In Hillel Furstenberg's series lectures on ergodic theory in fractal geometry, he mentioned his search on finding a one-to-one correspondence between fractal sets and trees, however, I couldn't not find any material online about this. Does anyone have reference on that?
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Check out M. Gavish's "Measures with Uniform Scaling Scenery" (google result) and the sources contained therein.
More precisely, read about the CP-Process (of H. Furstenberg) and its relation to trees.