Somehow I managed to miss this video when it first posted back in March  of a neodymium iron boride magnet being surrounded by Silly Putty filled with iron oxide particles.
I see a couple of items worth commenting on. First, this all occurs on a less-than-smooth surface. That allows the magnet to rotate into the magnetorheological material, further giving the impression that the grey matter is alive and intentionally swallowing the magnet. But secondly, I am fascinated by how the FeO2/Dow Corning 3179 Dilatant Compound composite sticks to the surface of the magnet and doesn't really flow over it. Look at the video starting at about 10 seconds where the bottom of the goop is starting to rise up. It rises up, but in a rotating fashion, indicating that there are strong levels of adhesion at the surface of the magnet that is preventing it from flowing upwards along the surface. Where ever a given volume of material first makes contact with the magnet, that is where it will stay. Silly Putty by itself has very little tackiness and adding inorganic fillers will do nothing to change that, so the adhesion is a direct result of the strength of the magnet and the ability of the iron oxide particles to stress the Silly Putty.
The Silly Putty by itself is not attracted to the magnet, only the particles in the putty. The iron oxide particles, without being covalently bonded to the polymer, are able to apply enough stress to the Silly Putty to get it to move it along with them. This is a fine balancing act. If the force tries to move the putty too quickly, the putty won't be able to relax and little or no fluid motion will occur. It is only by allowing the entanglements in the putty to slip past one another (a slow process) that fluid motion occurs, and this motion will only occur at low stress rates. So while this demonstration works with these small permanent magnets, the results would be far less interesting for a strong electromagnet or possibly if high levels of iron oxide were mixed in.
But the greatest part of the balancing act is that the strong attraction between the iron oxide particles and the magnet is enough to get the Silly Putty to flow towards the magnet, but then stop flowing once it makes contact with it. I wonder over the range of concentrations over which this could occur.
 Kinda neat how that opening gives you the impression that I am more in the loop on these kind of things than I actually am.
 Leave the putty around the magnet for a long enough time and all the iron oxide would end up at the surface of the magnet and the remainder of the putty would have returned to its original color.