another slabbing…

Take the set \tau\subseteq\mathbb{R}^{3} which is left invariant by the following map: T: (x,y,z) \rightarrow (2\sin(z-y),2\cos(x-z),7sin(y-x))

At each point in \tau, there is one and only one future itinerary. I will suppose that \tau contains all possible points, though any computer representation of \tau will necessarily be incomplete.

Since this map trifurcates, and each trifurcation upon other trifurcation doubles, we will want something like:

\bigoplus_{n=0}^{\infty} \frac{T^{n}(\tau)}{2.3^{n}}