1997).
H. Sagan. Am. Math. Monthly 93, 361 (1986).
H. Sagan. J. Franklin Inst. 328, 419 (1991).
H. Sagan. Int. J. Math. Educ. Sci. Technol. 23, 403 (1992).
H. Sagan. Math. Intell. 15, 37 (1993).
H. Sagan. Int. J. Math. Educ. Sci. Technol 25, 869 (1994).
H. Sagan. Space-Filling Curves, Springer-Verlag, New York, 1994.
R. Salem. Trans. Am. Math. Soc. 53, 427 (1943).
L. C. F. Sallows. Math. Intell 14, 55 (1992).
L. C. F. Sallows, M. Gardner, R. K. Guy, D. Knuth. Math. Mag. 64, 315 (1991).
G. Salmon. Higher Plane Curves, G. B. Stechert & Co., New York, 1934.
H. E. Salzer, N. Levine. Math. Comput. 15, 120 (1976).
M. S. Santos, E. S. Rodrigues, P. M. C. de Oliveira. Am. J. Phys. 58, 923 (1990).
E. S. Sarin. Phys. Solid State 36, 348 (1994).
H. G. Schantz. IEEE Antennas Prop. 43, 50 (2001).
R. Schaper. Grafik mit Mathematica, Addison-Wesley, Bonn, 1994.
G. Scharf. From Electrostatics to Optics, Springer-Verlag, Berlin, 1994.
D. Schattschneider. Visions of Symmetry, Notebooks, Periodic Drawings and Related Work of M. C. Escher, Freeman, New York, 1990.
D. Schattschneider. Leonardo 25, 349 (1992).
D. Schattschneider, M. Emmer (eds.). M. C. Escher’s Legacy, Springer-Verlag, New York, 2003.
A. E. Scheidegger. Bull Int. Ass. Sci. Hydrology 12, 15 (1967).
F. Schipp, P. Simon, W. R. Wade. Walsh Series, IOP Publishing, Bristol, 1990.
R. Schinzinger, P. A. A. Laura. Conformal Mapping: Methods and Applications, Elsevier, Amsterdam, 1991.
J. Schmidhuber. Leonardo 30, 97 (1997).
H. Schmidt. Die Inversion und ihre Anwendungen, Oldenbourg, Mtinchen, 1950.
B. Schmittmann, R. K. P. Zia. arXiv: cond-mat/9905103 (1999).
I. J. Schoenberg. Bull Am. Math. Soc. 44, 519 (1938).
O. Schramm. Duke. Math. J. 86, 347 (1997).
K. A. Schroder. Victor Vasarely, Preste, Mtinchen, 1992.
L. S. Schulman. Techniques and Applications of Path Integration, Wiley, New York, 1981.
L. S. Schulman in H. A. Cerdeira, S. Lundquist, D. Mugnai, A. Ranfagni, V. Sa-yakanit, L. S. Schulman (eds.). Lectures on Path Integration: Trieste 1991, World Scientific, Singapore, 1993.
