Distance-driven adaptive trees in biological metric spaces: uninformed accretion does not prevent convergence.

We present several variants of a stochastic algorithm which all evolve tree-structured sets adapted to the geometry of general target subsets in metric spaces, and we briefly discuss their relevance to biological modelling. In all variants, one repeatedly draws random points from the target (step 1), each time selecting from the tree to be grown the point which is closest to the point just randomly drawn (step 2), then adding to the tree a new point in the vicinity of that closest point (step 3 or accretion step). The algorithms differ in their accretion rule, which can use the position of the target point drawn, or not.