A Recursive Triangular Subdivision of a Square Generating a Fractal Structure

This paper presents a simple geometric construction that generates a fractal through recursive triangular subdivision, ideal for classroom exploration of recursion and fractal geometry. Beginning with a square divided by a single diagonal, each resulting triangle is subdivided by joining its vertices to its centroid, producing three smaller triangles. Repeating this process indefinitely yields a self-similar structure with exponentially increasing complexity. We describe the construction formally, establish a closed form for the number of triangles at each stage, compute perimeter growth, and discuss its selfsimilarity, area preservation, and unbounded perimeter growth.