Simple 4 & 12 piston extenders

Looking for quadruple piston extenders that operate on the principle of regular grammar isomorphism?
Spacewalker's 46-piston extender: • 46 extender
Avogaado's fast extender: • I Made the Ultimate Pi...
Mattbatwings math extender video: • The Fascinating Math b...
0:00 The things
1:24 Community context
2:48 Me standing by a whiteboard
3:48 Tutorial

[@quban234]

Spacewalker really nailed their username to fit as a name for these discovered extenders.

[@Minecraftster148790]

We absolutely need a video on the maths behind these, I would love to see a proof that these always fully retract.

[@popa42]

It is sooo fascinating that this always turns out to be working somehow… That’s why I love maths! :D

[@J2ko]

A while ago someone (maybe SpaceWalker?) laid out each step of a very long extender of this type. It looked fractally and chaotic at the same time!

[@SpaceWalkerChannel]

Yep, it's on one of my plots on Synergy! It has a few different ones, including a special case. If you take a hypothetical extender without any push limit, and let this algorithm loose on it, it settles into a super nice pattern. When you lay out each step next to each other it becomes obvious it's essentially doing binary counting, which creates a sort of Sierpinski triangle pattern. It's not until you impose a push limit on the extender that its behavior becomes incredibly chaotic.

[@CraftyMasterman]

Would love a follow up thats the complete opposite of matts and avos vid. How slow and long can a piston extender get? Are there patterns to the chaos of spacewalker brute force extenders? I think the most ive seen from them is a spreadsheet like 3 years ago

[@whitestonejazz]

There is a rigorous proof that Spacewalker extenders retract the block successfully for any size. But there isn't yet any good time analysis for just how slow they become. Once that's figured out, I'll make the math video. And there are patterns to the chaos. For now, I'll just say that the splitting and merging of the sub-extenders is oddly similar to the splitting of the "atomic elements" in the Look-and-say sequence (another chaotic math sequence that was figured out roughly 40 years ago).

[@ZephyrysBaum]

Yeah same lol!

[@wilh3lmmusic]

@@whitestonejazzwhat is the proof?

[@whitestonejazz]

@@wilh3lmmusic I'm making a full video on it so I won't give any detailed answer here. But I will say that in fancy math language, you show the piston behavior is determanistic backwards in time with an isomorphism to a regular grammar

[@vampire_catgirl]

I'm happy you brought up mattbatwings because I love that video and his channel

[@3Ppaatt]

I've never been happier that I subscribed to a channel!

[@andre_601]

I saw a version of a piston extender that also was infinitely expandable and somewhat faster. It was also 1 block wide and some blocks high. Downsides to it were 1) it uses slime blocks, so blocks next to those should not be movable by slime and 2) it uses more redstone dust which could be bad on performance. I cannot recall the pattern of repeaters (And their delays) and redstone used, but the pattern of each piston module was: SP O S = Slime P = Piston (Sticky) O = Observer (Face down) The redstone input would also be right to left in above setup, meaning the signal would go from right to left (Or always start at piston and ends at slime). If I find time, I'll play around a bit and try to find the setup again. It was a specific redstone dust and repeater pattern you follow.

[@creepinator4587]

Wow this this is fascinating! Eagerly awaiting your follow up. I wonder how this concept interacts with different clock cycle lengths...

[@EnderMega]

2:55 That was wholesome.

[@nano_redstone]

I’m really eager for the follow up !

[@Meatmallet]

Good work

[@redthunder6183]

This video gives off veratasium level vibes. AND ITS AWSOME, its like veratasium, but in Minecraft. u should really consider adopting a similar style as veratasium, 3blu1brown, numberphile, mark rober, etc. The video content is already perfect, just focus more on the cinematography, Like I really like the projector, and it'd be nice if it was full screen. things like a new camera, better lighting, adaptive music, maybe some math animations, and different camera angles (which u did really well with in this video). I don't want to sound like I'm criticising, but Its super awsome and I just wanna see more videos like this one, keep it up!

[@Elyrio3]

That's so cool!

[@Happy156]

woah that's awesome as hell

[@austinisawesome2066]

I love stuff like this, plz do the math!

[@TavishMcEwen]

nice hearing spacewalker's name :3

[@originalgames9363]

Keep it up

[@FIVEBASKET]

😮Nice

[@rick-sanchez]

I am wondering if this "chaotic" pattern relates to the logistics map* and thus may have some "stable island lengths" aka lengths that retract very quickly compared to their neighbors. Probably not but I am wondering what the time vs blocks on a graph looks like. And maybe how an circular system would behave (cant test that in minecraft) *veritasium video about said pattern kzbin.info/www/bejne/paetlKaCbNusqM0

[@papetoast]

that length is 69, not joking. docs.google.com/spreadsheets/d/1TsWICwHCjPV0JRmxDnU5vnZZ8W_uuXsN2pIdI00WaHc/edit?usp=drivesdk

[@wilh3lmmusic]

Even extenders (12gt) have tended to retract faster than odd extenders of similar length, except for 69 for some reason...

