Why π = 3.31 for zombies + How to make Minecraft farms 1% faster

Looking for mild improvements to your Minecraft farms using weird definitions of circles?
@DashPum4 's gold farm: • Minecraft Boat Looting...

[@1224chrisng]

Happy March 31st!

[@SonifyBruh]

I'm confused..

[@andyk3889]

@@SonifyBruh it was pi day yesterday, but pi day isn’t until the 31st for zombies.

[@PrivateLZG]

He kinda did a march fools joke there

[@FewVidsJustComments]

He means April 31st. Pi Day in Europe is 31/4, or April 31st

[@ashish_45playz42]

@@FewVidsJustComments Wrong, it's Nonnavimberter 4th

[@BeepirBypr]

very useful for my mob farms that are insufficient by 1.01%

[@jacob_997]

beepir you are the biggest minecraft nerd

[@BeepirBypr]

@@jacob_997 😔

[@Hietakissa]

You mean inefficient?

[@aklltv9598]

@@Hietakissa insufficient

[@Periwinkleaccount]

By 1%, not 1.01%.

[@theoverseer393]

“Why are your tunnels 20-25° askew?” “Makes it easier to run from mobs”

[@petersmythe6462]

Note this means that in order to escape something really fast pathing across the ground in Minecraft, you shouldn't be running in a straight line or diagonally but 20-25 degrees away from a straight line.

[@palladianaltruist8047]

diagonal lines are straight; you're thinking of 20-25 degrees away from a horizontal axis.

[@Hacker1o1]

@@palladianaltruist8047 no big diff, his point still stands

[@imboredrly5478]

move like a knight in chess

[@austinvw1988]

@@palladianaltruist8047 🤓☝ermmm technically ..............

[@cubicinfinity2]

i thik that reLLY is the best takeaway. sry, im just typig quickly with my two knuckles.

[@TheGoodMorty]

I feel like this is the perfect kind of content to make a kid who is kind of into minecraft actually find an interest in math

[@whitestonejazz]

It's always surprising to learn how many people find math interesting and think they don't.

[@p1nball729]

I actually got into math because of minecraft

[@cleverman383]

@@whitestonejazz most people think math is just memorizing formulas and plugging numbers into them, because that's all that's taught in school

[@jadedesigns6171]

@@whitestonejazz Because public school math is the most boring and disgusting appropriation of what math actually is

[@jarbarsi]

@@whitestonejazz I have always known that I find math pretty interesting, but I have always and will always hate math classes, drilling the same formula with different numbers over and over for weeks on end is infinitely less interesting than actually having an application to use those formulas in. (and I'm not talking about the freaks in word problems that want to buy 500 watermelons or own strangely geometric plots of land lol)

[@tsawy6]

This isn't taxicab geometry but the chessboard geometry (named after the movement of kings or queens), known in math spaces as the chebyshev metric

[@olafim299]

not really chess geometry as the diagonal distance is still counted at the square root of two not as one

[@tsawy6]

@@olafim299 are you sure about that for pathfindings sake? For speed, yes, but it seems from this vid like the pathfinding considers a diagonal as one block when doing 'pathfind to within 13 blocks' Diagonal as sweet of 2 is consistent with stando Euclidean geometry, which obviously isn't in play here

[@random832]

@@tsawy6 my understanding is that he's considering speed more relevant than pathfinding for mob farm efficiency because the mob occupies its spot in the spawn cap until it reaches the portal. Counting a diagonal as one block would make the 'circle' a square [a normal one, not a 45 degree diamond shape as in taxicab geometry. I believe the AI goal actually uses taxicab geometry to decide if a destination is close enough, and doesn't directly consider either the time or the number of pathfinding moves]

[@tsawy6]

​​@@random832 your second point is absolutely correct, and I'd forgotten that. It's a strange sort of hybrid geometry, where distances are calculated euclideanly, but the allowed paths are restricted. You can't travel the distance from (0,0) to (1,2) directly as the root(5) distance it is in euclidean, nor can you do it in the same time as travelling 2 blocks (the distance in chebyshev), nor does it take 3(as it would in taxicab). The minimum distance you can do it in is 1+root(2). Huh, this is a fascinating metric that I don't think we ever covered in my functional analysis course! Formally it's probably easiest to think of a vector space where paths are parameterised as a(1,0)+b(1,1)+c (0,1) where a,b,c integers. Then the distances are given by a+c+root(2)b. We can see from this I think that the distance from (0,0) to (x,y) is given by (for x

