search

jeffwack111 / Spiders

0 stars 0 forks source link

Rework calculation of external angles #25

Open jeffwack111 opened 3 months ago

jeffwack111 commented 3 months ago

New workflow: Start with Hubbard tree Node -> Node[] Identify regions and boundary Node -> region Label the accesses of each node by its neighbors Node -> region[] Identify the characteristic set, the preimages of which form the whole tree for each characteristic point calculate the binary expansion of its accesses. If we use forward orbits we can get the binary expansions of the forward orbits of these accesses. How can we use preimages to get the binary expansions of the preperiodic branch points?

jeffwack111 commented 3 months ago

Question: If we first calculate the binary expansion of the critical point, can we then determine the angles of the branch points using solely the angle and not the hubbard tree?

jeffwack111 commented 3 months ago

This is in a better state. The boundary stuff needs to be rethought. Check the external angles of the alpha fixed point of 3/11 for failure, and look in Teichmuller vol 2 for the answer.

jeffwack111 commented 1 month ago

Calculation of angles works reasonably well, but there are still improvements to be made. I'd really like for it to be done in a preimage way, where we calculate the orbit portrait using the characteristic points and all of their preimages