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a race of slow 7-fly dff:s
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by
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nesdori
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NESDORI                           2022-08-30 10:37
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RACE TIME! A NEW UNIQUE 7-FLY DFF WHICH TAKES 17 FRAMES TO MOVE ONE STEP AND A NEW 7-FLY VERSION OF THE "25-FORMATION" DECIDED TO HAVE A RACE. 25-FORMATION OF COURSE GET A LITTLE HEAD START. TO MAKE THINGS MORE INTERESTING, THE FINISH LINE IS DYNAMIC.  
  
BTW dustin, NOW THAT 7-FLY 25-DFF HAS TWO FREE FLIES THERE'S ONLY ONE PHASE OUT OF 25 WHERE ALL FLIES ARE NON-ISOLATED. THE ISOLATION HEURISTICS THEORETICAL SAFETY CONCERNS ARE "SLOWLY" BECOMING A REALITY :)  
  
SO FAR I HAVE FOUND 15 7-FLY DFF:S (10 OF WHICH ARE 2F+5B) BUT THERE ARE MANY FLY COMBINATIONS STILL TO BE CHECKED. I EXPECT THE TOTAL NUMBER OF 7-FLY DFF:S TO BE CLOSE TO 30.

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ARNO                              2022-08-30 10:41
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WOW! :-D

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DARKSTOORM                        2022-08-30 14:31
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ONCE ALL FORMATIONS GET SHOWCASED, WE DEFINITELY NEED ALL OF THEM IN ONE BIG CAVE AND GO CRAZY :D  
  
AND AGAIN, IT'S SO AMAZING HOW SIMPLE GAME CAN GET PRETTY COMPLEX :D  
  
WONDERING WHAT WILL BE THE NEXT DISCOVERY

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DUSTIN                            2022-08-30 15:48
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GREAT STUFF! :D  
17 FRAMES - THIS FITS WELL INTO THE "4N+1" SCHEME - A NECESSARY CONDITION FOR THE PRINCIPLE THAT SOME FLIES ARE INFLUENCED ONLY ONE PER SHORT LOOP AND SPIN AROUND OTHERWISE! I WANT TO ANALYSE THIS ONE AS QUICKLY AS I CAN :D

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NESDORI                           2022-08-30 16:54
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dustin, I HOPE YOU HAVE ENERGY TO WRITE DETAILED ANALYSIS FOR ALL OF US; I LIKE THE STYLE OF YOUR ANALYSIS :) I BASICALLY KNOW HOW THE FORMATION WORKS AND ANALYZING THIS WILL SURELY BE FUN :)

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DUSTIN                            2022-08-30 17:02
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nesdori, THANKS :) I TRIED TO SOMEWHAT COPY arno'S EXPLANATION STYLE ON THE HOMEPAGE DFF THREAD, MIXED WITH SOME OWN ELEMENTS :)   
  
MY FIRST RESULTS: INDEED 4 FLIES WITH MINIMUM INFLUENCE, ONE MORE BF WHICH ALSO GETS ONLY ONE INFLUENCE BUT NOT INTO THE MOVEMENT DIRECTION OF THE GROUP. TWO BF WHO ARE VERY BUSY. EVERYTHING ELSE LOOKS LIKE PURE COINCIDENCE. I DON'T SEE THE 3 BUSY BEES HERE.  
LONG LOOP: 51

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DUSTIN                            2022-08-30 23:01
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THE 17-FORMATION LOOKS TO ME JUST AS "ALIEN" AS CASSIOPEIA - IT SEEMS TO WORK COMPLETELY WITHOUT A VORTEX! :D

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DUSTIN                            2022-09-01 01:53
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ALRIGHT, SO HERE'S MY ANALYSIS OF THE NEW 17-DFF (THE LEFT ONE)!  
  
FIRST OF ALL, IT WORKS COMPLETELY DIFFERENT FROM THE 25-DFF - THERE'S NO SMALL ALMOST-DFF MOVING AROUND, AND ALSO, THERE'S NO VORTEX (WHENEVER A VORTEX IS BUILT, IT'S IMMEDIATELY BROKEN AGAIN!)  
  
