Boulder Dash Forum

I just discovered a new formation!
Well... the question is whether it counts as a formation, which depends on whether the number of flies in a DFF has to be finite - there's no clear definition w.r.t. this in the articles yet ;D
I call the DFF "The Killerflies"! It has infinitely many FF, and there's another strange thing about it - there's no influence between the flies! The formation becomes interesting because of the infinite number of possible free riders- these riders are in fact "the killerflies", while the formation itself just works as an "initial ignition".
So here it is! Capital letters=basic formation FFs, small letters=free riding FFs
XXLXXXLXXXL...
XRXXXRXXXRX...
XXrXXXXXXXX...
XXXrXXXXXXX...
XXXXrXXXXXX...
XXXXXrXXXXX...
...
...
Short loop=2, long loop=infinite, direction= 2 right
The direction is actually defined by the free riders.
I'll make a cave of it soon! ;D
Works with BF as well, the formation can be vertically mirrored! Also both the FF and the BF formation have a mirrored pair each, so we have four DFF in total! Scientists all over the world will be shocked by this discovery! Or perhaps it at least impresses one scientist in the Netherlands ;D

That's a great discovery Dustin! Congrat and yes, I'm definately impressed!

To me it looks like a conveyor belt. Perhaps a complete BD-factory could be build with horizontal and vertical conveyor belts delivering flies....! I'm curious to see your cave applying this idea!

Is this a dancing fly formation (DFF)? Well, the first thing I observe (at least in a "finite" version) is that the flies which form the conveyor belt are simply spinnig around and sticked to the same location. In the definition of a DFF (first post), I required that the whole group moves through the open space, without help of any items other than the empty space the flies themselves. So although it is definately a cool effect, it is not exactly a DFF, right? Or maybe I understand the infinity concept wrong...?

Nevertheless, I played around a bit with it and noticed a few interesting things. With the basic setup (horizontal belt of fireflies) it possible to move a stack of FF both above and below the belt. Above the belt, a vertical stack can be moved from right to left. Below the belt, like in your picture, a diagonal stack can be moved from left to right.

The same principles apply for vertical belts and for the variants with butterflies, but there is one exception. With a vertical FF belt, a diagonal FF stack doesn't work. This is due to the cave scanning order, in which the FF to be moved is scanned before the FF that should push him. So in total there are 7 ways (instead of 8 ) to move a fly along such belt.

All in all, thanks for this discovery! It's very well usable in caves!

Thx ;D Well, I think whether you regard it as a DFF depends on whether you accept an infinite number of flies. As you say, all FF in the conveyor belt stay in their 2x2 square so the whole belt does not move as long as there's a finite number of FF involved. However, if you really have an infinite number of FF, then it is not false to say "the whole formation moves right" because if you move an infinite horizontal line in a horizontal direction, the whole line does not change its position. So it's equivalent to say "the whole conveyor belt is stationary" or "it moves right". The difference is made by the free riders which move right, so with at lest one free rider, it is now uniquely correct to say "the whole formation moves right".
Remark - of course, the belt has to be infinite both to the left and to the right, so here's a little correction of my previous post.
...XXLXXXLXXXL...
...XRXXXRXXXRX...
...XXrXXXXXXXX...
...XXXrXXXXXXX...
...XXXXrXXXXXX...
...XXXXXrXXXXX...
......
... ...
Of course, it is not an easy question to answer whether such an infinite fly formation is a DFF or not. But all the concepts of DFF, such as short and long loop, phases, moving direction, free riders and mirrored pairs work very well here too!
As you correctly said, I have to correct myself - the BF version does not have a mirrored pair. So here's my summary so far.
1. The fly formation I gave in this post has a mirrored pair in the very sense that you defined mirrored pairs in your articles.
2. If you mirror my given formation on a vertical axis - i.e. not according to your definition! - and still replace FF by BF, you get another fly formation moving left. This one has no mirrored pair - as you wrote, a vertical FF belt cannot "transport" a diagonal FF line. So here I made a mistake in my previous post!
3. Then there's your cool discovery that the belt can also "transport" a vertical line of FF! This would then be, strictly speaking, a new fly formation.
......
......
...XlXXXXX...
...XlXXXXX...
...XLXXXLXX...
...RXXXRXX...
Again L,R = FFs of the basic conveyor belt, l=free riding FF.
This time we regard the conveyor belt as moving to the left! So we have
Short loop=2, long loop=infinite, direction=2 left.
This formation also has a mirrored pair in the very sense of your articles, which would then be a vertical BF belt "transpoting" a horizonal line of BF at its left side.
And then there's another mirrored pair of belt-formations - a horizontal BF belt transporting a vertical BF line above the belt {direction right} and a vertical FF belt transporting a horizontal line of FF to the left of the belt {direction down}.
BTW, the concept of infinite {D?}FF is not just theoretical, but can easily be realized with open borders! ;D