H. Schupp, H. Dabrock. Hdhere Kurven, BI, Mannheim, 1995.
W. Schuster. Math. Semesterber. 45, 77 (1998).
W. Schuster. Elem. Math. 53, 61 (1998).
C. J. Scriba, P. Schreiber. 500 Jahre Geometrie, Springer-Verlag, Berlin, 2001.
S. Seeger, A. Franz, C. Schulzky, K. H. Hoffmann. Comput. Phys. Commun. 134, 307 (2001).
A. K. Sen. Comput. Graphics 24, 471 (2000).
M. Senechal. The Mathematica Journal 4, n2, 10 (1994).
P. K. Sherard. Comput. Graphics 17, 175 (1993).
P. Sherman, J. C. Hart. Comput. Graphics 27, 143 (2003).
K. Sherrif. Comput. Graphics 17, 175 (1993).
Z. Shi, B. Toth. arXiv:math.PR/0006113 (2000).
E. V. Shikin. Handbook and Atlas of Curves, CRC Press, Boca Raton, 1995.
A. M. Shkel. Robot. Auton. Syst. 34, 179 (2001).
A. V. Shubnikov, V. A. Koptsik. Symmetry in Science and Art, Plenum Press, New York, 1974.
K. Simony. Theoretische Elektrotechnik, Deutscher Verlag der Wissenschaften, Berlin, 1977.
A. N. Singh in Squaring the Circle and Other Monographs, Chelsea, New York, 1953.
V. F. Sirvent. Theor. Comput. Sci. 180, 363 (1997).
F. Slanina, M. Kotrla. arXiv:cond-mat/0004401 (2000).
A. Smith. Proc. Am. Math. Soc. 34, 463 (1973).
C. S. Smith in D. W. Brisson (ed.). Hyper graphics, Westview Press, Boulder, 1978.
C. S. Smith. Leonardo 20, 373 (1987).
C. Smith, N. Blachman. The Mathematica Graphics Guidebook, Addison-Wesley, Redwood City, 1995.
K. Sneppen, P. Bak, H. Flyvbjerg, M. H. Jensen. Proc. Natl Acad. Sci. USA 92, 5209 (1995).
S. L. Snover, C. Waiveris, J. K. Williams. Discr. Math. 91, 193 (1991).
J. E. S. Socolar. Phys. Rev. B 39, 10519 (1989).
E. L. Somervell. A Rhythmic Approach to Mathematics, G. Philip, London, 1906.
J. C. Sprott. Comput. & Graphics 18, 417 (1994).
S. Stahl. The Poincare Half-Plane, Jones and Bartlett, Boston, 1993.
M. Stamer: in A. Beutelspacher, N. Henze, U. Kulisch, H. WuBing (eds.). Uberblicke Mathematik 1996/1997, Vieweg, Wiesbaden, 1997.
O. Steinbock, A. Toth, K. Showalter. Science 267, 868 (1995).
E. Steller in S. D. Chatterji, U. Kulisch, D. Laugwitz, R. Liedl, W. Purkert (eds.). Jahrbuch 1991 Uberblick Mathematik, Vieweg, Braunschweig, 1991.
