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three busy bees (a new dff!)
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by
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dustin
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DUSTIN                            2022-08-25 12:53
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SO HERE'S THE CAVE! TECHNICAL NOTES LATER, JUST ENJOY IT FOR NOW :D

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DARKSTOORM                        2022-08-25 13:10
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SO IS THIS NOW THE SLOWEST FORMATION IN THE BD UNIVERSE? :D

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ARNO                              2022-08-25 13:16
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VERY INTERESTING FORMATION! :-D

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DUSTIN                            2022-08-25 18:10
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GLAD TO SEE THAT SO MANY HAVE ENJOYED THE DFF ALREADY! :D  
  
FOR EVERYONE:  
DFF= DANCING FLY FORMATION = A FORMATION OF FIRE- AND/OR BUTTERFLIES WHICH PERIODICALLY MOVES INTO A CERTAIN DIRECTION IN EMPTY SPACE.  
  
IN THIS ONE, THREE BUSY BEES (BUTTERFLIES) MOVE FROM THEIR NEST WHERE THE QUEEN (FIREFLIES) RESIDES TO THE FLOWER (LOWER-LEFT BFLY) SO THE FLOWER CAN GROW (MOVE UP). AFTERWARDS, THE THREE BEES MOVE BACK TO THEIR QUEEN TO BRING HER THE NECTAR FROM THE FLOWER. THIS MAKES THE WUEEN EVEN MORE POWERFUL (IT ALSO MOVES UP) ONE YEAR (25 FRAMES) LATER, THE PROCESS RESTARTS!   
  
THIS DFF IS COMPLETELY DIFFERENT FROM ALL FORMERLY KNOWN DFFS! THE WORK-SHARING COULD NOT BE MORE DIFFERENT: THE LOWER-LEFT BFLY AND THE FFLIES JUST SPIN AROUND FREELY FOR 24 FRAMES AND THEN THEY'RE INFLUENCED BY THE BUSY BEES TO MOVE UP FOR ONE FRAME. THE OTHER THREE BUTTERFLIES DO ALL THE WORK: THEY MOVE FROM THE FFLIES TO THE BFLY BACK AND FORTH ONLY TO POKE THEM FOR ONE FRAME AND THEN MOVE BACK! :D  
  
WITH A SPEED OF 25 FRAMES PER STEP, THIS IS BY FAR THE SLOWEST DFF SO FAR (THE OLD RECORD WAS HELD BY THE SINKING-F6 FORMATION WITH 9 FRAMES/STEP!)  
  
IN FACT, THIS DFF FEELS TO ME LIKE A KIND OF "DEJA-VU". WHEN I READ arno'S ARTICLE ABOUT "WHAT HAPPENS IF A DFF RUNS INTO ANOTHER SPINNING FLY/VORTEX?", I IMAGINED A SMALL DFF MOVING FROM FLY A TO FLY B, THEN BEING INFLUENCED BY FLY B TO BUILD A DFF WITH REVERSE DIRECTION, MOVING BACK TO FLY A AND BEING INFLUENCED TO BUILD THE ORIGINAL DFF AGAIN. THIS ONE IS SIMILAR: ALTHOUGH THE THREE BUTTERFLIES DON'T BUILD A STABLE DFF ON THEIR OWN, THEY CAN MOVE IN EMPTY SPACE FOR MANY FRAMES BEFORE SPINNING. THAT'S EXACTLY WHAT HAPPENS HERE. ON THEIR WAY FROM THE FFLY VORTEX TO THE LOWER-LEFT BFLY, THE THREE "BUSY BEES" BUILD A FRIGHT3-LIKE FORMATION FOR MANY FRAMES. WHEN THE FORMATION FINALLY BREAKS, THE LOWER-LEFT BFLY IS ON THE SPOT AND INFLUENCES THE BUSY BEES FOR JUST ONE FRAME SO THEY'RE ABLE TO MOVE AGAIN! :_D  
  
I WANT TO PUBLISH A MORE DETAILED FRAME-BY-FRAME ANALYSIS SOON! :D

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DUSTIN                            2022-08-25 18:15
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BTW THIS IS THE FIRST DFF FOUND BY COMPUTER SEARCH AND MOST PROBABLY THE ONLY ONE WITH 6 OR LESS FLIES WHICH OUR HUMAN EYES HAD MISSED! :D  
  
