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Dancing fly formations explained
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Arno
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PostPosted: Sun Oct 27, 2019 10:25 am    Post subject: Reply with quote

Yess! A new DFF, congratulations! Very Happy

Here are a few quick observations from my side after recreating it in the editor:

A mirrored pair with fireflies is not possible. This was one of the first things I checked (as you might have guessed... Wink)

On the other hand, when I saw this DFF it immediately reminded me of the firefly 'parade' from this video: https://www.youtube.com/watch?v=pmFKt4joGhg, which also shows a tight group and seems infinitely extendable. Both phenomena appear like a caterpillar-tracked vehicle to me.
Of course, the FF "formations" need a wall to run along, but perhaps there are some similarties between their working and the "swarm". Something to be investigated further...

Lastly, when I add an additional BF to the left, it actually joins the formation and influences other flies. So it seems that instead of a DFF formation with free riders, you have discovered an (infinite?) class of unique DFF formations! Very Happy
(Altough I'm not completely sure what you meant with "free riders" as you mention that 7 or more are possible, while in my example I add only one... Smile)
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LogicDeLuxe
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PostPosted: Sun Oct 27, 2019 11:19 am    Post subject: Reply with quote

Arno wrote:
Both phenomena appear like a caterpillar-tracked vehicle to me.
Indeed. In small groups, this was my first association, too. When it becomes bigger, it more closely reminds me of a tornado. Especially the launching process, as it seemingly sucks in all those flies into a funnel.
I think, "funnel crawler" would be a good descriptive name for it.
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Dustin
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PostPosted: Sun Oct 27, 2019 12:34 pm    Post subject: Reply with quote

Thx Very Happy "Yess!" was kind of my first thought about the discovery too, or perhaps the second after "Whoa!!!" Very Happy
Well I just thought it was free riders without really checking who influences whom. The big BF square in my cave on Krissz's site was the one I originally threw into the editor. When I realized the butterflies wanted to move up quicker than my cave size allowed them, I made the cave bigger and saw that 15 flies kept moving upwards at high speed {actually it is the quickest DFF so far - so much about your "fear" that the DFF become slower and slower the bigger they get Very Happy }. Then I checked how many butterflies I could remove without breaking the formation, and 8 was the minimum, so I just claimed without further testing that the other 7 were free riders!

Your "firefly parade" cave on Youtube had slipped my attention so far, but it is really amazing! Clear similarities indeed! I saw this effect before, in an AD intermission where you also let some flies "walk down the stairs", but in this extension - wow!

Here's how I found it, perhaps it's interesting for further research. I started with a FF double vortex surrounded by the max of fflies because the DFS is also built around such a double vortex.
XLXLXU
DXULXX
XDXXRU
DXRXRX or similar.
This gave some well-known small FF formations, but nothing special. Then I "filled the gaps".
LLLLLU
DLULUU
DDRDRU
DRRRRR
and when this didn't give me anything over-spectacular either, I tried the BF-analogon of this square, which is exactly the formation that gave me the 15-BF-swarm!
Now I'm gonna rest on my laurels - or no, too many cave ideas in my head!
Very Happy Very Happy
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PostPosted: Sun Oct 27, 2019 1:55 pm    Post subject: Reply with quote

Ehm... I don't know whether you're already ready for the next discovery, but let's see Very Happy
Name Hmmm... it somehow reminds me of pi, the circular number, but this is still upgradeable Very Happy
Composition 6FF+2BF
Phases 2/12
Direction 1 left per short loop
Extension "U" at the top-right corner, to the right of the four "L" in phase 1

Phase 1
LLLL
XllU
XDXX

Phase 2
LLLL
DddX
XXRX

capital letters=FF, small=BF.
There's a clear connection to the "swarm". The direction is mirrored {up --> left}, same speed, and they also stay very close together. There's no mirrored pair BUT if you mirror it without replacing the 2BF by FF, you actually get the "swarm"!

