A universal twist $\gamma$ for all finite-dimensional Cayley-Dickson algebras is defined recursively and a tree diagram 'computer' is presented for determining the value of $\gamma (p,q)$ for any two non-negative integers $p$ and $q$.
"A Tree for Computing the Cayley-Dickson Twist." Missouri J. Math. Sci. 21 (2) 83 - 93, May 2009. https://doi.org/10.35834/mjms/1316027241