Exploring infinite processes through Logo programming activities of recursive and fractal figures

Logo is a powerful language that allows for explorations of advanced mathematical topics such as that of infinite sequences and series. In this paper, I revisit the design of a computer microworld for the exploration of such infinite processes. In this microworld, students of different ages (some as young as 14) constructed and investigated graphical models of infinite sequences of the type {1/k n}, as well as fractal figures, conceived here as “limit-objects” of infinite graphical sequences, such as the Koch curve. Students gave meaning to the processes under study by coordinating the visual and numeric outputs with the symbolic code contained in the procedures that they themselves had written.