More rain forecast tonight, so I swept leaves off the sidewalk and the bottom of the driveway to make space for new ones. I was about to pick a few off the grass for good measure when Mama Violet appeared on the sidewalk and gave me a Look. So I fed her instead.

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My expectation could be wrong though, reading http://arnoldia.arboretum.harvard.edu/pdf/articles/1995-55-3-roots-from-shoots-a-horticultural-review.pdf describes how not all meristem cells -- the cells that can turn into any plant organ -- carry the same ... genetics ("mutation"). On the other hand, i don't think the color is a mutation.
Anyhow, that article has a picture of an exposed root system of a sweetgum and the clones. I've suspected that our 100' sweetgum is the main stem of several other trees that extend from it in a line. It also provides a citation if you really want to give it a go.
Brown, C. L., and R. G. McAlpme. 1964 Propagation of sweetgum from root cuttings. Georgia Forest Research Paper 24.