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H. G. Muller wrote on Thu, Jun 25, 2020 08:16 AM UTC:

The X suffix for 'extended' atoms was somewhat of a hack, to quickly solve a problem that occurred. I am not very happy with it, expecially since the amount of extension is dependent on the lateral step of the atom. I don't like the coordinate notation (1,4) much either. For one, I would like to reserve the parentheses for grouping modifiers, or just for the purpose of enhancing readability. Brackets like [1,4] would look better, IMO.

The dilemma here (as always) is whether we want to go for something universal, which requires an infra-structural investment (in this case the brackets and the comma) to make it work even in simple cases, or use an ad-hoc solution that captures a few cases in a very simple way (such as the X suffix), but offers no universal relief. BTW, the suffix solution could be made universal by allowing repeated suffixes, like in Roman numerals vs arabic digits. Depending on the frequency distribution of the numbers encountered in practice, one system or the other would on average give the most compact representation. (Or, to say it differently, run-length encoding only gives compression on texts that frequently contain long repetitions of the same character.)

The X system is lame, however, and I now regret having implemented it. Perhaps it is not too late to change it. A better solution of this type would be to have two suffixes: X for adding an H step, and Y for adding an A step to any given atom, and allow repetition of as many X and Y as is needed. Primitive, but more consistent than the current X suffix. And HXX for [0,9] is still only 3 characters vs 5, HXXX for [0,12] is 4 vs 6, only after HXXXXX for [0,24] the coordinate system starts to need fewer characters. And would we ever want to describe pieces that leap more than 24?

The atom table would then become (1 quadrant shown): 

HX CX ZX GX DYY
DX NX AX CY ZY FYY
WX FX DY NY AY
H  C  Z  G
D  N  A  Z
W  F  N  C
#  W  D  H

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