C and Z are equivalent to original letters L (Long Knight) and J (Jump) which are now less commonly used in the world of chess variants.
There are directional modifiers, composed from the letters f, b, l, r, v, s and h (forward, backward, left, right, vertical, sideway and half).
The best known example of this is the cannon of Chinese chess, which moves as a rook but can only capture after jumping one occupied square.
In a later article on bent riders Betza introduced a way to glue moves corresponding to different board steps into a single trajectory: t[FR] would mean start as F, then continue as rook (in the outward directions).
This makes the hopper modifiers more similar to m or c, specifying what happens on the target square of the move leg they apply to.
The difference between p and g is that the latter turns a slider into a leaper after the step, so that it would be forced to end its move immediately behind the piece it hopped over.
This way a chu shogi lion can be written as KNADcaKmcabK, where the KNAD direct leaps to the 24 possible target squares are supplemented by caK for the hit-and-run and double captures, and mcabK for the rifle captures and conditional turn pass.
Some convenience extensions of XBetza are e as extra modality for en passant capture, O as an atom to specify castling, (the range indicating how far the king moves), and i as a modifier for indicating moves that only virgin pieces have (so that the complete FIDE pawn becomes fmWfceFifmnD).
The j modifier, when applied to a slider atom (B or R), for which the original meaning makes no sense, is used to indicate the first square of the path is skipped over, ignoring its contents.
the - operator (i.e. repeated continuation in the same direction), which can also be applied to a parenthesized expression that already describes a sequence of moves.
This can be used to resolve the ambiguity in nN of the original system, and re-interprets this latter notation as a multi-path piece that is allowed to make the move if at least one of the shortest possible paths (measured in K steps) is unblocked.
Bex notation also introduces a way to describe exotic effects as a step in a longer move.
A very elaborate proposed extension of the original notation borrowed the idea of chaining simple moves into longer paths with the aid of a hyphen operator, where each of the legs can be written using the full power of the original Betza notation.
Explicit specification of the atoms of each leg as in Bex and Betza 2.0 makes these notation easier to interpret.
On the other hand, Betza 2.0 and Bex are only easy to read when individual (multi-leg) move groups are parenthesized, because intuitively concatenation couples stronger than a hyphen (compare KNADcK-aKK-bK to KNAD(cK-aK)(K-bK)).
A quirky feature is that it allows modifiers on the range itself, to overrule the defaults of the chaining operator that is spread around by this exponentiation.
E.g. Nrf7 would mean N-rfN-rfN-..., a repeated knight step that deflects right-forward, i.e. a move of the circular slider qN.
It is a special case of the Cartesian coordinate plane, in which the Origin is always the current location of the piece.