Fractals, dimension, and formal languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 28 (1994) no. 3-4, pp. 361-386.
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     author = {Merzenich, W. and Staiger, L.},
     title = {Fractals, dimension, and formal languages},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {361--386},
     publisher = {EDP-Sciences},
     volume = {28},
     number = {3-4},
     year = {1994},
     mrnumber = {1282453},
     zbl = {0883.68078},
     language = {en},
     url = {http://archive.numdam.org/item/ITA_1994__28_3-4_361_0/}
}
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Merzenich, W.; Staiger, L. Fractals, dimension, and formal languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 28 (1994) no. 3-4, pp. 361-386. http://archive.numdam.org/item/ITA_1994__28_3-4_361_0/

[Ba88] C. Bandt, Self-similar sets 4: Topology and measure, in Proc. Conf. Topology and Measure V, Wiss. Beitr. Ernst-Mortiz-Arndt-Univ., Greifswald, 1988, pp. 8-16. | MR | Zbl

[Ba89] C. Bandt, Self-similar sets 3: Constructions with sofic Systems, Mh. Math., 1989, 108, pp. 89-102. | EuDML | MR | Zbl

[By88] M. R. Barnsley, Fractals Everywhere, Academic Press, Orlando, 1988. | MR | Zbl

[BM89] J. Berstel and M. Morcrette, Compact representations of patterns by finite automata, in Proc. Pixim'89, Hermes, Paris, 1989, pp. 387-402.

[BN80] L. Boasson and M. Nivat, Adherences of languages, J. Comput. System Sci., 1980, 20, 3, pp. 285-309. | MR | Zbl

[BN89] J. Berstel and A. Nait-Abdallah, Tétrarbres engendrés par des automates finis, in Journées AFCET-GROPLAN, no. 61-62, Bigre + Globule, 1989, pp. 167-175.

[CD90/93] K. Culik Ii and S. Dube, Rational and affine expressions for image description, Discrete Appl. Math., 1993, 41, pp. 85-120. | MR | Zbl

Preliminary version: Affine automata and related techniques for generation of complex images, in: Mathematical Foundations of Computer Science, 1990, Proc. Intern. Conf., Lect Notes Comput. Sci., No. 452, Springer-Verlag, Berlin, 1990, pp. 224-231. | Zbl

[CD90] K. Culik Ii and S. Dube, Automata-theoretic techniques for image generation and compression, in Proc. of FST-TCS 1990, Lect. Notes Comput. Sci., No.472, Springer-Verlag, Berlin, 1990, pp. 76-90. | MR | Zbl

[CD93] K. Culik Ii and S. Dube, Encoding images as words and languages, Intern. J. Algebra and Computation, 1993, 3, 2, pp. 211-236. | MR | Zbl

[Da64] M. Davis, Infinitary games of perfect information, in Advances in Game Theory, Princeton Univ. Press, Princeton N. J., 1964, pp. 89-101. | MR | Zbl

[Fa85] K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, Cambridge, 1985. | MR | Zbl

[Fe93] H. Fernau, Variaten iterierter Funktionensysterne und Methoden der Formalen Sprachen, Diss., Univ. Karlsruhe, 1993.

[Ga58] F. R. Gantmacher, Matrizenrechnung II, Deutscher Verlag der Wissenschaften, Berlin, 1958. | MR

[HKT93] A. Habel, H.-J. Kreowski and S. Taubenberger, Collages and patterns generated by hyperedge replacement, Languages of Design, 1993, 1, 2, pp. 125-145.

[HPS92] F. Von Haeseler, H.-O. Peitgen and G. Skordev, On the fractal structure of rescaled evolution sets of cellular automata and attractors of dynamical systems, Report Nr. 278, Inst. dynam. Systeme, Univ. Bremen, 1992.

[Ku70] W. Kuich, On the entropy of context-free languages, Inform. Control., 1970, 16, 2, pp. 173-200. | MR | Zbl

[La69] P. Lankaster, Theory of Matrices, Academic Press, New York, 1969. | MR | Zbl

[LS77] R. Lindner and L. Staiger, Algebraische Codierungstheorie - Theorie der sequentiellen Codierungen, Akademie-Verlag, Berlin, 1977. | MR | Zbl

[Ma77] B. B. Mandelbrot, Fractals, Form, Chance, and Dimension, Freeman, San Francisco, 1977. | MR | Zbl

[MW88] R. D. Mauldin and S. C. Williams, Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc., 1988, 309, 2, pp. 811-829. | MR | Zbl

[PS88] H.-O. Peugen and D. Saupe, The Science of Fractal Images, Springer-Verlag, New York, 1988. | MR

[PLH88] P. Prusinkiewicz, A. Lindenmayer and J. Hanan, Developmental models for herbaceous plants for computer imagery purposes, Computer Graphics, 1988, 22, 4, pp. 141-150.

[Sm84] A. R. Smith Iii, Plants, fractals, and formal languages, Computer Graphics, 1984, 18, 3, pp. 1-10.

[St83] L. Staiger, Finite-state ω-languages, J. Comput System Sci., 1983, 27, 3, pp. 434-448. | MR | Zbl

[St85] L. Staiger, The entropy of finite-state ω-languages, Problems Control Inform. Theory, 1985, 14, 5, pp. 383-392. | MR | Zbl

[St87] L. Staiger, Research in the Theory of ω-languages, J. Inf. Process. Cybern. EIK, 1987, 23, pp. 415-439. | MR | Zbl

[St85/89] L. Staiger, Combinatorial properties of the Hausdorff dimension, J. Statist. Plann. Inference, 1989, 23, pp. 95-100. Preliminary version in "GEOBILD'85" Proc. of the 2nd Workshop on Geometrical Problems of Image Processing, Wissenschaftliche Beiträge, Friedrich-Schiller-Univ., Jena, 1985, pp. 43-48. | MR | Zbl

[St89] L. Staiger, Quadtrees and the Hausdorff dimension of pictures, in: "GEOBILD'89" Proc. of the 4th Workshop on Geometrical Problems of Image Processing, Mathematical Research, No. 51,Akademie-Verlag, Berlin, 1989, pp. 173-178. | MR | Zbl

[St89/93] L. Staiger, Kolmogorov complexity and Hausdorff dimension, Inform. and Comput., 1993, 103, 2, pp. 159-194. Preliminary version in: "Fundamentals of Computation Theory" Proc. Intern. Conf., Lecture Notes in Comput. Sci., No. 380, Springer-Verlag, Berlin, 1989, pp. 334-343. | MR | Zbl

[SW74] L. Staiger and K. Wagner, Automatentheoretische und automatenfreie Charakterisierungen topologischer Klassen regulärer Folgenmengen, Elektron. Informationsverarb. Kybernet EIK, 1974, 10, pp. 379-392. | MR | Zbl