Tablet weaving, also known as card weaving, is an ancient method of making strips of fabric that is still used by hobbyists and crafters today. One important difference from other sorts of weaving is that the threads are twisted as the cloth is produced, with different design elements producing different directions of twist. It is desirable for this twist to be balanced across the length of the strip, and this feature has inspired the use of a mean-reverting Markov process known as the Ehrenfest model to randomly generate tablet weaving patterns. I applied this process to the technique known as “Coptic Diamonds”, with very good results. For perfectly balanced twist, however, some extra symmetry had to be artificially introduced into the patterns.