This thesis introduces a class of algorithms for modeling biological patterns with branching (tree-like) and network (with loops) topologies. The key idea behind these algorithms is the marking and subsequent colonization of empty space. Models are formulated in terms of iterative geometric operations on sets of points representing the elements of the pattern and markers of free space. This concept is formalized as the space colonization algorithm.
The practical value of this approach is demonstrated by modeling the architecture of trees and vasculature in plants. Trees are modeled using markers of empty space to mediate competition between branches. When vascular patterns are modeled, the markers of empty space represent sources of a vein inducing signal (auxin). Several algorithms are introduced to simulate vein development in a growing leaf blade. Additionally, a model simulating vasculature patterning in the stem is proposed and used to examine the relation between phylotaxis and stem vasculature.
The applications explored in this thesis demonstrate that a common mechanism, competition for space, is su?cient to recreate both the development of vascular patterns and the architecture of trees.
Adam Runions. Modeling Biological Patterns using the Space Colonization Algorithm. M.Sc. thesis, University of Calgary, January 2008.
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