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Charles, your suggestion of considering games with shogi drops added as a
cluster category got me thinking about mutators, and whether mutators
indicate clusters or something else. 

My first thought was no, they don't form clusters. It's like
dimensionality, it's not enough to determine a cluster of similar games.
Trivially, not all 2D CVs are in the same cluster. I considered the 2D and
3D versions of my shatranj game, and your current 3D game, and figured it
was apparent that 3D Great Shatranj is closer to Great Shatranj than it is
to Redistribution 3d Chess. Consider shogi, chessgi, and bughouse... yeah,
well, there is a bit of likeness in those games...

Second thought was that, yes, that is a very strong similarity. Consider
that the conceptual space of chess variants has more than 3 dimensions, and
I don't even know what to call all the ones we are using right now. I
considered that 'viewing angle' might be important to what made a
cluster, and that you could see things in different ways. But then consider
the line between GtS, 3DGtS, and Hyperchess. That reasoning would cluster
Great Shatranj [2D] with Hyperchess [4D]...

That line of thought took things to mutators, or conditions, or elements,
something that could apply to many different individuals, groups, and
clusters. Then I considered that what I was looking at was an evolutionary
taxonomy of CVs, so things like dimensionality and the shogi drop rule
represent environments that games must adapt to, to be able to exist in
that specific area of chess. An environment can tentatively be described as
a condition that can be applied to a whole range of games with success.
Like Alicing, which is its own environment on the fringes of neighboring
dimensions. The original Alice took chess to a limited 3D game, sort of
straddling the border between the two dimensions. But you can alice any 2D
game, or 3D, 1D, or 4. So third thought is no. You have described an
environment, not a cluster.

Do you agree this is a valid and useful distinction, or do you prefer
something else?