"A real snowflake is not perfectly symmetrical - but you get the idea". Yes, that picture's a wonderful but not perfect example of the point in the text: "If I give you a picture of one of the six spikes, you immediately know what the whole thing looks like: simply fit six copies of the spike around a common centre point, and that's your snowflake". On examination those spikes differ from each other in the size and disposition of the offshoots they bear, but not haphazardly. For example the "south east" spike sports offshoots whose length is clearly limited by those on the adjacent two spikes, that is until it reaches out far enough into sufficient space to branch out on its own more freely. The southwest spike is similarly having a crowding effect on the east spike, as does its colleague the northeast. So it's not one but at least two you need to predict. This triple may explain the overall hexagonal structure. What's the law here? Maybe that objects - gases, crystals, tree branches - expand into the available space, limited by neighbouring expansions. What rules do they use to accomplish this? Those may be along the lines of Fibonacci and related sequences which essentially describe asymmetric, not symmetric, division and expansion.