E. Steller. Computer und Kunst, BI, Mannheim, 1992.
I. Stewart. Another Fine Math You’ve Got Me Into…, Freeman, New York, 1992.
I. Stewart. Sci. Am. n1, p. 96, (1995).
J. Stillwell. Geometry of Surfaces, Springer-Verlag, New York, 1992.
J. Stillwell. Sourcs of Hyperbolic Geometry, American Mathematical Society, 1996.
K. G. Suffern in R. A. Earnshaw, B. Wyvill (eds.). New Advances in Computer Graphics, Springer-Verlag, Tokyo, 1989.
D. C. Sun, Z. Y. Wen. C. R. Acad. Sci. Paris Serl: Math. 310, 135 (1993).
W. C. Swift. Am. Math. Monthly, 68, 653 (1961).
M. Sykes. A Source Book of Problems for Geometry, Allyn and Bacon, Boston, 1912.
S. Tabachnikov. Billiards, Societe Mathematique de France, Paris, 1995.
S. Tabachnikov. Geom. Dedicata 80, 217 (2000).
T. Takagi. Proc. Phys-Math. Jap. 1, 176 (1903).
R. F. Talbot. Math. Sci. 12, 117 (1987).
T. Tao. arXiv.math. CA/0008098 (2000).
T. Tao. Notices Am. Math. Soc. 48, 294 (2001).
F. G. Teixeira. Courbes Speciales Remarquables, Coimbre, 1907.
A. Terras. Harmonic Analysis on Symmetric Spaces and Applications I, Springer-Verlag, New York, 1985.
E. Teufl. Combinat., Prob. Comput. 12, 203 (2003).
S. Tezuka. Uniform Random Numbers: Theory And Practice, Kluwer, Boston, 1995.
L. T. Q. Thang. Discr. & Comput. Geom. 14, 31 (1995).
P. S. Theocaris. Moire Fringes in Strain Analysis, Pergamon Press, Oxford, 1969.
W. Thirring. A Course in Mathematical Physics, v. 4 Quantum Mechanics of Large Systems, Springer-Verlag, New York, 1983.
M. J. Thomson. Mitt. Math. Gesell. Hamburg 10, n8, 773 (1980).
W. P. Thurston. Am. Math. Monthly 97, 757 (1990).
W. P. Thurston. Three-Dimensional Geometry and Topology, v.l, Princeton University Press, Princeton, 1997.
V. M. Tkachuk, O. Voznyak. Phys. Lett. A 301, 177 (2002).
M. Toda. Theory of Nonlinear Lattices, Springer-Verlag, Berlin, 1981.
H. Topfer. Math. Ann. 117, 65 (1940).
L. N. Trefethen, T. A. Driscoll. ICM 1998, Documenta Mathematica (1998). http://www.mathematik.uni-bielefeld.de/documenta/xvol-icm/15/Trefethen.MAN.ps.gz
C. Tricot. Curves and Fractal Dimensions, Springer-Verlag, New York, 1995.
M. Trott. The Mathematica GuideBook for Programming, Springer-Verlag, New York, 2004.
M. Trott. The Mathematica GuideBook for Numerics, Springer-Verlag, New York, 2004.
M. Trott. The Mathematica GuideBook for Symbolics, Springer-Verlag, New York, 2004.
S. Troubetzkoy. Geom. Dedicata 80, 289 (2000).
J. C. Turner. Fibon. Quart. 41, 63 (2003).
K. Ueda in T. Lyche, L. L. Shumaker (eds.). Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, Nashville, 2001.
P. Ullrich. Results Math. 31, 245 (1997).
S. Ushiki in K. Shiraiwa (ed.). Proceedings of the International Conference on Dynamical Systems and Related Topics, World Scientific, Singapore, 1991.
Z. Usikin, S. G. Wayment. Math. Mag. 45, 37 (1972).
R. A. Usmani. Indian J. Math. 22, 23 (1980).
III A. Valleriani, J. L. Vega. J. Phys. A 32, 105 (1999).
H. van Baravalle. Geometrie als Sprache der Formen, Freies Geistesleben, Stuttgart, 1980.
H. C. van de Hulst. Light Scattering by Small Particles, Wiley, New York, 1957.
F. M. J. van der Linden. Math. Biosci. 100, 161 (1990).
B. L. van der Waerden. Math. Z. 32, 474 (1930).
I. Vattulainen, K. Kankaala, J. Saarinen, T. Ala-Nissila. Comput. Phys. Commun. 86, 209 (1995).
J. J. P Veerman, M. M. Peixoto, A. C. Rocha, S. Sutherland. arXiv:math.MG/9806l54 (1998).
D. Veljan. El. Math. 51, 156 (1996).
I. Vermes. Annates Univ. Scient. Budapest 17, 131 (1974).
P. Viader, J. Paradis. J. Number Theory 73, 212 (1998).
M. Vicsek, T. Vicsek. CWI Quart. 10, 153 (1997).
G. X. Viennot in M. Lothaire (ed.). Mots, Hermes, Paris, 1990.
A. Vince in M. Baake, R. V. Moody (eds.). Directions in Mathematical Quasicrystals, American Mathematical Society, Providence, 2000.
O. Y. Viro. Leningrad Math. J. 1, 1059 (1990).
G. M. Viswanathan, V. Afanasyev, S. V. Buldyrev, S. Havlin, M. G. E. da Luz, E. P. Rapaso, H. E. Stanley. Braz. J. Phys. 31, 102 (2001).
