This demonstrates a dynamic environment map, using the excellent three.js. Different faces of the map use different textures: just two images in this simplified version. You can force a remap by clicking here.
The scene consists of three objects:
It also demonstrates what I think is a bug in three.js. Where a patch is not applied the sphere shows an environment map with all textures the same: they all have the same texture as the cube face most nearly pointing to the camera: that is face 5 or the 'back' face.
Click here to toggle the effect of the bug. (Patch applied, working as intended) (NO patch applied, showing bug)
The bug was that for some reason the matrices on the CubeCamera's internal cameras were not correctly updated.
The full version has more interesting dynamic textures, but this simplified version makes it easier to see what is going on.