Lindenmayer systems were originally conceived by Hungarian biologist Aristid Lindenmayer while studying algae growth. He developed L-systems as a way to describe the growth process of algae and simple plants. The result was a type of language in which the recursive and self similar properties of organism growth can be expressed. Indeed, L-systems can be used to generate natural patterns, but well known mathematical patterns can also be written as an L-system. In this article, I will explain different flavors of L-systems, and I will demonstrate them by rendering 2D Lindenmayer systems and 3D Lindenmayer systems using turtle graphics.