A condensed polynomial model, that captures the main features of high- or low-pressure catalytic oscillations, is used to simulate spatiotemporal patterns in a cylindrical catalytic surface. This model includes a single autocatalytic variable (activator) and a slow changing and localized inhibitor subject to a global interaction mechanism which maintains the spatial average of the activator at the set point. While for very short (small length L) or very narrow (small perimeter P) cylinders the pattern preserves the structures of the corresponding one-dimensional problems (a ring or a wire), two-dimensional patterns emerge for comparable L and P showing a large multiplicity of spatiotemporal behavior because of a very high sensivity to initial conditions. The effect of kinetic parameters and system size is studied. Approximate solutions for the bifurcation from one- to two-dimension patterns are derived.