I would like to make movies of phase portraits of automorphic/kleinian functions with varying traces -- On page 375 of Indra's Pearls there is a phase portrait of an automorphic function/fonction kleinneene. It says on the previous page that the function is a ratio $$ \left(\sum \frac{az+b}{(cz+d)^{3}}\right)\Big/\left(\sum\frac{1}{(cz+d)^{4}}\right) $$
I'm not entirely clear what the book means by this expression.
- How do I go from the traces $t_{a}, t_{b}$ in chapter 8 -- Grandma's recipe (page 261) -- to $a$, $b$, $c$, and $d$ in the above expression?
- What should the above expression read? It's not clear what the index of summation is as written