Jack's question of where "emergence" fits in Pattern Language
In natural systems work by connecting opposing matched parts of things, like two hands put together with a firm grip for a simple task or to convey deep feelings of trust, are a "perfect fit" with emergent properties. All natural systems work by connecting opposing parts that fit and work together. A door and door frame are receptors for each other, as are roots and leaves etc. Numbers in equations only measure one dimension, not "organization" of "matched parts" that "fit".
@Jackpark, Hi! Somehow this got long, but I think it's responsive. I just picked up your related 12/20 and 12/29 comments on where to put the focus, on the parts or the relationships. It does indeed appear that interesting emergent systems of relationships come from the organization of parts of things that develop somewhat mysteriously. It clearly develops using the parts but doesn't seem to really be coming from them. This really is one of the big questions that people have been going back and forth on, searching for a way to address.
How I address it is to start with a kind of vague idea of the parts having properties letting them link together to go with my vague idea of the organization of the system that emerges from how the parts somehow connected. For machines we can picture it as "matching receptors" or "links" of one kind or another, a wheel/axle pairing, a +/- charge match, a ball/socket fit, or other combinations of "co-operating parts". In machines they're simple enough for us to predict and control. In complex systems one is often left with "I had no idea at all that things could work that way". For complex systems you don't know what's working, so we fall back on the idea of "relationships". It's a vague term for things having found some way to work, but still refers to parts having come into an organized arrangement.
Generally you can confirm that presumption a bit at a time, studying the variety of complementary attributes that the parts of real working complex systems appear to need for fulfilling their roles, looking for patterns. I generally find the time the patterns of connection are clearest is when they're changing. In groups of people various people could fulfill various support or leadership roles. The 'chemistry' of the group may use different people in different ways too, depending on the environment they're put in, and not emerge till the right people find their right roles in that group and situation.
For example, if the business project for the week is to rearrange the whole workshop, maybe the best person to have the broom is not the janitor, maybe it's the CEO, for that week the janitor's job might be to engineer the move and the CEO's to stand around avoiding any real work. Both might very well love the role reversal. It would give the leadership roles to the people who better understand the operational tasks, leaving the CEO to "walk around" picking up on small tasks, taking deliveries, and having the time to notice things he left out of the plan... etc.
Of course unless you have a fairly intimate view of how a particular system self-organizes to use "reimagine the use of all its parts" you just don't see what does it at all. Why some teams work beautifully and others with the same talents don't is just mysterious. When you're studying some particular system you start with finding out all you can, either about the parts or the relationships. Even if I do figure out how the patterns of some system developed, I know I may not find any way to change them, or even be able to communicate what I find. Still, I rely on the principle that "its understanding the system that lets it work" and have confidence that the effect of anyone observing how things work will "rub off" to make things work better.
When I do field studies of a system whether it's of how to use extra help getting dinner on the table, or why social organizations committed to the same purposes can't work together, or any other interesting problem, I basically do two things to be a good systems observer. One is to taking as broad a view as possible, picking up both general and detailed patterns of things, letting my attention be drawn to things of interest, collecting documentation and records, collecting stories, etc. all while maintaining as broad a view as possible, so I can recognize change, as if taking regular snapshots of the whole arrangement.
Then to really study how the organization works and why the parts fit as they do I look for unplanned developmental changes, large or small, identifying the spontaneous emergence of new kinds of relationships. If you catch them in action you can much better trace where they originally came from and how they developed, noticing how the parts fit, and the changing relationships ripple through the whole system, either as they are "beginning to click" or "falling apart", etc.
Ideally, a person thinking about a system like that would catch on with at least a few others, and regular conversations would spread that way of watching and learning as people got better and better at seeing how things would fit.