On the base of some dilation invariant Roman mosaic rosettes, found in Merida (Spain), simple examples of finitely generated groups are considered. Some of the groups considered are abelian. In the latter, the meaning of torsion coefficients and Betti number appear in a simple and intuitive way. The computational simulation of those rosettes is also treated. Executing these simulations increases the interest of students in form preserving transformation when they are applied to rosettes generated by repeated dilations.
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