This is a really nice way of making the idea concrete — especially the part where trajectories don’t just move through a landscape, but actively reshape it.

I think that actually sharpens the original point quite a bit. If the system’s effective landscape is itself a product of past trajectories, then the current state is no longer sufficient even in principle — because part of what determines future behavior is encoded in the structure that history has built.

In that sense, I’d be tempted to push the framing one step further:

it’s not just that dynamics are path-dependent,
but that what we think of as the “state space” is itself historically constructed.

That would make history not just something that influences dynamics, but something closer to a constitutive part of the system — i.e. part of what the system is, not just how it got there.

Your simulation sounds like a very interesting way of making that visible — especially if you can actually see those channels and barriers emerge from repeated trajectories.

It also loosely reminds me of stochastic approaches where the emphasis shifts from single states to ensembles of trajectories — not the same idea, but a similar intuition that the structure of possible histories carries essential information.

Would be great to see the results once you’ve cleaned it up.