I SAY "MOST PROBABLY" BECAUSE IT SEEMS IMPOSSIBLE TO WRITE A PROGRAM WHICH DISCOVERS ALL DFF WITH A CERTAIN NUMBER OF FLIES WITH ABSOLUTE CERTAINTY. AT LEAST THIS WOULD BE A NEW CHALLENGE FOR COMPUTER SCIENTISTS :D

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DUSTIN                            2022-08-27 22:47
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SO HERE COMES A DETAILED ANALYSIS OF ALL 25 PHASES OF THIS INTERESTING DFF!  
TERMINOLOGY: 1,2=FIREFLIES, 3=BUTTERFLY (REGARDLESS OF THEIR DIRECTIONS)  
THE THREE "BUSY BEES" (ALSO BUTTERFLIES) ARE BY FAR MOST INTERESTING. THEY GET THE LETTERS U,D,L,R FOR THEIR CURRENT FACING DIRECTIONS.  
  
PHASE 1: (SEE THE MAP OF THIS CAVE)  
.....  
..R1.  
..R.2  
.L...  
.....  
..3..  
.....  
TWO BUSY BEES FORM A VORTEX, THE THIRD IS MOVING ON IT. FIREFLY 1 BLOCKS THE TOP BUSY BEE.THIS SCENARIO IS ACTUALLY VERY SIMILAR TO THE BUTTERFLY VERSION OF THE "FRIGHT CAGE" DFS (SEE FUNNY FLIES 18)!  
  
PHASE 2-4:  
..... ....2 ...2.  
..U.2 ...R. ....1  
.U.1. ..R.1 .U.D.  
..D.. .L... ..D..  
..... ..... .....  
..... ..... .3...  
..3.. .3... .....  
THE BUSY BEE TAKES QUICK REVENGE FOR BEING BLOCKED AND INFLUENCES FIREFLY 2 SO THE FIREFLY VORTEX IS TEMPORARILY BROKEN. BUT IT REBUILDS INSTANTLY ONE STEP ABOVE. THIS INTERACTION BETWEEN THE BUSY BEE AND THE F-VORTEX IS ACTUALLY VERY SIMILAR TO THE 3-FLY DFF "LIFTED F-VORTEX". IN FACT, THE BUSY BEE AND THE TWO FIREFLIES BUILD EXACTLY THAT DFF INSIDE THESE THREE FRAMES! BUT THEN IN THE NEXT PHASE, THE BUSY BEE GETS INFLUENCED BY ANOTHER BUSY BEE SO THE "LIFTED F-VORTEX" DFF BREAKS (FOR NOW).  
  
PHASES 5-10:  
....1 ...1. ....2 ...2. ....1 ...1.  
...2. ....2 ...1. ....1 ...2. ....2  
..R.. .U... ..R.. .U... ..R.. .U...  
.L.D. ..D.. .L... ..D.. .L... U.D..  
..... ...D. ..L.. .L... L.... .....  
..3.. ..... ..... .3... ..3.. .....  
..... ..3.. .3... ..... ..... ..3..  
TWO BUSY BEES FORM A VORTEX, THE THIRD MOVES AROUND IT FROM TOP-RIGHT TO BOTTOM-LEFT. THIS IS ACTUALLY VERY SIMILAR TO THE 3-FFLY DFF "FRIGHT-3" BUT VERTICALLY MIRRORED! HOWEVER, THREE BFLIES CANNOT BUILD A STABLE DFF ON THEIR OWN, SO LET'S SEE WHAT HAPPENS NEXT! THE FIREFLIES AND THE BOTTOM BFLY JUST SPIN AROUND WITHOUT ANY INFLUENCES.  
  
PHASE 11:  
....2  
...1.  
..R..  
.R...  
..D..  
.....  
.3...  
THE BUSY BEE WHICH WAS MOVING AROUND THE VORTEX NOW BREAKS IN AND KICKS ANOTHER BEE OUT. THIS IS STILL ANALOGOUS TO FRIGHT-3!  
  
