In this work he describes the constitution of the fractal object in a teaching experiment in which 60 seventh grade students (11-13 years old) participated, from an educational institution in Bogotá, Colombia. We designed a sequence of teaching episodes based on a phenomenological proposal of the fractal object that includes five metal objects that make up the concept: Self-similarity, recursion, scale factor, infinity, and fractal dimension. In the results, we identify the importance of experimentation to generate action schemes in students; we also emphasize the categorization of these schemes through mathematization.