The effect above is achieved by mapping the image onto the faces of cubes that tessellate the viewing volume. The extents of the cubes vary. When viewed head-on under orthographic projection, the viewer sees the image unchanged.

There are a few things here that are interesting to consider:

• The tessellation above is randomized (try reloading the page). However, how should the cubes be arranged? Purely random arrangements without any constraints may not be visually pleasing.
• You can transform between the two head-on perspectives in any arbitrary way. The one above is composed of pure rotations about two axes. However, notice that no more than two faces of the cubes are ever revealed (as is also the case in Koy's original). I found this makes the overall effect much more immersive — the viewer only sees the source and the destination faces without any distractors.