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3 - Introduction to L-systems and Turtle Graphics Interpretation

Published online by Cambridge University Press:  13 June 2025

Brent R. Bielefeldt
Affiliation:
Texas A & M University
Darren J. Hartl
Affiliation:
Texas A & M University
Marcelo H. Kobayashi
Affiliation:
University of Hawaii, Manoa
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Summary

To address the need for an inherently multiobjective preliminary design tool, this chapter introduces a heuristic alternative to the conventional topology optimization approaches discussed in the previous chapter. Specifically, a parallel rewriting system known as a Lindenmayer system (L-system) is used to encode a limited number of design variables into a string of characters which, when interpreted using a deterministic algorithm, governs the development of a topology. The general formulation of L-systems is provided before discussing how L-system encodings can be interpreted using a graphical method known as turtle graphics. Turtle graphics constructs continuous, straight line segments by tracking the spatial position and orientation of a line-constructing agent, leading to the creation of branched structures that mimic those found in numerous natural systems. The performance of the proposed method is then assessed using simple, well-known topology optimization problems and comparisons to mathematically known optimal or ideal solutions as well as those generated using conventional topology optimization methodologies.

Type
Chapter
Information
Topology Optimization via L-Systems and Genetic Algorithms
Bioinspired Encoding for Generative Design
, pp. 86 - 111
Publisher: Cambridge University Press
Print publication year: 2025

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