Having a play with noise based curve growth with self avoidance.
Thanks to cgwiki for the original source file: tokeru.com/cgwiki/index.php?title=HoudiniDops
and some great info and sample files on odforce: forums.odforce.net/topic/25534-differential-curve-growth/

I used pop streams to control the point velocity at the base of the shape otherwise it goes crazy. The mesh was exported as an alembic (7GB!) and rendered in V-Ray.

Houdini Differential Curve Growth from Hugh Johnson on Vimeo.

2nd version:

I wanted to calm the movement down compared to the previous test. So I keyed the pop drag from 1 to 10 as the shape growth progresses to slow the growth down.

I also changed the settings on the POP interact so that it wouldn’t repel the other points with as much force, The Position Force is set to 1.5 and the Velocity Force is at 1.

For this test I wanted to create a shape with a lot of intersections and came up with this.

After the curve is generated in pops, I use another resample to smooth the line again, and then use a poly wire node to generate the geometry on the curve. It’s then exported as an alembic and brought into Max to be rendered with Vray. Before rendering I subdivide the alembic again to get rid of the occasional poly spike made by the Poly Wire node.

Houdini Differential Curve Growth v02 from Hugh Johnson on Vimeo.