Abstract
Double wall map OL systems (dwMOL systems) are used to simulate the development of botanical organisms. Dw maps grow by half-wall segment substitution and by insertion of new double structured walls. This insertion of division walls is investigated exhaustively by specification of all possible sets of segment productions. (1) The case of segment parity between complementary half-walls : maps are characterized by synchronous divisions of all regions (or cells). Such systems are able, e.g., to simulate the inception of leaves at the top of plant shoots. (2) There is no segment parity in every wall : we assume some "streching" by interaction between half-walls and recover the parity. It results in a finite alphabet and maps with non dividing but still growing cells. The construction of this alphabet and the corresponding production set is realized via an IL system which generates "oppositely running double strings". Derivations of this system become production rules for a dwMOL system. Such map systems simulate growing plant-bodies with cells which become mitotically inactive but continue to elongate, just as in real organisms.
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References
Rosenfeld, A. and J.P. Strong (1971) — A grammar for maps. In "Software Engineering", J. Tou, ed., Academic Press, New York, 2: 227–239.
Lindenmayer, A. and G. Rozenberg (1979) — Parallel generation of maps: Developmental systems for cell layers. In "Graph Grammars and their Application to Computer Science and Biology", V. Claus, H. Ehrig and G. Rozenberg, eds, Lect. Notes in Comp. Sc., Springer-Verlag Berlin, 73: 301–316.
Abbott, L.A. and A. Lindenmayer (1981) — Models for growth of clones in hexagonal cell arrangements: Applications in Drosophila wing disc epithelia and plant epidermal tissues. J. Theoret. Biol. 90: 495–514.
Siero, P.L.J., G. Rozenberg and A. Lindenmayer (1982) — Cell division patterns: Syntactical description and implementation. Computer Graphics and Image Processing 18: 329–346.
de Does, M. and A. Lindenmayer (1983) — Algorithms for the generation and drawing of maps representing cell clones. In "Graph Grammars and their Applications to Computer Science", H. Ehrig, M. Nagl and G. Rozenberg, eds, Lect. Notes in Comp. Sc., Springer-Verlag Berlin, 153: 39–57.
Nakamura, A., A. Lindenmayer and K. Aizawa (1986) — Some systems for map generation. In "The Book of L", G. Rozenberg and A. Salomaa, eds, Springer-Verlag Berlin: 323–332.
Lindenmayer, A. (1987) — Models for spatial orientation and temporal regulation of cell divisions in meristems. In "Biologie théorique", H.B. Lück, ed, Edition du C.N.R.S., Paris. 2: 177–195.
Lück, J. and H.B. Lück (1981) — Proposition d'une typologie de l'organisation cellulaire des tissues végétaux. In "Actes du ler Séminaire de l'Ecole de Biologie théorique du C.N.R.S.", H. Le Guyader and Th. Moulin, eds, E.N.S.T.A., Paris: 335–371.
Lück, J. and H.B. Lück (1982) — Sur la structure de l'organisation tissulaire et son incidence sur la morphogenèse. In "Actes du 2ème Séminaire de l'Ecole de Biologie théorique du C.N.R.S.", H. Le Guyader, ed, Univ. de Rouen: 385–397.
Lück, J. and H.B. Lück (1983) — Generation of 3-dimensional plant bodies by double wall map and stereomap systems. In "Graph Grammars and their Applications to Computer Science", H. Ehrig, M. Nagl and G. Rozenberg, eds, Lect. Notes in Comp. Sc., Springer-Verlag Berlin, 153: 219–231.
Lück, J. and H.B. Lück (1985) — Comparative plant morphogenesis founded on map and stereomap systems. In "Dynamical Systems and Cellular Automata", J. Demongeot, E. Goles and M. Tchuente, eds, Academic Press London: 111–121.
Lück, J. and H.B. Lück (1985) — Un mécanisme générateur d'hélices phyllotaxiques. In "Actes du 4ème Séminaire de l'Ecole de Biologie théorique", G. Benchetrit and J. Demongeot, eds, Edition du C.N.R.S., Paris: 317–330.
Lück H.B. and J. Lück (1986) — Unconventional leaves (an application of map OL systems to biology). In "The Book of L", G. Rozenberg and A. Salomaa, eds, Springer-Verlag Berlin: 275–289.
Lück, H.B. et J. Lück (1987) — From map systems to plant morphogenesis. Lect. Notes in Biomath., E. Teramoto and M. Yamaguti, eds, Springer-Verlag Berlin, in press.
Lück, J. and H.B. Lück (1987) — Vers une nouvelle théorie des méristèmes apicaux des végétaux. In "Biologie théorique", H.B. Lück, ed, Eition du C.N.R.S., Paris, 2: 197–213.
Lück, J., A. Lindenmayer and H.B. Lück (1987) — Models of cell tetrads and clones in meristematic cell layers. Bot. Gaz., to appear.
Prusinkiewicz, P. (1986) — Graphical applications of L-systems. Graphics Interface '86 — Vision Interface '86, Vancouver, CIPS: 247–253.
Barlow, P.W. (1987) — Cellular packets, cell division and morphogenesis in the primary root meristem of Zea mays L., New Phytol. 105: 27–56.
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Lück, J., Lück, H.B. (1987). From 0L and 1L map systems to indeterminate and determinate growth in plant morphogenesis. In: Ehrig, H., Nagl, M., Rozenberg, G., Rosenfeld, A. (eds) Graph-Grammars and Their Application to Computer Science. Graph Grammars 1986. Lecture Notes in Computer Science, vol 291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18771-5_66
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DOI: https://doi.org/10.1007/3-540-18771-5_66
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