Once I'd bit the bug for randomness, I tried to add lots of less obvious randomness to the card. The orientation of each piece, for example, is largely random, although some pieces, such as the compass, always have a fixed orientation, while others like the letter tiles can't vary too much.
The material that the desk is made out of is randomly selected from a group of options. Less obvious is that the direction of the sun is different on each card, time is split into 54 sections, from an hour after dawn to an hour before dusk, and each time is assigned to a random card. The effect is subtle, and while this isn't useful, it gives an extra bit of variations to the images.