The Book of L pp 29-43 | Cite as

# Planar Map Generation by Parallel Binary Fission/Fusion Grammars

## Abstract

A new class of formal grammatical systems, based upon simultaneous (parallel) rewriting of symbols in strings, was introduced by A. Lindenmayer [1], intended as a theoretical model for development of filamentous biological organisms, e.g., by cell-division. Lindenmayer’s contributions have stimulated widespread interest and research in theoretical models for parallel generation in computer science as well as in biology. Initial advances pertained to string-based systems, i.e., linear or one-dimensional structures, but were followed by numerous proposals for addressing the difficult problem of generalization to nonlinear systems, capable of modeling development in two- or three-dimensional organisms or complex data structures. Some references to multi-dimensional or graph generation are given here [2,3,4,6,7,8,9,10,12,13,14,17], with emphasis on those relating to parallel generation, but space permits us only limited coverage, which may be augmented by consulting a recent comprehensive bibliography [16].

### Keywords

Expense Bors Paral## Preview

Unable to display preview. Download preview PDF.

### References

- [1]A. Lindenmayer, “Mathematical models for cellular interactions in development, Part I, Part II,”
*Journal of Theoretical Biology*18, pp. 280–299, 300-315 (1968).CrossRefGoogle Scholar - [2]A. R. Smith, “Two dimensional formal languages and pattern recognition by cellular automata,” pp. 144–152 in
*IEEE Conference Record of the 12th Annual Symposium on Switching and Automata Theory*(1971).Google Scholar - [3]A. Rosenfeld, “Array grammar normal forms,”
*Information and Control*23, pp. 173–182 (1973).MathSciNetMATHCrossRefGoogle Scholar - [4]J. W. Carlyle, S. Greibach, and A. Paz, “A two-dimensional generating system modeling growth by binary cell division,” pp. 1–12 in
*IEEE Conference Record of the 15th Annual Symposium on Switching and Automata Theory*(1974).Google Scholar - [5]O. K. Wilby and D. A. Ede, “A model generating the pattern of skeletal elements in the embryonic chick limb,” pp. 81–90 in
*Proceedings of the 1974 Conference on Biologically Motivated Automata Theory*, IEEE Computer Society (1974).Google Scholar - [6]G. Stiny,
*Pictorial and Formal Aspects of Shape and Shape Grammars*, Birkhauser Verlag, Basel (1975).Google Scholar - [7]B. Mayoh, “Another model for the development of multidimensional organisms,” pp. 469–485 in
*Automata, Languages, Development*, ed. A. Lindenmayer, North-Holland (1976).Google Scholar - [8]K. Culik II and A. Lindenmayer, “Parallel graph generating and graph recurrence systems for multicellular development,”
*Int. J. General Systems*3, pp. 53–66 (1976).MathSciNetMATHCrossRefGoogle Scholar - [9]H. Ehrig and G. Rozenberg, “Some definitional suggestions for parallel graph grammars,” pp. 443–468 in
*Automata, Languages, Development*, ed. A. Lindenmayer, North-Holland (1976).Google Scholar - [10]A. Paz, “Multidimensional parallel rewriting systems,” in
*Automata, Languages, Development*, ed. A. Lindenmayer, North-Holland (1976).Google Scholar - [11]S. Even,
*Graph Algorithms*, Computer Science Press, Potomac, MD (1979).MATHGoogle Scholar - [12]A. Lindenmayer and G. Rozenberg, “Parallel generation of maps: Developmental systems for cell layers,” pp. 301–316 in
*Graph-Grammars and Their Application to Computer Science and Biology*, ed. V. Claus, Springer-Verlag, Berlin (1979).CrossRefGoogle Scholar - [13]A. Paz and Y. Raz, “Complexity of pattern generation by MAP-L systems,” pp. 367–378 in
*Graph-Grammars and Their Application to Computer Science and Biology*, ed. V. Claus, Springer-Verlag, Berlin (1979).CrossRefGoogle Scholar - [14]M. de Does and A. Lindenmayer, “Algorithms for the generation and drawing of maps representing cell clones,” pp. 39–57 in
*Graph-Grammars and Their Application to Computer Science (2nd International Workshop)*, ed. H. Ehrig, Springer-Verlag, Berlin (1983).CrossRefGoogle Scholar - [15]J. W. Carlyle, S. Greibach, and A. Paz, “Matching and spanning in certain planar graphs,”
*Math. Systems Theory*16, pp. 159–183 (1983).MathSciNetMATHCrossRefGoogle Scholar - [16]M. Nagl, “Bibliography on graph rewriting systems (graph-grammars),” pp. 415–448 in
*Graph-Grammars and Their Application to Computer Science (2nd International Workshop)*,ed. H. Ehrig, Springer-Verlag, Berlin (1983).CrossRefGoogle Scholar - [17]A. Paz, “Geometry versus topology in map grammars,” pp. 288–296 in
*Graph-Grammars and Their Application to Computer Science (2nd International Workshop)*,ed. H. Ehrig, Springer-Verlag, Berlin (1983).CrossRefGoogle Scholar - [18]J. Carlyle, S. Greibach, and A. Paz, “Complexity of pattern generation via parallel binary fission/fusion grammars,” Tech. Rep. (in preparation) UCLA Computer Science, Los Angeles, (1985).Google Scholar