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Path finding is a smart connection between commands, signs, trains and train properties. Each switcher and destination sign turns into a node of a network trains can use to reach their destination. Blocker signs can kill off certain routes in this network but don't act as an actual node.
Each minecart can have its own destination set, which can be set using commands, destination signs or property signs. Switcher signs toggle the rails in such a manner that every minecart is sent into the correct direction. May trains collide along the way, the cart switcher can still cut the train apart and fix things up.
May this network of nodes ever fail, you can use the Reroute Command to fix things up.
Where to start
When first getting in contact with this system, I can understand it seems pretty complicated. In some ways it is, but once the first bit is done you quickly get the hang of it. Start off with some switcher signs, third and fourth lines left empty, placing them underneath the rails you wish to toggle using this system. Then end with two or three destination signs underneath the rails you want to get to. Use the Destination Command to set the destination on your train and let the system do its work.
Blocker signs can be placed down to make rails one-way only. This prevents trains driving into each other, cutting off routes between nodes in one direction even if it is shorter. Make sure to have the blocker sign use an always-powered mode ([+train]), otherwise path finding will ignore the sign. Path finding does not remember or use redstone-based routing logic.
There is no comment section, so I have to edit the wiki to do this. I still do not understand. The destination signs set the destinations on the train. So I add a destination sign that sets the destination but is the destination? Please explain this!!!