[@user-wm9sy9qd4h]

It would be really cool to plot the locations of the pistons on a graph with the piston# as x and the location as y. Time could either be the z axis or you could show the plot moving in a video.

[@Kavukamari]

Are there any designs where you use a flying machine to pull blocks back to the start 12 units at a time? I feel like that would be the fastest piston retractor for the size

[@paulfeeder4262]

i tried this with the pistons backwards(facing the other way) and it also seemed to work. am rlly hoping for the maths to be shown of.

[@HYTEOMEGAP]

common whitestonejazz W video

[@ashtonvillarreal1258]

Hello, im really hoping you can do another check in on the cookie clicker game if you still have the run going. Wich might be a simole video to make especially with how preoccupied youll be with school. Thanks and keep up the great work

[@Happy156]

is it tileable? it looks like it could be without the couple bits of redstone for the clock

[@karasmith441]

For the larger configurations are there issues with locationality? Like if you have four adjacent pistons and every third repeater is on, you'll have the front and back will fire simultaneously. Does location determine whether the first or last piston actually pushes or is there some tile-tick scheduling that makes this consistent?

[@electra_]

I really want to know why these always work now. Tempted to look into the math myself.

[@HelPfeffer]

3:19 yes plsss

[@MrCheeze]

One thing I'm not clear on - are all sizes 1-12 possible using this method? If so, why did you single out those two sizes? Is it just that size 12 is the largest efficient one, and size 4 just particularly easy to make a pulse of the right length?

[@ejacquem1587]

If I understood correctly, This system works for any length of piston extender, even after the 12 blocks push limit. And I tested that you need n-3 comparator for n piston extender length. so length 4 = 1 comparator, 5 = 2, 12 = 9,... (which is very satysfactory lol).

[@whitestonejazz]

Spacewalker extenders work for any size. So 1-to-12 are all possible and also 13-to-infinity are also possible. I chose 4 and 12 because they have good speed-to-size ratios compared with other sizes. For instance, 12 is the largest size that runs in about 15 seconds and anything larger takes a few minutes. And I chose 4 because quadruple piston extenders are very traditional in the redstone community.

[@greenstonegecko]

I need a proper math explanation on why this works and why it's uncertain if it ever fails

[@whitestonejazz]

The proper explanation will take me a while. But you can test the uncertainty pretty easily yourself! If you place the block in front of the last piston _while_ the extender is still running, you can sometimes create a non-retracting configuration. Interestingly, this isn't a problem for all sizes. The 4-piston and 12-piston extenders are immune and don't have any illegal configurations. I don't have my notes with me, but I think the 5-piston Spacewalker extender can fall into a non-retracting configuration if you place the block in at a specific time. In other words, some Spacewalker extenders _can_ fall into non-retracting (or "illegal") configurations. The tricky bit of math is proving that the default state (all pistons lined up with the block retracted all the way in) is a legal configuration for any amount of pistons.

[@ZephyrysBaum]

@@whitestonejazz I think you meant _while_ not /while/. (use _ _ not / /)

[@ZephyrysBaum]

@@whitestonejazz also sorry if that sounded mean, I love your work!

[@theagle43]

Is there a way to determine how many Comparators are needed for an extender of n-length? I saw 1 for the 4 piston and 9 for the the 12... is it as simple as numPistons-3?

[@whitestonejazz]

I did guess-n-check

[@Gekoloudios]

I still don't know how these work or where to find the math that explains them... I could directly ask space but like these must be covered somewhere already maybe in a forum or a spreadsheet Idk

[@sacha7958]

Do you mean piston extenders in general or this specific design?

[@Gekoloudios]

this specific design ofc, I know how extenders work lol

[@soranuareane]

math plz

[@PotatoCraft_TMC]

I don’t know if I like it. It’s so awful T_T but I mean… If we’re after compactness, it doesn’t get any better.

[@Rechenmaschine9752]

what happend to ur dc

[@whitestonejazz]

I don't know what dc means

[@sage5296]

@@whitestonejazz probably discord

[@whitestonejazz]

That makes sense. This deserves a longer response: I deleted the WhiteStoneJazz Discord profile cause I don't like Discord. That's partly cause people would start collaborations with me and then ghost, which was draining and hurt honestly. It's partly cause I enjoy face to face interactions more than virtual ones. But, not gonna lie, there's just a lot of inconsiderate and egotistic people on the MC discord servers. Half the stuff on this channel never would have been built if I'd listened to them (it isn't rare for my ideas to be called "fundamentally impossible" before I make them). I work better and feel better when I stay away from online communities. Similar story with Instagram and Twitter. For now, I'm happy with KZbin videos being my only online involvement. Though I still check the channel email daily to answer questions or hear ideas: [e-mail]

[@Rechenmaschine9752]

what is a twitter ? do u mean X ?

[@_BangDroid_]

@@Rechenmaschine9752 He means the site that uses twitter domain name