H. Voderberg. Jahresber. DMV 46, 229 (1936).
H. Voderberg. Jahresber. DMV 47, 159 (1937).
K. Volkert. Arch. Hist. Exact Sci. 37, 193 (1987).
W. von Koppenfels, F. Stallmann. Praxis der konformen Abbildung, Springer-Verlag, Berlin, 1959.
D. von Seggern. CRC Handbook of Mathematical Curves and Surfaces, CRC Press, Boca Raton, 1990.
D. von Seggern. Practical Handbook of Curve Design and Generation, CRC Press, Boca Raton, 1994.
Y. B. Vorobets. Russian Math. Surveys 51, 779 (1996).
H. Waadeland. Rocky Mount. J. Math. 21, 557 (1991).
S. Wagon. Mathematica in Action, Freeman, New York, 1991.
M. Walker. The Schwarz-Christojfel Transformation and Its Applications: A Simple Exposition, Dover, New York, 1964.
J. D. Walker. Am. J. Phys. 44, 421 (1976).
W. D. Walker. arXiv.physics/0001063 (2000).
M. Waldschmidt in M. Planat (ed.). Noise, Oscillators and Algebraic Randomness, Springer-Verlag, Berlin, 2000.
E. Weber. Electromagnetic Fields, v. 1, Wiley, New York, 1950.
J. Weber, J. Penn. Comput. Graphics, Proceedings SIGGGRAPH 95, 119 (1995).
J. Weeks. The Shape of Space, Marcel Dekker, New York, 1985.
G. Weisbuch, G. Deffuant, F. Amblard, J. P. Nadal. arXiv:cond-mat/0111494 (2001).
U. Weiss. Quantum Dissipative Systems, World Scientific, Singapore, 1993.
D. Wells. The Penguin Dictionary of Curious and Interesting Geometry, Penguin, London, 1991.
G. Wendt in S. Flugge (ed.). Handbuch der Physik Bd. 16, Springer-Verlag, Berlin, 1958.
D. H. Werner, S. Ganguly. IEEE Antenn. Prop. 45, 38 (2003).
P. B. Wiegmann, A. Zabrodin. arXiv:hep-th/9909/41 (1999).
H. Wieleitner. Spezielle ebene Kurven, Goschen, Leipzig, 1908.
U. Wilensky. Int. J. Comput. Math. Learning 5, 65 (2000).
J. B. Wilker. Trans. Am. Math. Soc. 250, 263 (1979).
L. Wilkinson. The Grammar of Graphics, Springer-Verlag, New York, 1999.
M. Wilkinson in I. V. Lerner, J. P. Keating, D. E. Khmelnitskii (eds.). Supersymmetry and Trace Formulae, Kluwer, New York, 1999.
A. T. Winfree. The Geometry of Biological Time, Springer-Verlag, New York, 1980.
W. Witschi. Comput. & Maths. Appl. 12B, 363 (1986).
W. A. Woyczynski in O. E. Barndorff-Nielsen, T. Mikosch, S. I. Resnick (eds.). Levy Processes, Birkhauser, Boston, 2002.
G. Wyszecki, W. S. Stiles. Color Science: Concepts and Methods, Wiley, New York, 1982.
Y. Xiong, D. Shi. Appl. Math. Mech. 22, 820 (2001).
Y. Xu. J. Austral Math. Soc. 66, 403 (1999).
M. J. Yacaman, M. Torres (eds.). Quasicrystals, North Holland, Amsterdam, 1993.
C. B. Yang, X. Cai. Eur. J. Phys. B 21, 109 (2001).
R. C. Yates. Am. Math. Monthly 66, 130 (1959).
K. Yoshida, S. Saito. arXiv:solv-int/0305001 (1998).
D. Yoshihara, F. Yura, T. Tokihiro. arXiv.nlin. SI/0208042 (2002).
F. Yura, T. Tokihiro. arXiv.nlin. SI/0112041 (2001).
W. Zakowicz. Phys. Rev. E 64, 066610 (2001).
G. M. Zaslavsky, R. Z. Sagdeev, D. A. Usikov, A. A. Chernikov. Weak Chaos and Quasi Regular Patterns, Cambridge University Press, Cambridge, 1991.
H. Zeitler. Math. Semesterber. 49, 185 (2002).
J. M. Ziman. Principles of the Theory of Solids, Cambridge University Press, Cambridge, 1964.
W. Zimmermann, S. Cunningham (eds.). Visualization in Teaching and Learning Mathematics, American Mathematical Society, 1991.
R. W. Ziolkowski, E. Heyman. Phys. Rev. E 64, 056625 (2001).
M. Znidaric, T. Prosen. arXiv.nlin. CD/0010036 (2000).
C. Zwikker. Advanced Plane Geometry, North-Holland, Amsterdam, 1950.
K. Zyczkowski. arXivmlin. CD/0210071 (2002).
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