Over... for today. Most likely, at least Very Happy
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PostPosted: Sun Oct 27, 2019 6:59 pm    Post subject: Reply with quote

Fantastic! Very Happy

Now it really seems that a full class of swarm-based DFF's exist, next to the class of vortex-based DFF's!

When playing around with it in the editor, I also found that you can stack fireflies on top of the basic formation. This resembles the "butterfly-swarm" formation and its extensions for fireflies, with the exception that the two butterflies in the centre must remain butterflies... So except for those 2 butterflies we have mirrored pair for each extesion; this is something I want to find an explanation for...

Now I see that the extended firefly "swarm" also resembles the tornado (as LogicDeLuxe calls it) from the Firefly Parade caves, but now it seems that those 2 butterflies enable the formation to move through open air rather than along a wall. Smile
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PostPosted: Sun Oct 27, 2019 9:30 pm    Post subject: Reply with quote

Yeah, cool! Cool
Some more thoughts -
1. All these "swarm formations" can probably only move up or left, perhaps up-left. This is due to the cavescan order - a down- or right-moving formation can never stay together that closely!
2. I expect that in the bigger swarm formations - the biggest I've found so far is the 15-BF-swarm in my swarm-cave - it doesn't matter whether the inside flies are FF or BF. The role of the inside flies is just firstly to move and stop alternately and secondly to influence their neighbors by their presence, and I don't see why the one fly gender should do this better than the other. In the two 8-fly-formations I've just presented here, there are no real inside-flies yet, so this expected effect is not yet visible.
3. So far I discovered, apart from the 8-BF and 15-BF swarm, also a 12-BF swarm. All three move upwards with speed 2 frames/movement. Maybe a n-BF-swarm moving up at this speed exists for every n greater or equal to 8. This would give great effects if a swarm could grow bigger and bigger by "taking over" more and more BF! In this case, though the additional BF are no free riders by your strict definition, the similarity between all these BF-swarms is so big that I still wouldn't call each of these formations unique. Perhaps one could define "semi-free riders" in a fitting way. Compare this with, for example, the Fright-n formations, which have different speed for each n so there's a clear difference between them apart from their size!
4. There seem to be two "types" of flies in the swarms. The inside flies move and stop alternately, while the outside flies kind of surround the whole group and keep them together. so that none of the inside flies can "break out"!
I'm looking forward to further investigations! Very Happy
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PostPosted: Mon Oct 28, 2019 7:58 pm    Post subject: Reply with quote

Very interesting!

Now I see that your last formation, with fireflies (going left) and 2 butterflies in the centre, is also possible with just 1 butterfly! You could replace the butterfly at front with a firefly in the same direction.

I also noted your extension with an extra "U" at the top right (I call this the tail). It seems that this version of the base formation is not extendable with extra FF. If I try this, it drop its tail. Also, this extra "tail" doesn't work in the butterfly-version of this formation.

So, the base formation for fireflies now exists in 4 versions: with 1 or 2 butterflies in the center and with/without the extra tail.

To be honest, for me it's getting a little confused now, and I really want to dive into these formations in more detail, including the relations with the "firefly parade" formations, and dedicate a full episode about all these. But first I'll finish the research and episodes on the "older" formations Wink

I do however have a name suggestion. I found the word "tornado" from LogicDeLuxe quite striking for this class of formations.
My suggestion:
- Tornado-Bx, for the butterfly version with x >= 8 the total number of butterflies (where x=8 gives the base formation and higher x an extension).
- Tornado-Fx(y)[+t], similarly for fireflies, but with y = 1 or 2 the number of butterflies in the centre and the optional "+t" (tail) indicating whether the additional tail is present (only for x=8 ).

