This is a classic effect in Houdini. I stumbled upon it over at Odforce. As you will see from that thread there are many elaborate ways of achieving this kind of growing curve. However we’re gonna build a very simple version which yet offers a nice way of controlling growth by passing along values from a noise field. Hope you have fun!
Growth along surface
As the Point Relax SOP offers an additional input for a surface to adhere to it is very straightforward to let the differential growth happen on a gven geometry. All we have to do is pipe the geo that we want the growth to happen on into the Relax SOP’s second input, tweak our simulation parameters and – boom, done. Growth on a surface. And because we love you (and Houdini) here’s a rendering and the corresponding setup using that exact technique: