Fitting line with branches to xyz coordinates in python

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I have a set of points in 3d space which I'd like to fit a line through. The points are pretty tight, but there are obvious branches, as illustrated crudely below. Essentially, I want to describe the "path" implied by this data using one/several equations*

*I should add- it would also work to find a set of coordinates describing the line rather than fitting an equation.

With the black points representing my data (simplified to 2D), the red line is what I'm after

black points representing my data (simplified to 2D), red line is what I'm after

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