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2022-08-15 22:45 Arno  
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here's my attempt to showcase the variants of the small 4-fly dfs from 'funny flies 16/17'.  
  
mirrored pairs are shown when possible; the magic wall forms the diagonal mirror line.  
basically, these variants show the possible positions/directions for the supporting (spinning) flies at the top and bottom of the "dancing couple". since there are two of them, and they spin independently, even more combinations can be created than shown here.  
  
a short explanation of the numbered pairs:  
1: the "base" dfs with fflies in the middle.  
2 and 3: variants of 1, with different supporting top fly.  
4 and 5: variants of 1, with different supporting bottom fly.  
6: the "base" dfs with bflies in the middle.  
7: variant of 6, with different supporting top fly.  
8 and 9: variants of 6, with different supporting bottom fly.  
  
except for implied combinations (e.g. the top fly from 2 with the bottom fly from 4...), these should be all possibilities, since i excluded others based on a test.  
  
by the way, does this dfs already have a name? if not, i thought of "the hug" because of the 1 frame break which the dancing couple makes just when both flies are next to each other... :-)

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2022-08-16 01:11 dustin  
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very nice compilation  Arno ! and i also like your name suggestion! :d

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2022-08-16 01:32 dustin  
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hmmm... but i think 8 should have a mirrored pair. i checked it and it worked! :)

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2022-08-16 08:44 Arno  
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ah, i must have missed that... cave is corrected. i also doublechecked number 2; this still seems the only variant without mirror counterpart.  
  
sorry for deleting demo's. :-)

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2022-08-16 12:44 dustin  
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well the cave wasn't too hard anyway :d  
  
yes, 2 shouldn't have a mirrored pair because the top bfly is at the firefly's top-right side, which means that column-wise scanning would scan the ffly first :)  
  
all in all i calculated 27 possible hug-dfs versions:  
  
with firefly huggers:  
top blocker: 3 variants (1,2,3), one of which doesn't have a mirrored pair  
bottom blocker:3 variants (1,4,5) with mirrored pair  
all in all: 2x3x2+1x3x1 = 15  
  
with butterfly huggers:  
top blocker: 2 vars (6,7) with mp  
bottom blocker: 3 vars (6,8,9) with mp  
all in all: 2x3x2 = 12  
  
total: 15+12 = 27 vars

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2022-08-16 12:49 dustin  
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i forgot to mention that there might also be vars where only the mirrored version works. but such a dfs cannot exist imo:  
  
the only possibility for such a hug-dfs would be that the right blocker is at the hug-fly's top-right side, then move down and block the hug-fly. but because of cso this would mean that the blocker blocks the hug-fly two frames in a row so the dfs would break.

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2022-08-16 13:12 Arno  
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nice calculation! :-D  
  
and yes, i also thought about variants where only the right side of the mirror would work, but i indeed excluded these possibilities by testing and observing that the dfs broke. :-)