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3D FractaL-Tree

Artistid Lindemayer (1975, 1989, 1990) invented a mathematics based on graph grammar rewriting systems to describe iteratively branching structures; these were named in honor of him and are referred to as L-systems. 3D FractaL-Tree allows scientists to collect data from actual specimens in the field or laboratory, insert these measurements into a spatially explicit L-system package, and then visually compare to the computer generated 3D image with such specimens. The measurements are recorded and analyzed in a series of worksheets in Microsoft ExcelŽ and the results are entered into the graphics engine in a Java applet. 3D FractaL-Tree produces a rotatable three-dimensional image of the tree which is helpful for examining such characters as self-avoidance (entanglement and breakage), penetration of sunlight, distances that small herbivores (such as caterpillars) would have to traverse to go from one tip to another, and Voronoi polyhedra of volume distribution of biomass on different subsections of a tree. These and other factors have been discussed in the Adaptive Geometry of Trees (Horn, 1971). Three different representations are available in 3D FractaL-Tree images: wire frame, solid, and transparent. Easy options for saving and exporting images are included.

Source

Author(s):
John R. Jungck, Beloit College
Jennifer A Spangenberg, Beloit College
Noppadon Khiripet, National Electronics and Computer Technology Center
Rawin Viruchpinta, National Electronics and Computer Technology Center
Jutarat Maneewattanapluk, National Electronics and Computer Technology Center

Published by: BioQUEST Curriculum Consortium

OS:

User Manuals and Curricular Materials
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Popular Text Citations

Doucet, Paul George. 1976. Studies on L-Systems. Utrecht: Rijksuniversiteit te Utrecht.

Horn, H. S. 1971. Adaptive Geometry of Trees. Princeton University Press.

Przemyslaw P., & Hanan J. 1989. Lindenmayer systems, fractals, and plants., volume 79 of Lecture notes in biomathematics. Springer-Verlag, New York.

Prusinkiewicz, P.; Lindenmayer, A. 1990. The Algorithmic Beauty of Plants. Springer-Verlag.

Lindenmayer, A. (1975). Developmental systems and languages in their biological context. In G. T. Herman & G. Rozenberg (Eds.), Developmental systems and languages (pp. 1-40). Amsterdam: North-Holland Publishing. 0-7204-2806-8

Deussen, O.; Lintermann, B. 2005. Digital Design of Nature : Computer Generated Plants and Organics. Springer.

Research Articles

Perttunen, et al. "LIGNUM: A Tree Model Based on Simple Structural Units." Annals of Botany 77.1 (1996): 87.

Dimond, A. E. 1966. Pressure and flow relations in vascular bundles of the tomato plant. Plant Physiology 41:119-131.

Kruszewski, P., and S. Whitesides. "A General Random Combinatorial Model of Botanical Trees." Journal of Theoretical Biology 191.2 (1998): 221-36.

Chen, Yi-Ping Phoebe, and Jim Hanan. "Partial Automation of Database Processing of Simulation Outputs from L-Systems Models of Plant Morphogenesis." Bio Systems 65.2 (2001): 187.

Allen, M.; Prusinkiewicz, P.; DeJong, T. (2005). Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH model. New Phytologist 166:869-880.

Allen, M.; Prusinkiewicz, P.; DeJong, T. (2004). Using L-Systems for Modeling the Architecture and Physiology of Growing Trees: The L-PEACH Model. In Proceedings of the 4th International Workshop on Functional-Structural Plant Models, pp. 220-225.

Perttunen, Jari, et al. "Application of the Functional-Structural Tree Model LIGNUM to Sugar Maple Saplings (Acer saccharum Marsh) Growing in Forest Gaps." Annals of Botany 88.3 (2001): 471-81.

Kruszewski, P., and S. Whitesides. "A General Random Combinatorial Model of Botanical Trees." Journal of theoretical biology 191.2 (1998): 221-36.

Chen, Yi-Ping Phoebe, and Jim Hanan. "Partial Automation of Database Processing of Simulation Outputs from L-Systems Models of Plant Morphogenesis." Bio Systems 65.2 (2001): 187.

Allen, M.; Prusinkiewicz, P.; DeJong, T. (2005). Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH model. New Phytologist 166:869-880.

Perttunen, et al. "LIGNUM: A Tree Model Based on Simple Structural Units." Annals of Botany 77.1 (1996): 87.

Education Research & Pedagogical Materials

Shields, N. Design your own fractal tree.

Tutorial & Background materials

List of publications by Aristid Lindenmayer from the DBLP Bibliography Server

McWorter, W. L-systems tutorial.

West, D. Self-Contacting Fractal Trees.

Math Forum, Fractals.

Wright, D. J., L-Systems

Algorithmic Botany, University of Calgary

Citation
Jungck John R., Spangenberg Jennifer A, Khiripet Noppadon , Viruchpinta Rawin , Maneewattanapluk Jutarat () 3D FractaL-Tree. A module of the Biological ESTEEM Collection, published by the BioQUEST Curriculum Consortium. URL: http://bioquest.org/esteem/esteem_details.php?product_id=403