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Given a random tree

g = TreeGraph[RandomInteger[#] \[UndirectedEdge] # + 1 & /@ Range[0, 30], VertexSize -> 0.5]

enter image description here

How can I make it look like it is vanishing into the horizon? Larger near the screen and smaller towards a vanishing point. (And maybe parts beyond the screen out of view, as if you are halfway in the graph)

I tried doing an ImagePerspectiveTransformation on the saved image, but it didn't seem natural

enter image description here

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