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2022-08-12 17:15 dustin  
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these dfs are extensions of funny flies 18. the ff and the bf version are closely related, so i'll explain only the ff dfs:  
  
there are two ff in the middle forming a vortex, and another ff at the top-right and one at the bottom-left which are freely spinning. let's call these four flies the "jailers". the other three flies, the "jailbirds", are moving on the edge of the same 4x3 rectangle. the jailbirds are alternately influenced by the jailers so they can't escape their rectangular jail.   
  
short loop = 4, long loop = 12 frames.  
  
funny flies 18 was the same but with only one jailbird.  
  
two different versions with two jailbirds also exist: their distance can be either 4 or 6.  
  
note that the 4x3 rectangle has only 10 places but the jailbirds still take 12 frames for one complete loop because they stop twice for one frame during their trip.  
  
further extensions don't seem to exist; the jailbirds must have distance 4 because with distance 2 they would influence the jailers and the dfs would break.

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2022-08-12 17:23 dustin  
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ah, i was wrong about the version with 2 jailbirds. there's only one such version (with distance 4). the distance of the jailbirds must always be (a multiple of) 4 because that's the period of the top-right and bottom-left single ff.

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2022-08-12 22:51 Arno  
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so your brother's algorithm has run for 7 flies?  
  
and are the searches for 3- to 6-fly dff/dfs now done? ;-)

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2022-08-12 23:24 dustin  
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 Arno , no, unfortunately not. the state is still the same as before. it was my human brain which came up with this extension. not by brute force, but by good-old human brain strengths: pattern recognition and extension of newly learned principles ;)