Degree distribution and patches of the image horizontal visibility graph mapped from two-dimensional Thue–Morse words

Jia Li and Min Niu

Physica A: Statistical Mechanics and its Applications, 2025, vol. 665, issue C

Abstract: In this paper, we aim to study the image horizontal visibility graph of order n (IHVGn) mapped from the 2D Thue–Morse words which also help us to understand their limit, i.e., 2D Thue–Morse sequence. Firstly, we map the series to complex networks by using the image horizontal visibility algorithm of order 4. Subsequently, using the iterative method and the construction of sequences, we obtain the exact analytic expressions of the degree distribution of the 2D Thue–Morse IHVG4. Furthermore, we also investigate 3-order patches of the 2D Thue–Morse IHVG4 and find that the patch profile converges to a constant. Finally, numerical simulations are used to verify that theoretical values of the degree distribution and patch profile are in agreement with the simulated values.

Keywords: 2D Thue–Morse words; Image horizontal visibility graph; Degree distribution; 3-order patch (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:665:y:2025:i:c:s0378437125001190

DOI: 10.1016/j.physa.2025.130467

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