simple curves controlling complex shapes


In the figure above, the two curves on top fully represent the more complex shape on the bottom. This was done by proving that simple curves, known as Bézier curves, are a type of fractal, meaning that these curves are made up of smaller copies of themselves. This enables us to put more than one of these curves together and represent a more complex fractal represented by sets of Bézier curves, allowing us to represent complex fractals using simple curves, and to animate complex fractals by making simple changes to the Bézier curves.