From the picture below, it seems that new leaves are formed something like this (if you imagine the plant as a regular, 12 hour clock):
new leaf at 12 o'clock, then at 7 o'clock, then at 2 o'clock, then at 9 o'clock, and so on.
I imagine it could be some things as simple as 'always add 190 degrees'. Are the exact rules for this documented somewhere for various plants?
The disposition of the leaves in your picture is not as simple as it seems. That's a spiral phyllotaxis, which can be very complicated.
The plant in your image is a houseleek, a plant from the Genus Sempervivum. In those plants, according to Jeremy Burgess (Introduction to plant cell developmnent):
... leaf primordia are separated from each other in an angular arc that approaches 137°.
By the way, 137° is (almost) the golden angle (φ).
Here is an image explaining the phyllotaxis of Sempervivum (from Burgess, 1989):
Even more interesting is the pattern made by the 137.5° GA spiral of Aloe polyphylla:
Sometimes this can produce invisible spiral patterns, a phenomenon called parastichy:
PS: I know that this is off-topic, but I'd like to share this video from Cristóbal Vila, which deals with Fibonnaci sequence, golden ratio and golden angle in nature. Look at the flower disposition at 1:44 : https://www.youtube.com/watch?v=kkGeOWYOFoA
