三維面著色的熵

Abstract

這個研究主要是要去計算三維度兩個顏色的熵，但首先必須利用有序矩陣以及矩陣自乘的性質所發展出來的遞迴公式去解決三維度兩個顏色下面著色的花樣生成問題。 接下來，給一個限制集則就可以定義出轉移矩陣而且它的遞迴公式也會被表現出來。最後，只需去計算矩陣的最大特徵值即可計算出熵的問題。

The work investigates spatial Entropy of 3-dimensional face coloring, but we need to solve three-dimensional pattern generation problem with edge- coloring by using the properties of ordering and self-multiply matrices to establish some recursive formulas, first. Now, given admissible set of local patterns then the transition matrix is defined and the recursive formulas are presented. Finally the spatial entropy is obtained by computing the maximum eigenvalues of a sequence of transition matrices.