@Dustin, Let me know what you think. It's your invension so you'll have the last word.... Wink
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PostPosted: Mon Oct 28, 2019 11:36 pm    Post subject: Reply with quote

Arno wrote:
Now I see that your last formation, with fireflies (going left) and 2 butterflies in the centre, is also possible with just 1 butterfly! You could replace the butterfly at front with a firefly in the same direction.

Ah, nice! That makes sense as this fly is actually an "inside fly" in the sense that it is fully trapped in one phase and allowed to move left in the other. In phase 1, it looks like it could move left, but actually the cavescan order allows the upper-leftmost ffly to move first and block the way. So our left-facing inside fly turns its direction in a way that moving left becomes its favourite direction, and this is true for both fly genders! Soin phase 2, when it's allowed to move left, it will do so no matter what other options might be possible for it. This pattern should be visible more and more often in bigger formations, so the gender of all inside flies becomes irrelevant!
Arno wrote:
So, the base formation for fireflies now exists in 4 versions: with 1 or 2 butterflies in the center and with/without the extra tail.

Yeah, I'm confused too! ;D
Arno wrote:
I do however have a name suggestion. I found the word "tornado" from LogicDeLuxe quite striking for this class of formations.
My suggestion:
- Tornado-Bx, for the butterfly version with x >= 8 the total number of butterflies (where x=8 gives the base formation and higher x an extension).
- Tornado-Fx(y)[+t], similarly for fireflies, but with y = 1 or 2 the number of butterflies in the centre and the optional "+t" (tail) indicating whether the additional tail is present (only for x=8 ).

I have just one objection. I'd really like to call the up-moving DFF "swarm" instead of "tornado". A swarm was my immediate association when I saw all these BF moving up, and also I think a tornado is more supposed to move in a horizontal rather than a vertical direction. That's why for the left-moving version, I find "tornado" quite fitting. Also, as I think that only the genders of the outside flies is definite, I'd find "tornado-Bx/Fx" somewhat irritating. So my suggestion is to call the up-moving DFF "swarm" and the left-moving "tornado".
Also, I'm not sure whether a name like "swarm-17" would already define a unique formation because it's very likely that there's more than one swarm DFF with 17 BF! It reminds me of chemical isomerism! So I think we need to understand these DFF in more detail before we can think about the precise naming! Very Happy Also we do have a little time for this, as there are still some old DFF waiting for their articles! ;D
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PostPosted: Tue Oct 29, 2019 11:34 am    Post subject: Reply with quote

Dustin wrote:
So I think we need to understand these DFF in more detail before we can think about the precise naming!
I agree. Details will follow when time is there.
But if you don't mind I add an entry to the list which represents the "big class" of formations for now, with name "Swarm".
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PostPosted: Wed Oct 30, 2019 8:36 am    Post subject: Reply with quote

Of course I don't mind, to the contrary! Very Happy
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PostPosted: Sat Nov 02, 2019 5:14 pm    Post subject: Reply with quote

Episode 12: What happens when a DFF hits another fly?

This episode is not dedicated to one particular dancing fly formation. Instead, we will discuss a set of interesting effects which occur for various known formations. It turns out that magical things can happen when a dancing fly formation collides with a spinning fly or vortex at some point in the open space, with the right timing.

For example, this video shows some amazing firefly effects. Fright-3 extends to Fright-4 or Crawling-F4, Fright-4 to Sinking-F5, et cetera... For butterflies, for instance, a simple BnB can be extended to Crawling-B4 when it hits a BF vortex. As another example, an innocent and lonely butterfly is able to split the powerful army of Sinking-F5 into an FnF going left plus a Fright-3 going right. So even when the spinning fly is of a different gender than the formation, it may transform the formation considerably.

These observations inspired me to reserve some time to find out all existing effects when a formation collides with a spinning fly or vortex, by simply testing all possibilities.

So, which tests did I perform?

