高維度元胞自動機的混合性質

Abstract

本篇論文證明若在多邊形的頂點上排列，且滿足特定條件，可以得到k-混合的結論，在高維度時的條件會非常複雜，但是我們有個簡潔的演算法來表示。證明長方形和非長方形的方式基本上是相似的，只是在非長方形的證明中，必須要遵循特定的方向性，最後我們給一個反例說明不能將「在頂點上排列」的條件捨去。

This thesis shows that corner-permutive function with certain conditions are k-mixing. Conditions for k-mixing may be quite complicated in multi-dimension, thus there is a brief algorithm to express it. Methods of proving rectangle and non-rectangle rules are the same basically, just need to follow a certain orientation in non-rectangle rule. We end this paper with a counter-example shows that corner-permutive is necessary.