Thanks for this, I've been obsessing about track layouts while playing trains with my kid, how to avoid getting stuck in permanent loops, having bi-drectional routes on all parts of the track etc. As I'm not a math person, I've not had a logical framework with which to think about it. my kid doesn't care but laying out tracks been a surprisingly fun mind game for me.
Ditto. The ideal track layout should allow trains to go in either direction across every segment. Bonus for going under a bridge. I also haven't really worked out the graph theory (something involving the +/- orientation of junction splits) but the temptation is immanent.
I also play trains with my kid, and I might be thinking about the same stuff. When I build a track, I think "given a position and direction, could I reach every other (position,direction) pair from here?". There's a certain minimum complexity required for a track to have that property, but I haven't really broken it down in a principled way.
I've been doing this too, with mine! A recent discovery is that if you keep all the Y pieces pointing in the same compass direction you seem to end up with a track which is always 100% traversable in either forward or reverse.
Traversable doesn’t change if you bend parts of a track, and that can change the compass direction the switches point at.
For example, if part of the track containing a switch has an S shape, moving the switch from the center horizontal to the top or bottom one turns it by 180 degrees without affecting traversability.
I know nothing about train tracks past my BRIO days, but a bit about graphs. Can you explain how a track would not be bidirectional except for a permanent loop?
One of the things that makes it more interesting in practice is that most electric model trains* use a "one rail is hot, one is return" electrical design-- so adding a wye or reversing loop to the design is asking for all sorts of electrical gimmicry to prevent it from shorting, while still maintaining usability.
*classic Lionel and Marklin designs used a third conductor in the centre. Since the outer rails are wired together, reversing designs are trivial.