Dustin, I agree with all points in your last post! Only, on the question whether this is a (set of) DFF(s), I still tend to say it's not.

Let's for a moment ignore the free riders (since DFFs with free riders are already skipped from the list of unique DFFs), and focus on the basic setup: the infinite horizontal line (or conveyor belt) of fireflies. Is this a DFF?

One criterion from the definition is clearly not satisfied: that the flies "influence each other’s movements". All flies (infinitely many) are independently spinning around in their 2x2 square, so they don't interact with each other.

Another criterion is indeed questionable: "the whole group moves gradually into a certain direction". Here my definition is not strict for infinitely large groups. In my mind this would mean that all individual flies move. As for the horizontal FF belt, I could number all fireflies using the integer numbers, so give one FF number 0, use 1,2,... to the right direction and -1,-2,... to the left direction. Then, after one short loop, number 0 has returned to its original position, and so it has not moved.

All in all, I think I'll take a practical view point, that this setup deviates too much from the conventional DFF's. That doesn't change that it is a great invention, and a very interesting research topic on its own!

Alright! So let's call it an "open border formation" instead

Episode 11: Sinking-F5

Until now we have discussed one unique dancing fly formations involving exactly 5 flies: Fright-5. In addition, we have seen various formations with free riders, which are composed of 5 flies in total:
- Fright-3 + 2 BF;
- Fright-4 + 1 BF;
- Lifted F-vortex + 2 BF;
- The 4 Elements + 1 FF.
This episode is fully focussed on another 5-fly dancing fly formation: Sinking-F5. It is a unique formation (i.e. there are no free riders), and it involves 5 fireflies moving downwards in quite a slow pace.

The properties of this formation are follows:
- Name: Sinking-F5
- Composition: 5 FF
- Short loop: 8 phases
- Long loop: 48 phases
- Shift per short loop: 1 Down

Probably the first cave which uses Sinking-F5 intendedly is Ultimate Firefly Teamwork. Here, a Fright-5 formation is converted to Sinking-F5 by an obstacle on its path.

How does this formation work?

As with many previously discussed formations, also this formation is built around a vortex – actually, two vortices, as you will see soon!
Below picture shows the 8 phases of the short loop of this formation.



Due to the involvement of 5 flies, the story behind this formation has become a little bit more complex, but also a little bit more “dramatic” compared to previously discussed formations.

Phase 1 -5:
The formation starts in a configuration similar to Crawling-B4. Two fireflies (red and blue) are dancing together in a vortex-shape, and another couple of fireflies (green and yellow) are walking around the dancing couple, looking forward to start a nice dance together soon. But… wait a minute! There is a 5th firefly, the purple one, at the bottom side of the group… What is he doing there?
The green/yellow walking partners are not aware of this “bachelor” firefly as he is strategically positioned at the other side of the dancers, intending to distort the plans of both the dancers and the walkers. I will call this firefly the sneaky single.
During phase 1-5, nothing spectacular happens. The green/yellow walkers, as well as the sneaky single, are simply following their natural path around the dancing couple.

Phase 6:
Now the sneaky single executes his evil plan. He breaks into the vortex at the top-left corner, like in Fright-3. This way, the sneaky single takes over the dance with the red FF. The blue FF is effectively kicked out, and has lost his dancing partner.
The blue FF seems a bit dizzy, not only because of what just happened, but also because he could not move in the usual way. His favourite move to his left is blocked by the sneaky single, while at the same time the way forward is blocked by the green fly. (Notice that the above picture therefore shows two red traffic signs for the blue FF in phase 6!)

