As an experiment, I just spray painted 66 magnet spheres in half, to make a physical display in 5 minutes. I manually rotated the sphere into position and it holds the image.

https://gist.github.com/unrealwill/b8f585758880009113805bd95...

Small spherical magnets are quite cheap.

There is hope of physically moving them if you put each sphere into a 3d-printed countersink hole over some metal sheet (so that the magnet is hold in place against the plastic), moving a electro-magnet head over you can rotate the magnet, like a scaled-up version of a 2d magnetic tape.

You may even create a Ising model if you put magnets too close to each other.