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I have a model train set with two trains and switches that look like this:

Duplo train switch

Is there some configuration of track so that two trains can run simultaneously, continuously, without human intervention, but not follow the same path?

Edit: As cleverly noted in the comments, the two trains must also must share at least some track.

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    Maybe add a pulley that catches onto the train and switched the cross-road each time it passes. Then its a matter of timing. With some tracks it has such a function built in. – 2017-01-18
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    This question might get closed for being off-topic. Perhaps adding some more mathematical content (e.g., setting this up as a graph theory problem with a set of rules), you might have more luck on this site. – 2017-01-18
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    That's a fantastic question. – 2017-01-18
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    One further assumption is needed though: the track is connected. (Otherwise you can take two disjoint loops.) – 2017-01-18
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    In fact, to make it interesting we need not just the track to be connected, but that there is a point on the track where both trains pass. Otherwise you can make two loops connected by a track in such a way that each train goes around one of the loops endlessly. – 2017-01-18
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    Too bad Math SE police, I already got my answer! You'll have to continue on your beat to preventing learning elsewhere! You may now proceed to close my question and ban my account. Cheers! – 2017-01-20

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Yes its possible. Like that: (Sorry for the poor drawing)enter image description here

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    I'm testing this when I get home. – 2017-01-19
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    @Tom Tell me how it goes! – 2017-01-19
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    it works fantastic! Now of course I want to know how you figured that out. Did you find a way to diagram it? Or reduce it to just switches and track? Is there some kind of rule here that can be applied to any track set up? Or did you just logically think each train needs a place to turn around and a place to pass? – 2017-01-19
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    @Tom Great! I realized that any configuration is just a [cubic graph](https://en.wikipedia.org/wiki/Cubic_graph) with a choice of an edge at each vertex. Then it's easy to construct many examples quickly. – 2017-01-19
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    @Tom Can I see a picture or a video? :) – 2017-01-19
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    I knew there was some sort of theory here, but I had no idea where to start. Thanks for the cubic graph link which opens up a whole lot for me to learn! Here's a [picture](https://goo.gl/photos/YVqKqgfC68dLY62V9), I'll try and get a video too. – 2017-01-20
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    This will work as long as the two trains have the exact same speed. My guess it that there are configurations where different speeds would work, as long as the speed ratios are (multiples of) circuit length ratios. – 2017-01-20
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    @Tom Thanks for the picture! It looks fun to watch! :) – 2017-01-20
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    @Spenser and the [video](https://goo.gl/photos/aXjUpxoptGDb9UZZ7) :) – 2017-01-20
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    @Tom Thanks for the video, it looks great! :) – 2017-01-20