Joint Colloquium: Barnsley -- Approximation of fractal functions by Weierstrass nowhere differentiable functions

I will describe a constellation of results, old and new (joint with A.  Vince, B.
Harding, P.  Viswanathan), centered around the functional equation f(x)-af(bx)=g(x),
where a and b are real parameters, in various Lp spaces.  The new results connect
Weierstrass to fractal interpolation theory, NCG, and a remarkable orthonormal basis
that reduces to {cos(nx),sin(nx)} when a=0.  For a light introduction to this lecture,
see http://www.anu.edu.au/news/all-news/finding-the-simple-patterns-in-a-complex-world.