A novel problem, of diffusion resistance in porous particles that catalyze kinetically unstable reactions, is introduced, analyzed and simulated in order to unveil the possible spatiotemporal patterns in the direction perpendicular to the surface. Pore-diffusion resistance is a core problem in chemical reaction engineering. The present problem is described mathematically by three variables: a very-fast and long-ranged pore-phase concentration, a fast and diffusing autocatalytic surface species (activator) and a slow and localized surface activity. Unlike homogeneous models of pore disfussion resistance, in which instabilities emerge only with strong diffusion resistance, the present model exhibits oscillatory or excitable behavior even in the absence of that resistance. Patterns are generated by self-imposed concentration gradients. A detailed kinetic model of a simple but reasonable reaction mechanism is analyzed, but the qualitative results are expected to hold in other similar kinetics. The catalyst particle is a three-dimensional system and it may exhibit symmetry-breaking in the directions parallel to the surface due to interaction between the fast diffusion of a fluid-phase reactant and the slow solid-phase diffusivity of the activator. A thin catalyst can be described then by a one-dimensional reaction-diffusion system that admits patterned solutions. We point out this possibility, but refer to another work that investigates such patterns in the general framework of patterns due to interaction of surface reaction and diffusion with gas-phase diffusion and convection.