WHEN a system is poised at a critical point between two macroscopic phases, it exhibits dynamical structures on all available spatial scales, even though the underlying microscopic interactions tend to have a characteristic length scale. According to the universality hypothesis(1,2), diverse physical systems that share the same essential symmetry properties will exhibit the same physical behaviour close to their critical points(1,3-5); if this is so, even highly idealized models can be used to describe real systems accurately, Here we report experimental confirmation that the scaling behaviour of thermodynamic variables predicted by the universality hypothesis holds over 18 orders of magnitude, We show that the equation of state of a two-dimensional system (an atomic layer of ferromagnetic iron deposited on a non-magnetic substrate) closely follows the behaviour(6) of the two-dimensional Ising model(7)-the first and most elementary statistical model of a macroscopic system with short-range interactions(3).