[@PhilfreezeCH]

The chebyshev metric would mean the mobs have independent x and y speeds, so it takes them the same amount to travel one block diagonally than it takes them to travel one block along the coordinate axis. I might be wrong but I don‘t think that is the case. In other words while traveling along the diagonals the mobs would have sqrt(2) times the soeed of traveling along one of the coordinate axis.

[@Zuchii]

As someone that thoroughly enjoys overcomplicating farms & avoiding typical "out of the box" tutorials, this content resonates extremely well with me. Sub'd !

[@_KK]

Chebyshev distance! Honestly when designing AI based farms (not a big fan) I usually timed mob lifetime and was spawning them manually around the outer edge finding where it's the needed value, usually for pigman farms in the end it was a shape looking like a mandelbrot set instead of a half circle, not sure if you did practical tests for this video

[@_KK]

If you need to find lifetime of a mob do the following commands: "/scoreboard objectives add [Name] dummy [Display name]" "/scoreboard objectives setdisplay sidebar [Name]" And put the last command in the repeating command block "/scoreboard players add @e[type=Pigman] [Name] 1"

[@owendeheer5893]

Could you elaborate this, I don't quite understand

[@_KK]

@@owendeheer5893 On what exactly? You take some number lets say 70 ticks and you spawn mobs around your platform and only keep positions where lifetime is

[@owendeheer5893]

@KK ah I see, that makes sense. And I guess the 70 ticks is the cycle time you choose for the farm or something like that as you don't want mobs to be too long on the platform

[@dantesk1836]

omaigosh. it's KK!

[@naturecomics]

For those of you wondering, distance between two coordinates here would be equal to max(x,z)+min(x,z)(sqrt(2)-1) where x and z represent the positive difference between the coordinates along the respective axes. Adding this to my list of distance types! Euclidean, Manhattan, Chebyshev, and now Minecraft(?)!

[@SteamShinobi]

Im sorry to bother, this looks very similar to the equation he used for determining zompi 8*(sqrt(2)-1) are they related? How is this working?

[@klobiforpresident2254]

"Minecraft distance" is Chebyshev / chessboard distance.

[@AlphaFX-kv4ud]

@@klobiforpresident2254 technically isn't it slightly different because it still only has 1 Euclidean distance always being the same as 1 Minecraft distance unlike in chess where it isn't always the same thing

[@naturecomics]

@@klobiforpresident2254 There actually is a difference. The diagonals in Chebyshev/chessboard distance have a length of 1 while in "Minecraft distance" the have a length of sqrt(2).

[@naturecomics]

@@SteamShinobi They are related! Basically, he calculated the "Minecraft distance" between two adjacent points on the "circle", multiplied that by eight, and then divided by the diameter. The result you get from this is 8*(sqrt(2)-1).

[@TMinusRecords]

It's amazing how you innovate in areas we don't even think about

[@darkwise8628]

you might know this already, but using the carpet ai_tracker module you can display the path finding of mobs!

[@pkalman2045]

great execution of a unique idea. your channel is going places, sir. (and now i'm gonna binge your other videos lol)

[@Axodus]

Not only does the spawning pad look cooler, it's also more efficient.

[@Orberror404]

If we're familiar with L_p norms, then the L_(10/3) norm seems to be a good approximation to the metric described in the video. For a summary, L_1 is taxicab geometry, L_2 is Euclidean geometry and L_infinity is Chebyshev geometry. The formula for pi in this case is given by: 2*integral_0^1 (1 + (x^(10/3)/(1 - x^(10/3)))^(7/3))^(3/10) dx, which is very close to 3.31 (check with wolfram alpha). And if you plot the unit ball onto desmos |x|^(10/3) + |y|^(10/3) = 1, you get a very similar looking 'squircle' to the shape in the video. Edit: noticing some answers saying that this is Chebyshev geometry - not quite because the time taken to walk a diagonal is NOT the same as the time taken to walk orthogonally (compare with a king on a chessboard for instance). But it's not quite Euclidean geometry either, because the zombies don't walk in a straight line. So the answer lies somewhere between L_2 (Euclidean) and L_infinity (chebyshev). And it turns out that L_(10/3) fits the bill.

