The simplest case of a well known theorem of Penner states that given a pair of filling curves, a positive twist about one curve together with a negative twist about the other curve is a pseudo-anosov mapping class. Suppose I have an explicit pair of curves that fill a closed surface, is there a reasonable way to explicitly compute the stable and unstable laminations of this map? 



Constructing Invariant Lamination of a Pseudo-Anosov Given By Dehn Twists
Your question is explicitly answered in Section 6 of Thurston's Bulletin article, freely available [here](https://projecteuclid.org/euclid.bams/1183554722). In the end it boils down to a calculation in $\mathrm{SL}(2, \mathbb{Z})$.