In short, for all unique DFF’s (as listed in the first post), I have tested all possibilities to let the formation collide with either a spinning fly or a vortex (of both genders). In general, this gives quite a lot of configurations to test, since both the position and the timing w.r.t the formation are relevant configuration parameters.
Consider Fright-3 as an example. This formation moves to the right and has a height of 3 positions. Because flies are spinning in a 2x2 square, there are 4 vertical positions to place a spinning fly such that the Fright-3 will hit it. A spinning fly has 4 phases and a vortex has 2, so in total there are 6 phases to test. Combining the phases with the vertical positions gives 6*4 = 24 configurations to test. Since both genders are considered, each test is executed both for fireflies and butterflies. Thus in total 2*24 = 48 configurations have been tested for Fright-3.
Yet, there’s another complicating factor. Some formations move more than 1 position per short loop. For example, Fright-4 is similar to Fright-3 in terms of its height and its moving direction, but an important difference is that it moves 2 positions to the right per short loop. This implies that when Fright-4 approaches a spinning fly (or vortex) there are 2 phases when the formation could hit the fly/vortex. Therefore, each configuration is tested twice, where the initial distance between the formation and the fly/vortex differs one position between both scenarios. Thus, for Fright-4, twice as much configurations as for Fright-3 have been tested: in total 2*48 = 96 configurations.

Overview of all effects

Below list shows all interesting effects which I have observed while performing the tests as described above, for all unique DFF’s. Video links are provided when possible. Effects without a video link are still “in the fridge” waiting to be used in a cave at some point time… Wink
For each group of effects, a screenshot from the Editor (at Krissz’ site) shows how you could recreate these setups by yourself. This way, you could see the effect in action so you know how to use it in a cave, if you wish.

Note that for the majority of the tested configurations nothing really spectacular happens. For instance, the formation breaks and all flies end up spinning around. These effects are not included in the list as they are not quite special. Also, I have seen many occasions where a big formation breaks in to a small formation (e.g. FnF or Fright-3) and a set of spinning flies. Such effects were also not spectacular enough for me to mention in the list.
In general, the effects that I did add to the list are those which fall into one of the categories:
- Merge: the formation is extended to a bigger formation.
- Split: the formation is split into multiple smaller formations (with few or zero left-over flies).
- Deflection: the formation converts to another formation of the same size, or the same formation has shifted in horizontal or vertical direction.
- Stagnation: the formation stops moving while ending up in a funny pattern.

The choice what to add to the list and what not is of course a bit subjective, I admit, but on the other hand, without being selective the list would also become 3 times as long as it already is.
That said, the list of effects, grouped together with the accompanying screenshots, is as follows. (Note that I use abbreviations FFv and BFv for a firefly- or butterfly-vortex.)


001: FnF + FF: FnF shifted 1 down
002: FnF + FF: FnF shifted 1 down (other way)
003: FnF + BFv: Lifted B-vortex (+1 FF spinning)
004: BnB + BFv: Crawling-B4 (cave: Cursed Bricks, Shredder)
005: BnB + BF: BnB shifted 1 right
006: BnB + BF: BnB shifted 1 right (other way)
007: BnB + FFv: Lifted F-vortex (+1 BF spinning)
008: Fright-3 + FF: Crawling-F4 (cave: Firefly Circus)
009: Fright-3 + FF: Crawling-F4 (other way)
010: Fright-3 + FF: Fright-4 (cave: Firefly Circus)
011: Fright-3 + FFv: Continues with other vortex
012: Fright-3 + FFv: Fright-3 shifted 1 down
013: Fright-3 + FFv: Fright-3 shifted 1 down (other way)


