二維網格模型之花樣形成與貼磚

Abstract

這篇論文的目的主要是在討論對於一個會改變的基本集合其花樣形成的問題。我們可以得到相對於這個基本集合的置換矩陣的遞迴公式，然後可藉由置換矩陣的最大特徵值來計算熵。最後我們討論平面上貼磚的花樣形成問題。

Patterns generation and transition matrices in multi-dimensional lattice models has been studied in [1,2]. One motivation for studying such problem in [1,2] is the construction of mosaic patterns of CNN with spatial invariant (or independent) templates. On the other hand, when the template varies spatially, in one-dimensional CNN case, the number of mosaic patterns may grow exponentially as shown in [6]. In this paper, we study the patterns generation problem of two-dimensional CNN with variant templates. We extend the results obtained in [6]. Furthermore, we also investigate the patterns generation problems on general lattices in $\mathbf{R}^{2}$.