We'll discuss growth patterns in the plane. The most famous such model is DLA where new particles arrive via a Brownian motion and get stuck once they hit an existing particle: it forms the most beautiful fractal patterns (pictures will be provided). Despite this, DLA is actually fairly poorly understood and we will quickly survey the existing ideas (many of which are due to Harry Kesten). I will then present a new type of growth model that behaves similarly (many more pictures will be shown) and which can be very precisely analyzed (in certain cases). No prior knowledge is necessary, I'll explain everything from first principles.