Fractional Brownian Motion

Grasshopper
1

Hi everybody,

Below, you can see two images I created in Houdini.
The one on the left shows a random point population inside a mesh volume, where the point positions haven’t been relaxed.
The image on the right shows the same point population, but the point positions have been altered with fractal browning motion to form noisy point clusters.

fbm
fbm1420×703 212 KB

I’m interested in re-creating this, the fractal browning motion in Grasshopper, but since Houdini is pretty intransparent on how things work under the hood, it kinda hard to see what a component does.
The positions of the points are passed to an anti-aliased noise component that generates anti-aliased (fractional brownian motion) noise by using the derivative information of the incoming position to compute band-limited noise. The default output range of noise is -0.5 to 0.5. (cf. Anti-Aliased Noise)

Any ideas? Tips?

2

There’s this


But it needs numpy

3

Thanks @Graham, but that seems way complicated. I’m looking for alternatives (if there are any) to achieve the same or a similar effect, of random points forming regional clusters.

4

Hmm a bit of googling suggests that 2D Fractional Brownian Motion has been used for terrain generation - I wonder whether there are any other terrain generation techniques which could be used for this purpose where the z component gets mapped to the point density?
Do you want it to be static or time-varying?

5

Simply static is good enough for me.