A condensed model that captures the main features of high- or low-pressure catalytic oscillators is used to simulate spatiotemporal patterns in a catalytic disk or square. This model includes a single autocatalytic variable (activator), a slowly changing and localized inhibitor, and a very fast and highly diffusive variable that provides the long-range interaction. The extremely rich plethora of patterns is classified according to their symmetries, capitalizing on the inversion symmetry of the model. The simpler case of the bistable system (with no inhibitor) exhibits a vey high sensitivity to initial conditions that leads to large multiplicity of stationary patterns. The effect of the parameter that defines the system stability (oscillatory, excitable, or bistable) is investigated, in the three variable model, either by using the same initial conditions for all simulations or, in an "experimental mode," by stepping up or down the parameter. Patterns on a disk may be classified as circular, like stationary or oscillatory or moving (inwards or outwards) target pattern, rotating patterns, like stationary or oscillatory or moving spiral waves, and other patterns. Successive bifurcations, with changing parameter, reduce the system to states with lower symmetries and to asymmetric or even chaotic motions. Motions on a square are similar to those on a disk and include target-like pattern, propagating pulses, and oscillating or breathing stationary pulses.