INSTEAD, WE HAVE ONE BFLY MOVING THROUGH THE WHOLE DFF AND TAKING AND GIVING LOTS OF INFLUENCE, WHILE ALL THE OTHER FLIES WORK WITH THE MINIMAX PRINCIPLE, TAKING NO MORE THAN 1 INFLUENCE IN THE WHOLE SHORT LOOP!  
  
TO ILLUSTRATE THIS, I'M STARTING WITH A DIFFERENT PHASE THIS TIME (NOT THE ONE IN THE MAP, BUT 5 FRAMES LATER).  
  
IN THE FOLLOWING ASCII-ART I'LL USE THE FOLLOWING DESIGNATIONS:  
1-6 ARE THE SIX NOT-SO-BUSY FLIES WHICH ARE NUMERATED IN CAVE SCANNING ORDER (THIS ORDER WON'T CHANGE A LOT DURING THE SHORT LOOP). NOTE THAT 2, 5 ARE FFLIES AND 1,3,4,6 ARE BUTTERFLIES.  
THE LETTERS L,R,U,D ARE FOR THE SEVENTH AND BY FAR MOST INTERESTING FLY (A BFLY) WHICH I'LL REFER TO AS THE "BUSY BEE".  
  
LET'S GO! :D  
  
PHASE 1:  
......  
1...2.  
.....3  
..4...  
...5.6  
....D.  
IN THE FIRST FRAME, THERE ARE NO INFLUENCES AT ALL.  
  
PHASE 2:  
......  
.1....  
....2.  
...5.3  
..4.6.  
...L..  
NOW THE FUN STARTS. 3 INFLUENCES 6 TO MOVE FORWARD (ONE OF THE VERY FEW INFLUENCES WHERE THE BUSY BEE ISN'T INVOLVED!) SO THAT 6 INFLUENCES THE BUSY BEE TO ALSO MOVE FORWARD (SO ACTUALLY, THE BEE IS INDIRECTLY INVOLVED!). THAT'S THE START OF THE BEE'S TOUR THROUGH THE WHOLE DFF!  
  
PHASE 3:  
......  
......  
.1...2  
..5.3.  
.4.6..  
..L...  
THE BUSY BEE IS NOW INFLUENCED BY FFLY 5. NO OTHER INFLUENCES.  
  
PHASE 4:  
......  
.....2  
1...3.  
.4.6..  
..5...  
.L....  
NO INFLUENCES NOW.  
  
PHASE 5:  
......  
1...2.  
.....3  
..4.6.  
.U.5..  
......  
BUT THE BUSY BEE GETS NO TIME TO SPIN AROUND! NOW IT GETS INFLUENCED BY BFLY 4 TO MOVE UP FURTHER. NO OTHER INFLUENCES.  
  
PHASE 6:  
......  
.1....  
....2.  
.U.5.3  
..4.6.  
......  
ONCE MORE, THE BUSY BEE IS INVOLVED IN THE ONLY INTERACTION OF THE FRAME, BUT THIS TIME IN THE ACTIVE ROLE. IT MOVES RIGHT AND INFLUENCES FFLY 5 TO MOVE UP. THAT'S THE ONLY INFLUENCE WHICH THIS FFLY TAKES IN THE WHOLE SHORT LOOP, AND IT'S NECESSARY SO THE FLY MOVES UP WITH THE GROUP!  
  
PHASE 7:  
......  
......  
.1.5.2  
..R.3.  
.4.6..  
......  
NO INFLUENCES FOR ONE FRAME:  
  
PHASE 8:  
......  
.....2  
1.5.3.  
.4.6..  
..D...  
......  
NOW, HOWEVER, IT TURNS OUT THAT FFLY 5, WHICH HAS JUST BEEN FORCED BY THE BUSY BEE INTO A NEW 2X2 SPINNING SQUARE, NEEDS NEW SPACE AND THROWS 4 OUT OF ITS LOOP. SO 4 MOVES UP, AND ALSO FOR THIS FLY, IT'S THE ONLY INFLUENCE IT TAKES DURING THE WHOLE SHORT LOOP OF THE DFF!  
  
