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This paper describes how was implemented a computer simulation of an ionizing radiation detection system similar to those found in traditional modern Physics laboratories. The simulation models a system with a 'source' of photons of arbitrarily chosen energies, a 'detector' that behaves like a Geiger-Müller detector and the effect of different attenuating materials with variable thickness inserted between the source and the detector. Details of the calculation of the radiation attenuation using data from the United States National Institutes of Standards and Technology (NIST) database are presented, and employed to explore characteristics of the radiation interaction with matter, from cross sections to statistical fluctuations. Examples and suggestions of exploratory activities are also presented. The simulation was used with two groups of about undergraduate students from a distance learning Physics course at UFSC in the beginning of 2011, along with the execution of the real experiment. Throughout the text, comments on the motivations and problems of using simulations in this context are discussed. Finally, it is discussed how this work relates to the main goals of introductory Physics laboratories, according to an American Physical Society Committee specifically created to evaluate that. [ABSTRACT FROM AUTHOR]