Phase 7:
Because the blue FF could not move either left or forward, the Boulder Dash engine rules specify that the blue FF stays at the same position, facing his direction to his right side. And so it happens: the blue FF twists to its right without moving. This is the first time that we see this rule applied within a dancing fly formation! (By the way, more of such occasions will follow, when we will discuss the more complex formations.)
The purple and red FF are still dancing, and the green and yellow FF are still following their path.

Phase 8:
Did you expect that the green and yellow FF are a strong couple, where both partners are always loyal to each other? Well, surprisingly the green FF has an eye on the fresh new single, the blue FF, as he starts a new dance with this FF, at the same time breaking into the purple/red vortex at the left-bottom corner, similar to Crawling-F4.
Now, out of all 5 flies, the yellow FF is the most unlucky one. The blue FF blocks his way while starting the dance with the green FF. Quite rudely, the yellow FF is pushed aside by his rival. And so the yellow FF, having just lost his partner, and being the only FF who hasn’t danced yet, disappointedly backs down to the sidelines.

Phase 1’:
A new dancing couple has been formed by the green and blue FF. The red and purple FF were drifted apart, and continue in the role of the walking couple. For the yellow FF the time has come to make a fresh new start, as in the new cycle he will fulfil the role of the sneaky single!

So, each FF has a unique role during the short loop of this formation. If I would give all 5 FF a name based on their role, I would come up with the following:
- Red - the temptress: the sneaky single choses him (her?) as dance partner.
- Blue - the Casanova: shortly after losing his partner he finds a new one. (In fact he needs only 2 frames for that...! )
- Green - the cheater: leaves his (her?) dance partner for another (the Casanova).
- Yellow - the unlucky one: loses his partner even before the dance…
- Purple - the sneaky single: speaks for itself!

Interesting to note is that in this formation, two role groups of different size exist. The purple and yellow FF change roles after each short loop. In other words, the unlucky one becomes the sneaky single, while the sneaky single becomes the unlucky one (as punishment for being sneaky? ).
The other group is formed by the red, green and blue FF. So the temptress becomes the cheater, afterwards the Casanova, and finally the temptress again.
This is the first dancing fly formation in this article series which contains role groups of different sizes.
Below picture shows the paths followed by both the purple/yellow group and the red/green/blue group.



As expected, after 2 short loops the FF which starts as the purple FF (sneaky single) has moved exactly 2 positions downward. Also, after 3 short loops the FF starting as the red FF has moved 3 positions downwards.
From this it follows it takes 6 short loops (since 6 is the least common multiple of 2 and 3) until all flies have returned to their original position within the formation. Therefore, the long loop takes 6*8 = 48 phases.

Why does this formation move downwards?

This formation combines the principles of Fright-3 and Crawling-F4. As we have seen above, within one short loop of this formation, the vortex moves two times:
- Between phase 6 and 7, the vortex moves 1 step to the right, à la Fright-3.
- Between phase 8 and 1’, the vortex moves 1 step down-left, à la Crawling-F4.
The net effect of these two moves is that the vortex moves 1 step down. Thereby the whole formation moves 1 step down.

How to launch this formation?

This is not so trivial this time. Given that this formation is built around a vortex, you might expect that sliding 3 fireflies along a specific side of the vortex works. Well, actually it does work, but the explanation is not so simple as for the smaller vortex-based formations.
Remember that Sinking-F5 combines the break-in-styles of Fright-3 and Crawling-F4. Also remember that the walkers in Fright-3 and Crawling-F4 are reversely timed, w.r.t. the vortex’ two stages. This makes that their natural paths around the vortex are more or less located at the opposite sides of the vortex. Given these differences, while for Sinking-F5 you need both break-in variants combined, it seems not feasible to just slide 3 fireflies along the vortex at a certain side.
Happily, it turns out that Sinking-F5 is still indirectly launched if you slide 3 FF, coming from the right, over the top side of the vortex, as shown by this video.
Here is in short what happens:
- The 3 FF (call them A, B, C) move to the left, over the top side of the vortex, while the vortex keeps spinning as usual.
- When all 3 FF have reached the left side of the vortex, the first FF (A) has already been spinning downwards and breaks into the vortex at the bottom-left side, à la Crawling-F4.
- The FF from the vortex (call them D, E) are drifted apart and A starts a dance with C. B continues walking at the bottom side of the newly created vortex.
- Few frames later, exactly phase 8 of Sinking-F5 is created, with B in the role of sneaky single, a vortex of A/C, and walking couple D/E.

