Tablet weaving, also known as card weaving, is a method of making strips of fabric that has been used from ancient times in many parts of the world. Unlike in most other sorts of weaving, in tablet weaving the warp threads are twisted around each other as the cloth is produced. Since different design elements produce different directions of twist, it is desirable for this twist to be balanced along the length of the weaving. This feature inspired the use in previous work of a mean-reverting Markov process known as the Ehrenfest model to randomly generate tablet weaving patterns. In this paper we apply the process to the technique known as “Egyptian Diagonals”. The result successfully reflects the traditional design aesthetics of this technique, although the process was more difficult than in previous work.