  Generalising results of Erd\H{o}s-Freud and Lindstr\"om, we prove that the
largest Sidon subset of a bounded interval of integers is equidistributed in
Bohr neighbourhoods. We establish this by showing that extremal Sidon sets are
Fourier-pseudorandom, in that they have no large non-trivial Fourier
coefficients. As a further application we deduce that, for any partition
regular equation in five or more variables, every finite colouring of an
extremal Sidon set has a monochromatic solution.
