The Pattern Complexity of the Sierpiński Triangle

2025/10/07 by Johan Nilsson, Nilsson, Johan
Computer Science · Mathematics · #05A15 #05B45 #52C20 #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2510.06493

openalex publication_date 2025/10/07 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We give exact formulas for the number of distinct triangular patterns (or subtriangles) of a given size that occur in the Sierpiński Triangle.

Citations

• The Pattern Complexity of the Squiral Tiling
• The Pattern Complexity of the 2-Dimensional Paperfolding Sequence

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• The Pattern Complexity of the Squiral Tiling
• The exact complexity of a Robinson tiling
• Sierpinski's triangle and the Prouhet-Thue-Morse word
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