[@soninhodev7851]

Yes, in fact i know why, if you as the player where to mimic the way the pigman move diagonally, what you would do is rotate your camera so its 45º from the grid, and then press 'w', and if you were to mimic chebyshev diagonal movement, you would rotate your view so alings with the grid, and then press 'w'+'d' which as any PvPer could tell you, makes you move sqrt(2) times faster.

[@Windows__2000]

You get your honorable spot in "might be useful later" playlist

[@cetusdf3380]

watched your vanilla skyblock series on the old channel so long ago, super pleased to see the algorithm has fed me this video to lead me back here. glad to see you're still around.

[@petervasil6159]

im so happy that i found this small channel , this is top tier content and i hope you had a great pi day (you tube recommended was a bit slow )

[@dimaryk11]

I really like your energy and general curiosity. Thank you for lighting up my day

[@FQT_Keller-Ash]

wtf i stumbled onto this video and its genuis i love looking at technical parts of video games and i havent seen anyone else do this in minecraft idk hope you keep making content and also Erin Go Bragh

[@deegobooster]

I remember gnembon did a video on this topic a long time ago but I keep falling asleep. Your explanation is much cleaner and understandable for me 😅

[@thedenominator_]

cool, i love these sorts of pathfinding farms and optimizations!

[@Carhill]

4:11 - For the eighth of a circle, I'd borrow from our lovely musician friends and say hemi-demi-semi-circle. 😂

[@sgrey9181]

This is genuinely the best Minecraft farm video I have seen in years. You earned yourself another sub!

[@PieterZijlstra]

you're growing like crazy! Well-deserved!

[@theweeniemobile]

I loved all the analysis and math, and then finding an application for it all in making the farms fractionally more efficient

[@andrewevenson2657]

Fascinating, this is some unique pi day content right here!

[@YounesLayachi]

easiest subscribe of my life. i was really hoping to see more minecraft videos when i clicked your channel, instead of more pi videos (i mean, with the passion you speak about it, it could have went either way). was not disappointed !

[@CivetKittyMC]

I wonder how this will shape the oldschool donut gold farms as these are freakishly hard to build without external tools.

[@ArchDennam]

I'm not quite sure if those will change, since those are based on spheres around the player, not the walking distances of the zombie piglins. But if there's some further optimisation that could be done for them on, say, the path from the donut to the player I'm right there with you wondering too.

[@rigierish3807]

That's what I love about sandbox games such as Minecraft : when you take advantage of the game's mechanics to do the most efficient farm, there's always something to discover to make it even more efficient than before, and after exploiting every mechanics, after optimizing the number of blocks or the space your design takes, after doing it in the most convenient place in the most practical way, you can still improve it by understanding how the games calculate things as basic as the path finding of mobs to make the platform the most efficient for their path finding. That's incredible.

[@FM_MC]

amazing video man keep it up!!!

[@roderik1990]

4:12 Reasonably sure that an eighth of a circle would be a hemidemisemicircle.

[@slicedlime]

That’s a really cool analysis!

[@NicoisLOST]

Super cool stuff man, good job!

[@rukus_1]

This stuff is really cool that I doubt most others think about. Keep it up

[@retu3510]

This is such a fun and weird channel, I also want to have so much fun messing around in minecraft! :D too bad I don't have a math background.

[@nyanezt9636]

very interesting and informative video, thanks!

[@Pipinder_]

Such a great content! For the whole video I thought you have at least 100k views. Very underrated, keep going!

[@calvin5374]

Love how you just notice something in minecraft and start a study about it. I do it sometimes as well, but with everyday stuff

[@FloppyDonk]

Wow this is really interesting! Super cool use of math tailored to minecraft!

