The Pattern Complexity of the 2-Dimensional Paperfolding Sequence
Johan Nilsson
TL;DR
This paper provides an exact formula for counting the number of unique crease patterns in a square region of a 2D paperfolding structure, advancing understanding of its combinatorial complexity.
Contribution
It introduces a precise mathematical formula for the pattern complexity of 2D paperfolding sequences, a novel contribution to folding pattern analysis.
Findings
Exact formula for crease pattern counts
Quantitative measure of pattern complexity
Enhanced understanding of 2D folding structures
Abstract
We present an exact formula for the number of distinct crease patterns in a square shaped region of a given size that appear in the 2 dimensional paperfolding structure.
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Taxonomy
TopicsCellular Automata and Applications · semigroups and automata theory · Coding theory and cryptography