The fractal nature of Bezier curves

Fractals are attractors - fixed points of iterated function systems. Bezier curves are polynomials - linear combinations of Bernstein basis functions. The de Casteljau subdivision algorithm is used here to show that Bezier curves are also attractors. Thus, somewhat surprisingly, Bezier curves are fractals. This fractal nature of Bezier curves is exploited to derive a new rendering algorithm for Bezier curves.