PHASE 9:  
......  
1...2.  
.4...3  
..5.6.  
.L....  
......  
ONE MORE FRAME OF RE-ORIENTATION WITHOUT INFLUENCES:  
  
PHASE 10:  
......  
.1....  
..4.2.  
.U.5.3  
....6.  
......  
THE BUSY BEE HAS JUST FINISHED A LOOP INSIDE A 2X2 SQUARE, BUT NOW IT'S HIGH TIME FOR IT TO MOVE ON! 4, WHO HAS JUST BEEN INFLUENCED BY 5, NEEDS NEW SPACE AND FORCES THE BUSY BEE TO STOP FOR ONE FRAME (IT CANNOT MOVE FORWARD BECAUSE 1 BLOCKS THAT POSSIBILITY).  
  
PHASE 11:  
......  
......  
.1.5.2  
.L4.3.  
...6..  
......  
NOTE THAT BECAUSE THE BEE HAD TO STOP, THE CHESSBOARD PATTERN OF THE WHOLE DFF IS NOW BROKEN, WHICH WAS VALID IN ALL PREVIOUS PHASES!  
NO INFLUENCES IN THE NEXT FRAME, WHICH MEANS THE BUSY BEE MOVES UP FURTHER, EXPLORING THE NORTH-WEST REGION OF THE DFF NOW:  
  
PHASE 12:  
......  
.....2  
1U5.3.  
.4.6..  
......  
......  
  
ANOTHER INTERACTION WITH FFLY 5 FORCES THE BEE FURTHER UPWARDS!  
  
PHASE 13:  
......  
1U..2.  
.4...3  
..5.6.  
......  
......  
(REMARK: THAT'S THE PHASE YOU FIND IN THE CAVE MAP!)  
THE BUSY BEE, WHO HAS ALREADY HELPED TWO FLIES TO MOVE UP WITH THE GROUP, NOW DOES ITS DUTY A THIRD TIME AND INFLUENCES 1. PERHAPS THE BEE ALSO WANTED TO HAVE REVENGE FOR BEING BLOCKED BY 1 A FEW PHASES EARLIER! :D  
  
PHASE 14:  
1.....  
..R...  
..4.2.  
...5.3  
....6.  
......  
OUR BUSY BEE IS STILL NOT DONE WITH ITS TRIP: IT'S INFLUENCED BY 4 TO MOVE RIGHT AGAIN!  
  
PHASE 15:  
.1....  
...R..  
...5.2  
..4.3.  
...6..  
......  
AND ANOTHER INFLUENCE BY 5 - THE BEE KEEPS MOVING RIGHT!  
  
PHASE 16:  
......  
.1..R2  
..5.3.  
.4.6..  
......  
......  
THE BEE BEGS FOR A LITTLE BREAK AND IT GETS IT! IT'S BLOCKED BY 2 AND 3 SO IT STOPS, FINALLY RESTORING THE CHESSBOARD PATTERN: AND IN RETURN, IT INFLUENCES 2 TO MOVE UP. ONCE AGAIN, IT'S THE ONLY INFLUENCE 2 GETS IN THE WHOLE SHORT LOOP, WHICH MEANS THIS IS ALREADY THE FOURTH FLY WHICH MOVES WITH THE GROUP ONLY THANKS TO THE BUSY BEE!  
  
PHASE 17:  
.....2  
1...U.  
.4...3  
..5.6.  
......  
......  
AND FINALLY, ONE FRAME WITHOUT INTERACTIONS TO REBUILD THE ORIGINAL FORMATION:  
  
PHASE 1':  
1...2.  
.....R  
..4...  
...5.3  
....6.  
......  
THE GROUP HAS MOVED UP! HOWEVER, IF YOU COMPARE PHASE 1' WITH PHASE 1, YOU'LL FIND THAT THREE BFLIES HAVE SWITCHED PLACES: THE BEE HAS TAKEN 3'S PLACE, 3 HAS TAKEN 6'S AND 6 HAS BECOME THE NEW BUSY BEE, WORKING HARD IN THE NEXT SHORT LOOP!  
  
