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After reviewing some well known facts about phase-ordering - the process
whereby an ordered phase is built out of a disordered one when a
ferromagnetic system is quenched from above to below the critical
temperature - I will present some recent findings in two dimensions
showing the existence, next to the growing domains whereby local order is
established, of a fractal object with the topology of the critical cluster
of random percolation. I will discuss how these two radically different
structures develop and coexist in the system and the rather broad generality of the phenomenon with
respect to different models, lattices, kinds of quenched disorder etc...