There are other ways to launch Sinking-F5. These methods work in two steps: they start with a simpler formation and let this formation collide with a spinning firefly. If timings are right, the spinning FF is connected to the formations and the group continues as a bigger formation (and mostly in another direction). This video shows two of such creations of Sinking-F5:
- Crawling-F4, plus 1 spinning FF;
- Fright-4, plus 1 spinning FF.
Both these methods trigger a configuration as explained above for the clean launch method.

Relations with other dancing formations?

Sinking-F5 does not form a mirrored pair with a butterfly-counterpart. Phases 6 and 7 contain a conflicting position where row-by-row scanning and column-by-column scanning would give different results. For example, in phase 6 the blue and purple FF compete for the same position. Due to row-by-row scanning the purple “wins” while with column-by-column scanning the blue would “win”.
If you create the mirror image of these two phases in the Construction Kit, you will see that both lead to 5 spinning butterflies. This implies that the condition for a mirrored pair is not satisfied.

Also, Sinking-F5 doesn’t have a p-mirrored counterpart. Phases 6 and 7 are the only phases for which the mirror image doesn’t work. For all others, the mirror image does work in the sense that the next frame equals the mirror image of the next phase. If you test the mirror image of phase 8, for a short while it looks like a 5-BF formation moving to the right, until phase 6 is reached, then the formation breaks. Thus, there is no phase for which the mirror image gives another dancing formations, and therefore Sinking-F5 does not form a p-mirrored pair.

There is, however, a funny relation of a different type. As mentioned at the top of this article, Fright-5 can be converted to Sinking-F5, by letting it collide with a small obstacle. This works very similar to the earlier discussed conversions of Fright-4 to Crawling-F4 and The 4 Elements to Crawling-B4. This video shows the conversion, together with the other two alternative launch methods of Sinking-F5.

Interesting to note is that the opposite conversion, from Sinking-F5 to Fright-5, is not possible. At least, it is not possible by simple collision with a small object. The problem is that since Sinking-F5 moves down, the vortex will stand still just above the object, while Fright-5 must be created by sliding 3 FF along the bottom of the vortex. In other words, the object blocks a position which must be free to create a Fright-5.

Perhaps, other relations of Sinking-F5 will be discovered in the future when studying the bigger FF formations.

Final note

Although Sinking-F5 does not form a mirrored pair, there exists at least one mirrored pair other than those discussed earlier. This pair will be the topic of a next article!

Drama, baby!

I've also found something interestingly new!

It is not a dancing fly formation, but it is closely related. It has all the requirements of a DFF, except one: it does not move. Instead, the group stays "dancing" at the same location until the end of times... I would therefore call it a dancing fly stagnation (DFS)!

This variant consists of 7 fireflies dancing within the same 5x3 box. You can build it in the Construction Kit as follows, anywhere in open space:

LLxxU
xxRDx
xRxRx

Looking closely you could easily recognize 2 vortices placed next to each other, and 3 "sneaky singles" walking at the left and bottom side of the 2 vortices.
After some quick investigation I found that this DFS has 7 phases in the short loop. After these 7 phases the group has not moved because:
- the right vortex is broken without creating a new one;
- the left vortex is 2 times shifted 1 position to the right à la Fright-3, thereby taking over the role of the right vortex;
- a new vortex is created at the left side of this vortex.

I have no idea if more DFS's exist. Anyway, a mirrored or p-mirrored counterpart for butterflies does not exist. This is a standalone DFS.

I've been wondering for a while if the phenomenon of a "stationary DFF" or DFS exists. Now I finally found one! Actually, I found it while experimenting with an existing DFF, so I have a "launch"-method as well.
Altough this DFS is interesting, I won't expect it has lots of use in BD caves. But I have an idea for a funny cave....

I've worked out some details behind the dancing fly stagnation (DFS) from my previous post.

I'd like to name it Static-F7.