WHAT A WORKBY THE BUSY BEE! WHILE MOVING AROUND IN THE WHOLE DFF (WHILE ALL OTHER FLIES MOVED INSIDE 3X2 RECTANGLES THE WHOLE TIME!), IT HAS WORKED SO MUCH FOR THE GROUP:  
  
| THERE WERE 15 INTERACTIONS DURING THE SHORT LOOP, ONLY 2 OF THEM WITHOUT THE BUSY BEE BEING INVOLVED.  
  
| THE BEE HAS GIVEN 1,2,4 AND 5 THEIR ONLY INFLUENCES WHICH MADE THEM MOVE UP WITH THE GROUP. SO THE BEE WAS ALONE RESPONSIBLE FOR MORE THAN HALF OF THE GROUP MOVING UP TOGETHER!  
  
| AS ALREADY MENTIONED, ALL THE OTHER 6 FLIES MOVED ONLY INSIDE 3X2 RECTANGLES. HOWEVER, THE BUSY BEE HAD A BIG PATH THROUGH THE WHOLE DFF:  
......  
.\\\\\  
.\....  
.\\...  
.\\...  
.\\\\.  
  
WHO WOULD NOT THINK THAT THE BEE HAS DESERVED A BIG BREAK? IT WILL GET ONE: AS WE'VE SEEN, THE BUSY BEE NOW OCCUPIES 3'S PLACE, AND 3 IS THE ONLY FLY IN THE GROUP WHO HAS NOT BEEN INFLUENCED AT ALL DURING THE WHOLE SHORT LOOP - IT WAS JUST SPINNING INSIDE ONE AND THE SAME 2X2 SQUARE! SO THE BUSY BEE CAN FINALLY HAVE SOME SLEEP WHILE 6 DOES THE WORK! :D  
  
BTW, YOU MIGHT WONDER HOW IT'S POSSIBLE THAT 3 HASN'T TAKEN ANY INFLUENCE BY OTHER FLIES. AFTER ALL, THE DFF IS SUPPOSED TO MOVE, SO DON'T ALL FLIES NEED SOME INFLUENCE TO MOVE WITH THE GROUP? WELL, ACTUALLY YES, BUT NOT NECESSARILY DURING A SHORT LOOP. 3 HAS NOW TAKEN 6'S ROLE IN THE DFF, AND ONE SHORT LOOP LATER, IT WILL TAKE THE BUSY BEE'S ROLE, AND WE'VE JUST SEEN THAT THIS ACTUALLY MEANS A LOT OF INFLUENCE! :D  
  
EVEN AFTER A DEEP FRAMEWISE ANALYSIS, I HAVEN'T FOUND ANY KIND OF "PRINCIPLE" THAT MAKES THIS DFF WORK. NO VORTEX AS IN 90 PERCENT OF THE OTHER DFFS, NO SMALLER FORMATION AS IN THE NEW 25-DFF, JUST ONE SINGLE FLY DOING ALL THE WORK FOR THE GROUP! I'M NOT SURE IF I EXPECT ANY OTHER BIG DFF TO WORK IN A SIMILAR WAY AS THIS ONE - IN FACT, I'M NOT EVEN SURE WHAT "WORKING LIKE THIS DFF" WOULD MEAN...! :D

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NESDORI                           2022-09-05 12:14
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dustin, NICE ANALYSIS! THIS FORMATION INDEED IS QUITE ALIEN AND THE NUMBER OF INTERACTIONS IS SURPRISINGLY LOW. IT'S LIKE A GAME OF TAG; THE BUSY BFLY TRIES TO CATCH OTHER FLIES AND IF TAGGED, THEY MUST MOVE UPWARDS :)

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DUSTIN                            2022-09-06 22:22
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nesdori, THAT'S A NICE COMPARISON! :D