---
abstract: |
    Let $M$ be a $2\times2$ real matrix with both eigenvalues less than 1 in modulus. Consider two self-affine contraction maps from $\mathbb R^2 \to \mathbb R^2$, $$T_m(v) = M v - u \ \ \mathrm{and}\ \ T_p(v) = M v + u,$$ where $u\neq0$. We are interested in the properties of the attractor of the iterated function system (IFS) generated by $T_m$ and $T_p$, i.e., the unique non-empty compact set $A$ such that $A = T_m(A) \cup T_p(A)$. Our two main results are as follows:

    -   If both eigenvalues of $M$ are between $2^{-1/4}\approx 0.8409$ and $1$ in absolute value, and the IFS is non-degenerate, then $A$ has non-empty interior.

    -   For almost all non-degenerate IFS, the set of points which have a unique address is of positive Hausdorff dimension – with the exceptional cases fully described as well.

    This paper continues our work begun in [@HS].
address:
- |
    Department of Pure Mathematics\
    University of Waterloo\
    Waterloo, Ontario\
    Canada N2L 3G1
- |
    School of Mathematics\
    The University of Manchester\
    Oxford Road, Manchester M13 9PL\
    United Kingdom.
author:
- 'Kevin G. Hare'
- Nikita Sidorov
title: 'Two-dimensional self-affine sets with interior points, and the set of 