I've been thinking a little about these pieces, as well as the ‘helical’ crooked riders that Fergus suggested here.
It seems to me these are instances of (modulo one detail, which I'll get to below) the same pattern that brought us the ‘modern’ elephant — i.e. the FA — wrt the original 2‐space‐diagonal Elephant: we have an original piece with a non‐coprime (as Charles Gilman would have it) leaping move and fill in the gap.
As such, it seems to me that, in line with mỹ initial intuitions in both cases, it's probably clearest imo to think of the helical pieces and the 2.bent riders as variations on respectively and lama–osprey/zephyr–ostrich rather than totally distinct pieces (or for that matter as immediate bishop/rook/queen or manticore/griffin derivatives)
The main difference between these and the modern elephant is that, the original piece having riding tendencies already, it seems more natural to have the ‘modern’ component be lame/stepping rather than leaping as in the elephant case. The ‘running’ elephant (as coined in the previous comment) would be a lame/stepping FA, or equivalently a B2.
I wonder whether there are many other piece‐types for which ‘running’ (or indeed ‘modern’) subspecies are useful? Running dababba‐/alfil‐/alibabariders, skip‐riders (panda/bear/harlequin), and slip‐riders (Tamerlane picket ⁊ al.) are just rooks/bishops/queens (and ‘modern’ ones the same but less blockable and this probably OP); running crooked dababba‐/alfil‐/alibabariders likewise reduce to lame contrabrueghels/‐proselytes/‐halcyons. Running alpacas/quaggas/okapis/⁊c. (i.e. alternating pairs of orthogonal and diagonal steps) — straight, curved, or switchback — are perhaps more promising, and not, imo, all too exotic; running nightriders/roses/nightfliers/‐sidlers/‐ladies, the same but starting with a single step, also bear considering, even if not strictly non‐coprime to begin with.
There's one other curious difference between the bent and crooked members of this family: as described, the bent ones can only make the remaining part of its move if the non‐coprime part is made in its entirety (i.e. the ferz/wazir move is to the exclusion of the rook/bishop one), whereas the crooked pieces must make both componets regardless (this difference is more pronounced when considering the time‐reversed versions, i.e. running contrazephyr/contraproselyte/⁊c.: the former is committed to a full alfil leap if it starts with a non‐zero rook move — the alternative would be the existing fimbriated griffon — while the latter has to make its final turn and ferz step lest it become equivalent to the aforementioned running crooked alfilrider (as well as curtailing its first, rather than its last alfil run; the pair with one time‐inverted but not the other is also possible, if a bit obtuse)). I'm not yet sure how best to describe that difference without special‐casing.
tl;dr: new category of pieces (tenatively named ‘running’) combining recent suggestions, with some further suggested extrapolations and some unanswered questions re semantics.
Assuming anyone actually makes it through this, any thoughts?
I've been thinking a little about these pieces, as well as the ‘helical’ crooked riders that Fergus suggested here.
It seems to me these are instances of (modulo one detail, which I'll get to below) the same pattern that brought us the ‘modern’ elephant — i.e. the FA — wrt the original 2‐space‐diagonal Elephant: we have an original piece with a non‐coprime (as Charles Gilman would have it) leaping move and fill in the gap.
As such, it seems to me that, in line with mỹ initial intuitions in both cases, it's probably clearest imo to think of the helical pieces and the 2.bent riders as variations on respectively and lama–osprey/zephyr–ostrich rather than totally distinct pieces (or for that matter as immediate bishop/rook/queen or manticore/griffin derivatives)
The main difference between these and the modern elephant is that, the original piece having riding tendencies already, it seems more natural to have the ‘modern’ component be lame/stepping rather than leaping as in the elephant case. The ‘running’ elephant (as coined in the previous comment) would be a lame/stepping FA, or equivalently a B2.
I wonder whether there are many other piece‐types for which ‘running’ (or indeed ‘modern’) subspecies are useful? Running dababba‐/alfil‐/alibabariders, skip‐riders (panda/bear/harlequin), and slip‐riders (Tamerlane picket ⁊ al.) are just rooks/bishops/queens (and ‘modern’ ones the same but less blockable and this probably OP); running crooked dababba‐/alfil‐/alibabariders likewise reduce to lame contrabrueghels/‐proselytes/‐halcyons. Running alpacas/quaggas/okapis/⁊c. (i.e. alternating pairs of orthogonal and diagonal steps) — straight, curved, or switchback — are perhaps more promising, and not, imo, all too exotic; running nightriders/roses/nightfliers/‐sidlers/‐ladies, the same but starting with a single step, also bear considering, even if not strictly non‐coprime to begin with.
There's one other curious difference between the bent and crooked members of this family: as described, the bent ones can only make the remaining part of its move if the non‐coprime part is made in its entirety (i.e. the ferz/wazir move is to the exclusion of the rook/bishop one), whereas the crooked pieces must make both componets regardless (this difference is more pronounced when considering the time‐reversed versions, i.e. running contrazephyr/contraproselyte/⁊c.: the former is committed to a full alfil leap if it starts with a non‐zero rook move — the alternative would be the existing fimbriated griffon — while the latter has to make its final turn and ferz step lest it become equivalent to the aforementioned running crooked alfilrider (as well as curtailing its first, rather than its last alfil run; the pair with one time‐inverted but not the other is also possible, if a bit obtuse)). I'm not yet sure how best to describe that difference without special‐casing.
tl;dr: new category of pieces (tenatively named ‘running’) combining recent suggestions, with some further suggested extrapolations and some unanswered questions re semantics.
Assuming anyone actually makes it through this, any thoughts?