014: Fright-3 + BF: Free-riders formation (cave: Free Riding Butterflies)
015: Fright-3 + BF: Lifted F-vortex (+1 FF spinning)
016: Fright-3 + BF: Continues, but BF moved to left
017: Fright-3 + BFv: Free-riders formation (cave: Free Riding Butterflies)
018: Fright-3 + BFv: Lifted B-vortex (+FFv)
019: Fright-3 + BFv: BFv moved to left
020: Fright-4 + FF: Crawling-F4 (+1 FF spinning)
021: Fright-4 + FF: Crawling-F4 (+1 FF spinning) (other way)
022: Fright-4 + FF: Sinking-F5 (cave: Firefly Circus)
023: Fright-4 + FF: Fright-4 shifted 1 down
024: Fright-4 + FFv: Fright-4 shifted 3 down
025: Fright-4 + FFv: Continues with other vortex
026: Fright-4 + FFv: Fright-4 shifted 1 down


027: Fright-4 + BF: Free-riders formation (cave: Free Riding Butterflies)
028: Fright-4 + BF: Crawling-F4 (+ BF spinning)
029: Fright-4 + BF: BF moved to left
030: Fright-4 + BF: Lifted F-vortex (+ FFv)
031: Fright-4 + BF: Fright-4 moved down + BF moved left
032: Fright-4 + BFv: Free-riders formation (cave: Free Riding Butterflies)
033: Fright-4 + BFv: Crawling-F4 (+ BFv)
034: Fright-4 + BFv: Gear Wheels + FFv
035: Fright-4 + BFv: Lifted B-vortex + FnF + FF spinning
036: Fright-4 + BFv: BFv moved left
037: Fright-5 + FF: Pyramid of 6 spinning FF (cave: Frightful Attack)


038: Fright-5 + FFv: Continues with other vortex
039: Fright-5 + BF: Free-riders formation (cave: Free Riding Butterflies)
040: Fright-5 + BF: Fright-4 climbing along the BF 3 positions (extentable)
041: Fright-5 + BF: BF moved to left
042: Fright-5 + BFv: Free-riders formation (cave: Free Riding Butterflies)
043: Fright-5 + BFv: Sinking-F5 + BFv
044: Fright-5 + BFv: Gear Wheels + FFv + FF spinning


045: Lifted F-vortex + FF: Fright-3 + BF
046: Lifted F-vortex + FFv: Fright-3 + FF + BF
047: Lifted F-vortex + FFv: Fright-4 + BF
048: Lifted F-vortex + BF: Free-riders formation
049: Lifted F-vortex + BF: 2 funny dancing BF/FF couples
050: Lifted B-vortex + FFv: Formation shifts left
051: Lifted B-vortex + FFv: Fright-3 + BFv
052: Lifted Gear Wheels + FF: Fright-3 with free riding BF (+BF)
053: Lifted Gear Wheels + BF: Lifted F-vortex + BFv
054: Lifted Gear Wheels + BFv: Funny row of FFv + 2 BFv


055: 4 Elements + FF: Lifted B-vortex + BnB
056: 4 Elements + FF: Free-rider formation (cave: The Hitchhiker)
057: 4 Elements + FF: Crawling-B4 + FF
058: 4 Elements + FFv: Gear Wheels + BFv
059: 4 Elements + BFv: Continues with other vortex (horizontal)
060: 4 Elements + BFv: Continues with other vortex (vertical)


061: Crawling-F4 + FF: FnF + Fright-3
062: Crawling-F4 + FF: Glider-F5
063: Crawling-F4 + FF: Fright-4 + FF
064: Crawling-F4 + FF: Sinking-F5 (cave: Firefly Circus)
065: Crawling-F4 + FF: Fright-5 (cave: Firefly Circus)
066: Crawling-F4 + FFv: FnF + Fright-4


067: Crawling-F4 + BF: Fright-4 + BF
068: Crawling-F4 + BF: Fright-3 with free riding BF + FF
069: Crawling-F4 + BFv: Gear Wheels + 2 FF
070: Crawling-B4 + FF: Lifted B-vortex + BFv
071: Crawling-B4 + FF: 4 Elements + FF
072: Crawling-B4 + FFv: Gear Wheels + BFv
073: Crawling-B4 + FFv: Lifted F-vortex with free riding BF + BFv


