The reaction 2CO+O2→2CO2 on Pt nanoparticles was studied using the Monte Carlo simulation method. The CO2 production rate depends on the CO partial pressure pCO, and presents two critical points ζ1 and ζ2 that define a reactive zone. The production of CO2 is zero outside this interval. The surface of the catalyst, in steady state and within the interval (ζ1, ζ2), is partially covered with particles of CO and O. The adsorbates are arranged on the surface forming fractal structures. This work determines the Hausdorff dimension of the adsorbate distribution in the reactive zone as a function of CO partial pressure when CO desorption and diffusion processes are considered.