First some video links to various caves showing the Static-F7:
- Dancing Fly Stagnation
- Chicken Heap
- Summit Interrupted

Below picture shows the 7 phases from the short loop:



To clarify what happens here, I've made up the following story:

Phase 1:
Here we see two dancing couples (vortices), a blue and green one, in reversed timing state. 3 "rivals" purple, red and yellow are walking around them.
Phase 2:
Purple breaks into the green vortex, seemingly ready to start a dance with red.
Phase 3:
But red is kicked aside by light-blue. So purple lost touch with red. However, he still successfully split the green vortex. Light-green moves through the blue vortex (which works as a swing door for him).
Phase 4:
Due to the movement of light-green (with 1 frame timing difference), purple is now able to break into the blue vortex, starting a dance with light-blue (à la Fright-3). Dark-blue is kicked out and cannot move either left of forward, and will therefore turn right.
Phase 5:
The purple/blue vortex has taken over the blue vortex and shifted 1 position to the right. Dark-green moves through this vortex as if it were a swing door. Yellow has come to a position of breaking in.
Phase 6:
Yellow breaks in, while at the same time red is ready to break in.
Phase 7:
Yellow starts a vortex with dark-green. At the same time red takes over the dance with purple. So red and purple have found each other in the end!
Phase 1':
Two new vortices have been formed at the original locations.
Effectively, over each short loop, the right-side vortex breaks, the left-side vortex is 2 times shifted to the right, and a new left-side vortex is created. So the formation as a whole has not moved!

Also note that the yellow and light-blue FF switch role between Phase 1 and 1'. The remaining 5 FF all change their role after each short loop. So this DFS has two role groups of 2 and of 5 FF, respectively. This implies that the long loop takes 10 (= least common multiple of 2 and 5) short loops, so 70 phases in total!

With this finding, I'm now wondering: is this the end of the series of dancing firefly formations? For fireflies we have DFF's of 2, 3, 4, 5 and 6 fireflies. Now, with 7 fireflies the formation stops moving. So is this a sign that no 8-, 9- or more-ffly formations exist? Perhaps we'll find out once.

Arno wrote:Altough this DFS is interesting, I won't expect it has lots of use in BD caves.

Objection! I think this formation is very interesting as stationary guards!
Let's consider a 7x5 cave with the DFS right in the middle. I number the rectangle as follows.
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35
So the DFS is caught in the rectangle 09-13-27-23, the rest is empty space.
Now let's try to get from one corner of the 7x5 rectangle into another. There follows a list for each phase where Rockford can be and to which direction he can move in order to survive at least the actual frame. It's based on the cave-scanning order, which gives the following rules.
--> Above the DFS, i.e. 01-07, RF may touch a FF but not move into a direction where he would touch a FF.
--> To the left of the DFS, RF also may touch a FF and move upwards without any danger. If he wants to move downwards, he must not run into a FF. For example, if RF is located at 15 and wants to move to 22, there may be a FF at 16 but not at 23.
--> Below the DFS, RF must not touch a FF but then he can move into either direction. So in this case, I'll only give the numbers of RF's possible locations.
--> To the right of the DFS, RF must never touch a FF. If he intends to move up, this is the only condition, if he wants to move down, he also must not run into a FF.


Scenario 1 - trying to get from 01 to 07 or vice versa. "x" means that RF does not move in the actual frame.
Phase 1 - 01x 02l 03r 04x 04r 05x 05l 06l 06r 07x
Phase 2 - 01x 01r 02l 02x 02r 03l 03x 04l 05r 06x 06r 07l 07x
Phase 3 - 01x 01r 02l 02x 03l 06r 07x
Phase 4 - 01x 01r 02l 02x 03l 05r 06x 06r 07l 07x
Phase 5 - 01x 02l 02r 03x 04l 05r 06x 06r 07l 07x
Phase 6 - 01x 01r 02l 02x 03l 04r 05x 06l06r 07x
Phase 7 - 01x 01r 02l 02x 03l 05r 06x 06r 07l 07x
Now if we try to built a connected path from 01 to 07 out of this, we find that there is no way to do so. The same goes for 07-->01.
Conclusion - both routes are impossible!

Scenario 2 - trying to get from 01 to 29. The vice-versa-scenario is trivially possible, so I'll only consider directions x and d, not u.
Phase 1 - 01x 08d 15x 15d 22x 22d 29x
Phase 2 - 01x 01d 08x 15d 22x 22d 29x
Phase 3 - 01x 01d 08x 08d 15x 22d 29x
Phase 4 - all is allowed
Phase 5 - 01x 08d 15x 15d 22x 22d 29x
Phase 6 - 01x 01d 08x 15d 22x 22d 29x
Phase 7 - 01x 01d 08x 08d 15x 22d 29x
There are several possibilites to get from 01 to 29. For example, Rockford could start moving down at phase 2 and just keep running.
Conclusion - both directions are possible and easy!