PHASE 12:  
...2.  
....1  
.....  
..D..  
.D...  
.3D..  
.....  
AS A RESULT OF THE BEE'S BREAK-IN, WE HAVE NOW ALL THREE BEES FACING INTO THE SAME DIRECTION. UNLIKE FRIGHT-3, THEY WOULD NOW INDEPENDANTLY SPIN AROUND FOREVER... IF IT WASN'T FOR BUTTERFLY 3 WHICH FINALLY COMES INTO PLAY! 3 IS NOW INFLUENCED BY A BEE AND IT'S LIFTED UPWARDS.   
  
PHASE 13:  
....1  
...2.  
.....  
.L...  
L3...  
.L...  
.....  
3 HAS BEEN LIFTED UP (WHICH IS ACTUALLY THE ONLY TIME WHERE 3 EXPERIENCES ANY INFLUENCE, IT'S JUST SPINNING AROUND FOR 24/25 FRAMES!) SO FAR, THE BEES HAVEN'T BEEN INFLUENCED BY 3 YET, AND THIS STAYS THE CASE FOR THE NEXT PHASE:  
  
PHASE 14:  
...1.  
....2  
.U...  
U....  
.U3..  
.....  
.....  
BUT NOW, THE BOTTOM BEE CANNOT MOVE RIGHT AS IT WOULD LIKE TO. THIS IS THE ONE AND ONLY PHASE WHERE A BUSY BEE GETS INFLUENCED BY 3! IN FACT, THE BOTTOM BEE CANNOT MOVE AT ALL IN THIS FRAME, SO IT STAYS WHERE IT IS AND TURNS LEFT.  
  
PHASE 15:  
....2  
...1.  
..R..  
.R...  
.L...  
..3..  
.....  
3 HAS STOPPED THE BEES FROM SPINNING AROUND FOREVER, SO ITS JOB IS DONE AND IT WON'T INTERACT ANY FURTHER WITH ANYTHING FOR THE REST OF THE PHASES!   
NOW THE "MAGIC" COMES INTO PLAY: FOR THE NEXT TEN FRAMES, THE BUSY BEES MANAGE TO REBUILD THEIR STARTING FORMATION, LIFTED BY 1 STEP, WITHOUT ANY FURTHER EXTERNAL HELP!   
  
PHASE 16-25 AND PHASE 1':  
...2. ....1 ...1. ....2 U..2. .R..1 ...1. ....2 U..2. .R..1 ..R1.  
....1 ...2. ....2 UU.1. ..R.1 ...2. .D..2 LU.1. ..R.1 .U.2. ..R.2  
..... .U... UUR.. ..... ..... .UD.. .L... ..... .U... ..D.. .L...  
.UD.. UL... ..... ..D.. .L... ..... ..D.. .L... ..... ..... .....  
L.... .3... ..3.. ..... ..... .3... ..3.. ..... ..... .3... ..3..  
.3... ..... ..... ..3.. .3... ..... ..... ..3.. .3... ..... .....  
..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .....  
ET VOILA! :D   
  
SO WHAT HAPPENED ALL IN ALL? THREE BUSY BEES LIFTED ONE FFLY FOR JUST ONE FRAME, THEN THEY MOVED ALL ALONE DOWN TO BUTTERFLY 3 AND ALSO LIFTED THIS ONE FOR ONE FRAME. AFTERWARDS, THE BEES MOVED AGAIN ALL ALONE BACK TO THE FIREFLIES, LIFTING THEMSELVES AS WELL DURING THE PROCESS!ALTHOUGH WE KNOW THAT THREE BUTTERFLIES CANNOT BUILD A STABLE DFF ON THEIR OWN, THESE BUSY BEES GET AS CLOSE AS POSSIBLE TO IT: DURING 25 FRAMES, THEY NEEDED NO MORE THAN 2 EXTERNAL INFLUENCES AND THEY DID ALL THE REST ON THEIR OWN! :D  
  
HOPE THE FORMATTING WORKS NOW...

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DUSTIN                            2022-08-27 22:48
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YEP, FORMAT IS PERFECT :)

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DUSTIN                            2022-08-27 22:52
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AH, I FORGOT TO MENTION: THE THREE BUSY BEES SWITCH ROLES DURING ONE SHORT LOOP, SO THE LONG LOOP OF THE DFF IS 75!