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Stochastic L-system inference from multiple string sequence inputs

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Abstract

Lindenmayer systems (L-systems) are a grammar system that consists of string rewriting rules. The rules replace every symbol in a string in parallel with a successor to produce the next string, and this procedure iterates. In a stochastic context-free L-system (S0L-system), every symbol may have one or more rewriting rule, each with an associated probability of selection. Properly constructed rewriting rules have been found to be useful for modeling and simulating some natural and human engineered processes where each derived string describes a step in the simulation. Typically, processes are modeled by experts who meticulously construct the rules based on measurements or domain knowledge of the process. This paper presents an automated approach to finding stochastic L-systems, given a set of string sequences as input. The implemented tool is called the Plant Model Inference Tool for S0L-systems or PMIT-S0L. PMIT-S0L is evaluated using 960 procedurally generated S0L-systems in a test suite, which are each used to generate input strings, and PMIT-S0L is then used to infer the system from only the sequences. The evaluation shows that PMIT-S0L infers S0L-systems with up to 9 rewriting rules each in under 12 hours. Additionally, it is found that 3 sequences of strings are sufficient to find the correct original rewriting rules in \(100\%\) of the cases in the test suite, and 6 sequences of strings reduce the difference in the associated probabilities to approximately \(1\%\) or less.

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Data availability statement

One of the L-systems used in the data set is published, and appropriate citations are provided. The remainder are made by procedural generation, and so really belong as part of the code. The L-systems used as the basis for making the procedural generation routine are stored in the University of Calgary’s L-system repository, which we accessed with their permission.

Code Availability

PMIT-S0L is open source and available at https://github.com/jbernard-McMaster/PMIT.

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Acknowledgements

The authors thank Dr. Farhad Maleki for his assistance in acquiring the images for this paper.

Funding

This research was conducted as part of the Plant Phenotyping and Imaging Research Center, funded in part by the Canada First Research Fund, by National Science Engineering Research Council grant #2016-06172 (IM), and the Alexander Graham Bell Scholarship (JB).

Author information

Authors and Affiliations

  1. Department of Surgery, McMaster University, Hamilton, ON, Canada

    Jason Bernard

  2. Department of Computer Science, University of Saskatchewan, Saskatoon, Canada

    Ian McQuillan

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  1. Jason Bernard
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  2. Ian McQuillan
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Contributions

JB had the original idea for the algorithm, designed, developed, evaluated PMIT-S0L, wrote the first draft of the paper, and helped with the revision process. IM supervised the research, and revised the paper.

Corresponding author

Correspondence to Jason Bernard.

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Appendix A

Appendix A

This appendix contains some S0L-systems procedurally generated for this research and the resulting L-systems predicted by PMIT-S0L for a different number of input strings. Turtle graphics symbols were not included as it has been shown that including turtle graphics symbols makes inferring L-systems inductively easier (Bernard and McQuillan 2021). In all cases, the axiom for each system was set to “A”, and \(M = 3\). The solution for each system was created by executing PMIT-S0L once. See Tables 4, 5, 6, 7, and 8

Table 4 Three sample procedurally generated S0L-systems and solution with \(|V| = 2\)
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Table 5 Three sample procedurally generated S0L-systems and solution with \(|V| = 3\)
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Table 6 One sample procedurally generated S0L-systems and solution with \(|V| = 5\)
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Table 7 One sample procedurally generated S0L-system and solution with \(|V| = 6\)
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Table 8 One sample procedurally generated S0L-system and solution with \(|V| = 7\)
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Bernard, J., McQuillan, I. Stochastic L-system inference from multiple string sequence inputs. Soft Comput 27, 6783–6798 (2023). https://doi.org/10.1007/s00500-022-07683-8

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