From:

Subject:

> I would be curious to hear how you are doing your search. [...]

I use a simple brute-force method, that is, I compute the order of

each transform and the number of quarter turns. If there is already

a transform with that order & number of qt, I forget all about it and

go to the next transform.

This sounds to me as though you're assuming that all transforms with a

given order are equivalent as far as deriving further transforms of

other orders go. That is, if you find that a given transform X of

length L has order N, it sounds as though you're assuming that there is

no need to store any other transforms of length L and order N. I'm not

convinced this is justified. If you've found X of (say) length L and

order N, and then find a different Y of length L and order N, I can't

see any justification for the assumption that you can prune the entire

subtree below Y, because if the cycle decompsition of Y is different

from that of X, they may behave entirely differently when followed by

more twists, even though they have the same order.

der Mouse

mouse@collatz.mcrcim.mcgill.edu