## $$L$$-systems and mutually recursive function systems.(English)Zbl 0790.68056

The authors investigate the relationships between two different approaches to generate fractal images – $$L$$-systems and Mutually Recursive Function Systems (MRFS). Two different ways in which $$L$$- systems have been used to generate images are considered. The first is the well-known turtle geometry method, and the other is the vector interpretation method as used by Dedekind. It is shown that a uniformly growing D0L-systems can be simulated by an MRFS, and any D0L-system can be simulated by an MRFS with a control set produced by an iterative GSM.

### MSC:

 68Q45 Formal languages and automata 68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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### References:

 [1] Barnsley, M.F.: Fractals everywhere. New York: Academic Press 1988 · Zbl 0691.58001 [2] Barnsley, M.F., Jacquin, A., Reuter, L., Sloan, A.D.: Harnessing chaos for image synthesis. Computer Graphics, SIGGRAPH 1988 Conference Proceedings [3] Barnsley, M.F., Elton, J.H., Hardin, D.P.: Recurrent iterated function systems. Construct. Approx.5, 3-31 (1989) · Zbl 0659.60045 [4] Barnsley, M.F., Devaney, R.L., Mandelbrot, B.B., Peitgen, H-O., De Saupe, Voss, R.F.: Science of fractal images. Berlin Heidelberg New York: Springer 1988 · Zbl 0683.58003 [5] Culik K. II, Dube, S.: Affine automata and related techniques for generation of complex images, Theor. Comput. Sci. Preliminary version in Proceedings of MFCS’1990 (Lect. Notes Comput. Sci., vol. 452, pp. 224-231) Berlin Heidelberg New York: Springer 1990 · Zbl 0779.68062 [6] Culik, K. II, Dube, S.: Rational and affine expressions for image Discrete Appl. Math. (to appear). Preliminary version: Automata-Theoretic Techniques for Image Generation and Compression, Proceedings of FST-TCS’1990 (Lect. Notes Comput. Sci., vol. 472, pp. 76-90). Berlin Heidelberg New York: Springer 1990 · Zbl 0733.68098 [7] Culik, K. II, Dube, S.: Balancing order and chaos in image generation. Comput. and Graphics (to appear) Preliminary version in Proceedings of ICALP’91 (Lect. Notes Comput. Sci., vol. 510, pp. 600-614) Berlin Heidelberg New York: Springer 1991 · Zbl 0769.68120 [8] Dekking, F.M.: Recurrent sets. Adv. Math.44, 78-104 (1982) · Zbl 0495.51017 [9] Dekking, F.M.: Recurrent sets: A fractal formalism. Report 82-32, Delft University of Technology, 1982 · Zbl 0495.51017 [10] Frijters, D., Lindenmayer, A.: A model for the growth and flowering ofAster novae-angliae on the basis of table (1, 0) L-systems. In: Rozenberg, G., Salomaa, A. (eds.) L-Systems. (Lect. Notes Comput. Sci., vol. 15, pp. 24-52) Berlin Heidelberg New York: Springer 1974 · Zbl 0293.92007 [11] Giessmann, E.G.: Generation of fractal curves by generalizations of Lindemayer’s L-systems. Proceedings of FRACTAL’90, Plymouth State College, New Hampshire 1990 [12] Hogeweg, P., Hesper, B.: A model study on biomorphological description. Pattern Recogn.6, 165-179 (1974) [13] Lindenmayer, A.: Mathematical models for cellular interaction in development, Parts I & II. J. Theor. Biol.18, 280-315 (1968) [14] Mandelbrot, B.: The fractal geometry of nature. San Francisco: W.H. Freeman 1982 · Zbl 0504.28001 [15] Prusinkiewicz, P.: Applications of L-systems to computer imagery. In: Ehrig, H., Nagl, M., Rosenfeld, A., Rozenberg, G. (eds.) Graph grammars and their application to computer science. (Lect. Notes Comput. Sci., vol. 291, pp. 534-548) Berlin Heidelberg New York: Springer 1987 [16] Prusinkiewicz, P.: Graphical applications of L-systems. Proceedings of graphics interface’86-Vision Interface’86, pp. 247-253 (1986) [17] Prusinkiewicz, P., Lindenmayer, A.: The algorithmic beauty of plants. Berlin Heidelberg New York: Springer 1990 · Zbl 0850.92038 [18] Shallit, J., Stolfi, J.: Two methods for generating fractals. Comput. and Graphics13, 185-191 (1989) [19] Smith, A.R.: Plants, fractals, and formal languages. Computer Graphics18, 1-10 (1984) [20] Szilard, A.L., Quinton, R.E.: An interpretation for D0L systems by computer graphics. Sci. Terrapin4, 8-13 (1979)
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