Sure...

It all runs using dynamics - it creates IK handles for each joint, and then constrains these to active rigid bodies.

Each of these bodies is affected by gravity, but it's the 'attractor' field that does all of the work.

The attractor field is initially positioned in the same place as the IK Handle - but it is parented to two joints up the chain from the join that the IK handle is attatched to. This means that the joint with the IK handle is always trying to get back into a certain position relative to the joint above it.

The script doesn't actually use parenting like I've described - it creates other cubes which it point and orient constrains, and then parents to these - this was because the guy I originally wrote this script for couldn't change his joint hierarchy....