The bi-Lipschitz rigidity conjecture for 2-attractors

A 2-attractor is the self-affine attractor associated with an expanding matrix and a two-element digit set. Two such attractors are affinely similar if one is the image of the other under an affine similarity, and bi-Lipschitz equivalent if there is a bi-Lipschitz bijection between them.

Bi-Lipschitz rigidity conjecture. If 2-attractors are not affinely similar, then they are not bi-Lipschitz equivalent.

This conjecture proposes affine similarity as the complete classification up to bi-Lipschitz equivalence for 2-attractors. The source gives no resolution, so its status remains open.