Lay out a virtual 2D circuit for a game application perhaps like the WireWorld cellular automaton. How do we deal with connecting two points but not wanting to disturb any intervening circuitry? The prototypical problem is crossing two wires.
Easy, just create a new layer and define which points connect through to the previous layer. Furthermore, because it is all virtual, the layers do not need to be stacked obeying 3D geometry. Layers can connect in arbitrary ways, sort of like a graph instead of a linked list. We can enforce a constraint that layers must maintain a 1:1 scale with each other, or allow arbitrary points in one layer to connect with arbitrary points in another. The latter permits signals faster than the speed of light within a layer.
Because it is all virtual, we need not limit layers to 2D. The inspiration was Minecraft with its three-dimensional redstone circuitry. Additional layers can be thought of as routing circuitry through alternate universes vaguely like the Nether or the End.
Could also do it with one-dimensional layers, then all the layers could be viewed simultaneously on a 2D screen.
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