074: Crawling-B4 + BF: Glider-B5
075: Crawling-B4 + BF: 4 Elements + BF
076: Sinking-F5 + FF: Crawling-F4 + FFv
077: Sinking-F5 + FF: Glider-F5 + FF
078: Sinking-F5 + FF: FnF + Fright-3 + FF
079: Sinking-F5 + FFv: Crawling-F4 + Fright-3
080: Sinking-F5 + BF: FnF + Fright-3 + BF (cave: Traffic Agent)
081: Sinking-F5 + BF: Glider-F5 + BF


083: Sinking-F5 + BFv: Gear Wheels + 3 FF (on a diagonal row)
084: Glider-F5 + FF: Crawling-F4 + FnF
085: Glider-F5 + FF: Fright-4 + FnF
086: Glider-F5 + FFv: Static-F7 (cave: Dancing Fly Stagnation)


087: Glider-F5 + BF: Fright-3 + FnF + BF
088: Glider-F5 + BFv: Fright-3 + Lifted F-vortex + BF


089: Glider-B5 + FFv: Lifted F-vortex + Crawling-B4
090: Glider-B5 + BF: BnB + Crawling-B4
091: Glider-B5 + BF: BnB + 4 Elements


092: Sinking-F6 + FF: Fright-5 + 2 FF (convertable to FnF with boulder)
093: Sinking-F6 + FF: Glider-F5 + FFv
094: Sinking-F6 + FF: Crawling-F4 + 3 FF (on a diagonal row)
095: Sinking-F6 + BF: Fright-5 + FF + BF
096: Sinking-F6 + BF: FnF + Fright-4 with free riding BF


097: Cassiopeia + BF: 4 Elements + BFv
098: Cassiopeia + BF: Crawling-B4 + BFv
099: Cassiopeia + BFv: Glider-B5 + BFv


100: Swarm-B8 + BF: Extends with extra BF
101: Swarm-B8 + BF: Extends with extra BF (other way)
102: Swarm-B8 + BF: Swarm-B Shifted 1 right
103: Swarm-F8 + FF: Extends with extra FF
104: Swarm-F8 + FF: Swarm-F + FnF
105: Swarm-F8 (with 2 BF in centre): Fright-4 + FnF + spinning flies

How successful is this method in finding new formations?

The above list of effects clearly shows that the method of colliding a DFF with a spinning fly/vortex is quite an effective method to discover other DFF’s. Suppose that we only know the simple FnF and BnB formations. Using the described method, the Fright-3, Crawling-B4, Lifted F- and B-vortex can be derived from these two. These formations in turn generate Fright-4, Crawling-F4, The 4 Elements, Lifted Gear Wheels and Glider-B5. Then, the next “generation” consists of Sinking-F5, Fright-5 and Glider-F5. This way, we could build up a “family tree” of DFF’s, where FnF and BnB are both a root of several bigger formations.
On the other hand, not all known DFF’s are found by this method. For instance, Cassiopeia is not found. This DFF appears to be a root-formation by itself, which doesn’t generate bigger formations. In other words, Cassiopeia is an orphan DFF without offspring.
Another DFF which is not found is Sinking-F6. Although Sinking-F6 is a vortex-based formation, it doesn’t show up when applying this method on other known vortex-based formations (like Sinking-F5).
Finally, the recently discovered Swarm-formations seem to be an independent set as well.

Conclusion

Although the method of hitting DFF’s with a spinning fly is not the ultimate generator of DFF’s, it does give us many funny effects which can be used very well in BD caves.
The next episode will again be fully focused on a specific DFF-set: the mirrored pair of Glider-F5/B5.
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PostPosted: Sat Nov 02, 2019 6:13 pm    Post subject: Reply with quote

Wow, great work! This is really a big source of new cave ideas! The first thing I aks myself is whether out of these effects, it's ossible to build a "closed curve" where the same effects reeat again and again!
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PostPosted: Sat Nov 02, 2019 9:13 pm    Post subject: Reply with quote

Dustin wrote:
Wow, great work! This is really a big source of new cave ideas! The first thing I aks myself is whether out of these effects, it's ossible to build a "closed curve" where the same effects reeat again and again!

