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Around the inner cylinder, the system cools down and spinodal decomposition sets in. Starting from a non-radially symmetric pattern at the inner cylinder, domains of coexisting mole fractions emerge. At later times, one of the following structures forms: (a) a set of nested rings or (b) spirals growing from the inside to the outside. The spiral shape is of particular nanotechnological interest, since it allows the creation of a long continuous path from the inside to the outside. If one of the domains is electrically conductive, a flat spiral coil can be created. By crosslinking one component and removing the other, a spiral, percolating path can be formed through the solid component. 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