Scenario 3 - trying to get from 29 to 35 or vice versa.
Phase 1 - 29 30 32 34 35
Phase 2 - 29 30 31 33 34 35
Phase 3 - 29 31 32 34 35
Phase 4 - 29 30 32 33 35
Phase 5 - 29 30 31 33 34 35
Phase 6 - 29 30 32 33 34 35
Phase 7 - 29 31 33 34 35
From left to right, RF might start in phase 1 and just keep running. From right to left, there's no way to run through, but RF can start in phase 5, run left four times, stop for one frame and then move on.
Conclusion - both directions are possible, thought from right to left, there's no way to run without stopping.

Scenario 4 - trying to get from 07 to 35 or vice versa.
Phase 1 - 07x 21u 21x 21d 28u 28x 28d 35u 35x
Phase 2 - 07x 07d 14u 14x 28u 28x 28d 35u 35x
Phase 3 - 07x 21u 21x 21d 28u 28x 28d 35u 35x
Phase 4 - 07x 07d 14u 14x 14d 21u 21x 35u 35x
Phase 5 - 07x 07d 14u 14x 28u 28x 28d 35u 35x
Phase 6 - 07x 21u 21x 21d 28u 28x 28d 35u 35x
Phase 7 - 07x 07d 14u 14x 28u 28x 28d 35u 35x
From up to down, no route exists. From down to up, RF starts, for example, at phase 1 and keeps running.
Conclusion - possible from 35 to 07 but not vice versa!

Overall conclusion about possible routes.
none
b 01 02 03 04 05 06 07
o 08 09 10 11 12 13 14
t 15 16 17 18 19 20 21 u
h 22 23 24 25 26 27 28 p
29 30 31 32 33 34 35
both

I did not consider possibilities to break into the 5x3 firefly host, as it seemed unlikely to me that RF could survive this, but there may be a tiny chance that such a strategy makes one of the three directions possible that aren't possible yet.

Wow, great effort to figure this all out! And indeed, this DFS is more useful than I thought first, for example as in your "Which edges can you pass?"-cave.

Oh, I discovered some other funny effect with this DFS. Cave later...

Also, this question...

Arno wrote:With this finding, I'm now wondering: is this the end of the series of dancing firefly formations? For fireflies we have DFF's of 2, 3, 4, 5 and 6 fireflies. Now, with 7 fireflies the formation stops moving. So is this a sign that no 8-, 9- or more-ffly formations exist? Perhaps we'll find out once.

...I find quite interesting. How many big fly formations are there? Have we found almost all of them or is it more likely that there are DFF of the type "20FF and 17BF, 62 phases, moves 5 right and 7 up" that we will never find?

OK guys, this time I really have breaking news! I just discovered several highly-numbered BF formations moving quickly upwards and staying very closely together. Nothing even close to a vortex visible. I will reveal them and how I found them as soon as I have fully extracted them from the big BF group that I just tested just for fun. Where is my chessboard? A perfect emulator for BD caves, except for its small size! Oh man, I'm so excited!

A new DFF!
Name I think "swarm" would be fitting, because the group stays very close together, far closer than in any other known DFF.
Composition 8 butterflies
Phases Short loop 2, long loop 12
Direction 1 up per short loop
Free riders 7 or more BF, perhaps infinite?
Special remark Not vortex-based!

Phase 1 x = empty space
uxx
uur
uux
ulx

Phase 2
urx
ulx
uld
lxx

Optically, this DFF is very impressing. There are 3 columns with 4, 3, and 1 BF. While the two columns of 4 and 3 BF move upwards quite regularly and gradually, the rightmost BF seems to "fidget" up and down all the time, as if it would be less calm than the others! Or perhaps it just needs to go to the toilet urgently
My little cave on Krissz's site shows 7 free riders, I doubt that this is the max because this formation just occured by chance out of a big BF square!

There are two BF who always keep their position in the group, while the other 6 switch their position every short loop. So the long loop is 6x the sort loop.

So? We're far from done with our DFF research, it seems!