spherical random path generator sculpture

Hi there,

I know very little about electronics and so would be very thankful for any advice.

I would like to build a sculpture based on a sphere with a structure similar to the image link below:

**broken link removed**

I would like to have L.E.Ds that light up in turn and create the illusion that an pulse is randomly wandering around the sphere from junction to junction.

So when the pulse arrives at a 'Y' junction, having traveled say from the bottom to the center it randomly goes left or right. Once it has done this the same process is repeated over and over again.

Is this possible?

I hope this makes sense,

cheers,

greenlegs