A Graphical method for generating fractals

Document Type : Research Paper

Author

Amirkabir University of Technology

Abstract

This research focuses on introducing the theory of L-systems (Lindenmayer systems), initially designed to model the behavior of multicellular plants. However, it has evolved into a successful tool for simulating the growth processes of plants and trees with the design of graphical interpreters. Beginning with the introduction of various types of grammars, the study explores the structure and position of L-systems in formal language theory. By introducing a turtle graphics interpreter, one can convert the output strings from L-system grammars into concise commands for generating fractal curves and nearly natural images of plants and trees. In general, a key feature of L-system theory is the parallel and simultaneous execution of rules on variables, leading to broad applications in evolutionary biology and various areas of theoretical computer science.

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References

[1] M. Delkhosh, Introduction to Fractals and Fractal Dimensions, Mathematics and society, 2 (2017) 1-23.
[2] D. P. Feldman, Chaos and Fractals, An Elementary Introduction, Oxford University Press, Oxford, 2012.
[3] A. Lindenmayer, Mathematical models for cellular interaction in development, Parts I and II, Journal of Theoretical Biology, 18 (1968) 280–315.
[4] A. Lindenmayer, Developmental systems without cellular interaction, their languages and grammars, Journal of Theoretical Biology, 2 (1971) 455–484.
[5] P. Linz, An Introduction to Formal Languages and Automata, Fourth ed, Jones and Bratlett Publishers, Boston, 2008.
[6] B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, 1982.
[7] S. Manousakis, Musical L-Systems, MS. thesis, The Royal Conservatory of The Hague, June 2006.
[8] P. Prusinkiewicz, Graphical applications of L-systems, In Proceedings of Graphics Interface ’86 — Vision Interface’, 86 (1986) 247–253.
[9] P. Prusinkiewicz, Applications of L-systems to computer imagery, In H. Ehrig, M. Nagl, A. Rosenfeld, and G. Rozenberg, editors, Graph grammars and their application to computer science; Third International Workshop, 534–548, Springer-Verlag, Berlin, 1987, Lecture Notes in Computer Science 291.
[10] P. Prusinkiewicz and J. Hanan, Lindenmayer Systems, Fractals, and Plants, Springer-Verlag, Berlin, 1989.
[11] P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, Springer-Verlag, New York, 1990.
[12] G. Rozenberg and A. Salomaa, Lindenmayer Systems Impacts on Theoretical Computer Science, Computer Graphics, and De-velopmental Biology, Springer-Verlag, Berlin, 1992.
[13] Examples from: http://en.wikipedia.org/wiki/L-system, 2016.
[2] D. P. Feldman, Chaos and Fractals, An Elementary Introduction, Oxford University Press, Oxford, 2012.
[3] A. Lindenmayer, Mathematical models for cellular interaction in development, Parts I and II, Journal of Theoretical Biology, 18 (1968) 280–315.
[4] A. Lindenmayer, Developmental systems without cellular interaction, their languages and grammars, Journal of Theoretical Biology, 2 (1971) 455–484.
[5] P. Linz, An Introduction to Formal Languages and Automata, Fourth ed, Jones and Bratlett Publishers, Boston, 2008.
[6] B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, 1982.
[7] S. Manousakis, Musical L-Systems, MS. thesis, The Royal Conservatory of The Hague, June 2006.
[8] P. Prusinkiewicz, Graphical applications of L-systems, In Proceedings of Graphics Interface ’86 — Vision Interface’, 86 (1986) 247–253.
[9] P. Prusinkiewicz, Applications of L-systems to computer imagery, In H. Ehrig, M. Nagl, A. Rosenfeld, and G. Rozenberg, editors, Graph grammars and their application to computer science; Third International Workshop, 534–548, Springer-Verlag, Berlin, 1987, Lecture Notes in Computer Science 291.
[10] P. Prusinkiewicz and J. Hanan, Lindenmayer Systems, Fractals, and Plants, Springer-Verlag, Berlin, 1989.
[11] P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, Springer-Verlag, New York, 1990.
[12] G. Rozenberg and A. Salomaa, Lindenmayer Systems Impacts on Theoretical Computer Science, Computer Graphics, and De-velopmental Biology, Springer-Verlag, Berlin, 1992.
[13] Examples from: http://en.wikipedia.org/wiki/L-system, 2016.

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History

  • Receive Date: 26 January 2016
  • Revise Date: 21 March 2018
  • Accept Date: 04 April 2018
  • Publish Date: 23 August 2018

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