Thanx! Very Happy Well, for example cave Alternating Dance shows a "closed curve", although a very simple one with just two formations and instead of a fly it uses a wall as obstacle to transform the formations. Wink
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PostPosted: Sat Nov 02, 2019 11:41 pm    Post subject: Reply with quote

Yeah, I've seen that funny cave! But what I meant was a closed curve without obstacles "in DFF style" - walls don't exist, we're in empty space... ;D
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PostPosted: Sun Nov 10, 2019 7:39 pm    Post subject: Reply with quote

Episode 13: Glider-F5 and –B5

In earlier episodes we have discussed the concept of a mirrored DFF pair and presented two examples of mirrored pairs: FnF & BnB and Crawling-F4 & Crawling-B4. In this episode we will discuss the third example of a mirrored pair.

The properties of both formation are as follows:
- Name: Glider-F5 / Glider-B5
- Composition: 5 FF / 5 BF
- Short loop: 9 / 9 phases
- Long loop: 54 / 54 phases
- Shift per short loop: 2 Left, 1 Down / 2 Up, 1 Right

Both formations reminded me of the gliders from Conway’s Game of Life. That’s why I choose to name them Glider-F5/B5.

How do these formations work?

This set of formations is closely related to Crawling-F4/B4 and Sinking-F5. Below picture shows a phase from all 3 formations for fireflies.



The basis of these 3 formations is the Crawling-F4 setup: one couple of flies (Red-Blue) is dancing in a vortex shape, while another couple (Green-Yellow) is walking around the vortex, ready to take over the dance at a certain moment in the future.
When extending Crawling-F4 to Sinking-F5, a sneaky single (the Purple fly) comes into play. He will distort the plans of both couples such that a very different formation arises, which moves into a different direction as well.
Glider-F5 involves a sneaky single as well, but this time his start position has shifted one step to the left, and therefore oppositely timed w.r.t. the vortex, compared to Sinking-F5. As we will see, this slight timing difference has major impact on the formation, its story and its direction.

Below pictures are showing the 9 phases of both Glider-F5 and –B5.

Glider-F5:


Glider-B5:


The story behind these formations is as follows. It is told for Glider-F5, but of course Glider-B5 works similarly.

Phase 1-2:
The formation starts like Crawling-F4. 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. Yet again, a sneaky single (Purple) is strategically positioned at the other side of the dancers, with different intensions.
During phase 1-2, the Green/Yellow walkers, as well as the sneaky single, are simply following their natural path around the dancing couple.

Phase 3-4:
The sneaky single breaks into the dancing couple, drifting both partners apart, and he starts a new dance with Green. At first sight, this break-in looks similar to the Crawling-F4-style of breaking in. However, since Green walked one additional position behind Purple, the new vortex starts at the same height as the original vortex. Red and Blue are drifted apart and instead of walking along the new vortex, both will first move through the new vortex as if it were a swing door.
The Yellow fly has lost his partner and is now walking alone.

Phase 5-8:
Blue seems to take revenge immediately, as he is positioned at the right-top of the new vortex, ready to break in like in Fright-3. However, his timing w.r.t. the dancing couple is just opposite to the timing he needs. Therefore, his attempt fails and instead Blue runs through the “swing door” (the dancing couple). Next, Blue and Red are walking around the dancing couple. Yellow must still content himself with a position along the sidelines, without any chance to start a dance soon.

Phase 9-1’:
Now Red takes a successful revenge. He breaks into the couple (in the style of Crawling-F4) and starts a new dance with his (her?) original partner, Blue. Apparently, this time Red and Blue are a strong couple, since both partners are loyal to each other!
Purple and Green were drifted apart and take over the role of the walkers.
Yellow, the only fly who hasn’t danced during the entire short loop, now takes over the role of the sneaky single.

