  The affinity dimension is a number associated to an iterated function system
of affine maps, which is fundamental in the study of the fractal dimensions of
self-affine sets. De-Jun Feng and the author recently solved a folklore open
problem, by proving that the affinity dimension is a continuous function of the
defining maps. The proof also yields the continuity of a topological pressure
arising in the study of random matrix products. I survey the definition,
motivation and main properties of the affinity dimension and the associated SVF
topological pressure, and give a proof of their continuity in the special case
of ambient dimension two.
