Resources
3D FractaL-Tree
Author(s): John R Jungck^{1}, Jennifer Spangenberg^{2}, Noppadon Khiripet^{3}, Rawin Viruchpinta^{3}, Jutarat Maneewattanapluk^{3}
1. Interdisciplinary Science Learning Center at the University of Delaware 2. Beloit College 3. National Electronics and Computer Technology Center
1266 total view(s), 282 download(s)
- Fractal.xls(XLS | 56 KB)
- FractaLII_15June2006.jar(JAR | 6 MB)
- hookrajong_tree.txt(TXT | 278 B )
- java3d-1_5_1-beta2-windows-i586.exe(EXE | 3 MB)
- lelawadee_tree.txt(TXT | 184 B )
- teenped_tree.txt(TXT | 216 B )
- Tree_Model_Comparison.ppt(PPT | 2 MB)
- License terms
Overview
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 Excel 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.
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
Skirpan, M. Make Your Own Fractal Tree!
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.
Algorithmic Botany, University of Calgary
Citation
Researchers should cite this work as follows:
- Jungck, J. R., Spangenberg, J., Khiripet, N., Viruchpinta, R., Maneewattanapluk, J. (2018). 3D FractaL-Tree. ESTEEM, QUBES Educational Resources. doi:10.25334/Q48139
Fundamental Mathematical Concepts
Developed By
Primary Reference
Aristid Lindenmayer, "Mathematical models for cellular interaction in development." J. Theoret. Biology, 18:280--315, 1968.