Like Sinking-F5, also in this set of formations, two role groups of different size exist. Blue and Red (the strong couple) start and end with a dance, but both change roles after each short loop. The other group is formed by Purple, Green and Yellow. Purple takes over the role of Green, Green the role of Yellow, and Yellow the role of Purple.
From this it follows that it takes 6 short loops until all flies have returned to their original position within the formation. Therefore, the long loop takes 6*9 = 54 phases.

Why do these formation move in those semi-diagonal directions?

Let’s have look at Glider-F5 first. Within one short loop of this formation, the vortex moves two times:
- Between phase 3 and 4, the vortex moves 1 step to the left.
- 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 2 steps left and 1 step down. Thereby the whole formation moves into this semi-diagonal direction.

Since Glider-B5 is the mirrored partner of Glider-F5, its direction can be mirrored in the diagonal line. Thus, Glider-B5 moves into another semi-diagonal direction: 2 steps up and 1 step right.

How to launch these formations?

Launching the Glider-formations works similar to all other formations which are built around a vortex. That is:
Step 1: Create a vortex
Step 2: Connect 3 flies at a certain side of the vortex, and with the correct timing.

In this case, the first 2 connected flies should have a distance of one position in between. This way, a Crawling-formation of 4 flies is created first. Next, the 3-rd fly connects as the sneaky single, which almost immediately transforms the Crawling-formation into a Glider-formation.
The following videos show the solutions of two “mirrored caves”, each illustrating the launch of a Glider-formation:
- Glider-F5 launch
- Glider-B5 launch

There are other ways to launch a Glider-formation. For example by starting with a simpler formation and let this formation collide with a spinning fly. If timings are right, the spinning fly is connected to the formations and the group continues as Glider-formation. From the list of effects from the previous episode, the following transformations are possible:
- Crawling-F4 + FF: Glider-F5
- Crawling-B4 + BF: Glider-B5
- Sinking-F5 + FF: Glider-F5 + FF
- Sinking-F5 + BF: Glider-F5 + BF
- Sinking-F6 + FF: Glider-F5 + FFv
- Cassiopeia + BFv: Glider-B5 + BFv

Relations with other dancing formations?

As Glider-F5 and –B5 are a mirrored pair, they cannot have a p-mirrored relation with another dancing formation. Actually, given the complexity of these formations, it is quite remarkable that they form a mirrored pair. Remember that the condition for a mirrored pair is broken when at any point two flies compete for the same position to move, such that row-by-row or column-by-column cave scanning would give different result. Despite the fact that 5 flies are involved, this situation does not occur in any of the 9 phases. Also note that the above pictures do not show any “yellow star”, meaning an empty position where two flies want to move to.

Until now, three mirrored pairs have been discovered and discussed. Below picture shows an overview of the involved formations and their direction.



Of course, the directions of each pair can be mirrored in the diagonal line. All 3 mirrored pairs have a different set of directions.
At this moment it is unknown whether more mirrored pairs exist, other than the 3 shown above. For example, does a pair moving down and right exist? Or a pair moving along the diagonal, so that both partners actually move to the same direction?
I have my doubts, but time will tell, perhaps...

Other relations exist. For example, using an obstacle of the correct shape, Glider-F5 can be converted to Fright-5. Also, as shown in this video it is possible to drain a Glider-F5 into Static-F7, a dancing fly stagnation which was discussed earlier in this thread. Finally, there are several ways to split a Glider-formation into smaller formations (see previous episode).

Final note

As we progress with this set of DFF-articles, the formations become more and more complex. Out of all 5-fly formations that have been discovered until now, only one has not yet been discussed: Cassiopeia. This is quite an interesting formation because it is not build around a vortex, as we’ll see in the next episode.
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