[@DoctorPlasmaMC]

"there's no pi on this 4-func calculator" ... "oh yeah" *types it* my favorite reason I learned a bunch of pi

[@DashPum4]

Woah ive been watching u for a while so this video is especially cool lol

[@ShrekPNG]

4:10 They are called sectors. A sector is a part of a circle, delimited by two of its radiuses. A segment is a part of a circle, delimited by its chord

[@EebstertheGreat]

In StarCraft, the distance function is very simple to save resources. It requires no divisions or square roots (the divisions in the source code are compiled to bitshifts) and uses a linear approximation of distance mirrored a few times. The result is that a curve of constant distance from a point is not a circle but instead (approximately) a regular dodecagon. The distance function takes an ordered pair data type called an xy which has the differences in the x- and y-coordinates of the two points in fixed-point 8.8 binary format and returns an approximation of the Euclidean length of the xy. It looks like this: int xy_length(xy vec) const { unsigned int x = std::abs(vec.x); unsigned int y = std::abs(vec.y); if (x < y) std::swap(x, y); if (x / 4 < y) x = x - x / 16 + y * 3 / 8 - x / 64 + y * 3 / 256; return x; } So in the first quadrant, if y > x/4 or x > y/4, it just uses that larger value. If not, it will use a line with slope of -236/99 = -2.3838... if x is larger or -99/236 ≈ -0.419491 if y is larger, with this reflected for the other three quadrants. The endpoints almost meet up, but not quite due to the rounding built into the calculation. It's extremely efficient and surprisingly convincing in practice, though it does cause a lot of headaches for AI-controlled units. Additionally, although there are 256 possible angles in StarCraft (32 of which have unique sprites), most of the time units only move along the 8 primary directions, at least if they are traveling any significant distance and don't encounter an obstacle. However, although they can only move in 8 directions, they still move at a roughly constant speed (in the Euclidean sense), so it still takes longer to move along the diagonal of a square than one of its sides. So you don't get this King's-move behavior.

[@andrewcpu]

I just stumbled onto your channel, I've been out of the Minecraft dev scene for a while, but damn, i love this video. idk if its how you speak or something but, for real, good video

[@maxinac]

Thanks for sharing your parrot project at the end, I didn't know they were telling you the nuclear launch codes!

[@ProbablyBarney]

this video snipes the sweetspot of my brain that has a weirdly vested interest in both math and minecraft

[@gregwhite6998]

Wow the KZbin algo is weird. Recommends a bunch of weird stuff but glad it recommended this! Great video, good content, pace and feel. You rattling off Pi at the end was disgusting lol Great stuff please keep it up, got a new sub!

[@BurkeMcCabe]

This is such a good example of why non-euclidean metrics are useful! This channel is everything I ever wanted ❤

[@dukecatfishjunior6291]

this video should've totally been 6:28 long for 2*pi

[@muffinman9018]

Imagine if a farm was 0.5% away from reaching maximum efficiency...

[@bruhmoment1835]

Sectors, segments, and arcs are the words you're looking for

[@introvertswag6494]

Oh my god I never knew you kept making videos. I'm still subscribed to RedstoneJazz lol

[@1224chrisng]

2:55 this reminds me of Snell's Law, wonder if it'd apply here somehow

[@mrchampion7134]

This knowledge will be applied to villager operated farms and bee farms, increasing productivity by 1% or more. 😊

[@youvebeensubbedto8009]

this is really cute and informative :>

[@Sawyernilsson]

Man i was impressed when you went past the 50th diget, i can only do up to 3.141592653589793238462643383279 (31 digets if i can count correctly)

[@thechosenone7849]

And went to the 69th digit (after the decimal). Nice

[@wheresmymuffins]

another application for this specific kind of movement is tabletop gaming, like D&D or Warhammer, where minis are confined to the grid, and moving diagonal 1 block is considered the same as moving 1 block along the grid (depending on the rules; in some games/editions, a diagonal move might count as double movement instead)

[@lightguy250]

minecraft's william osman in all seriousness this is very interesting, just when you thought we had gotten the "perfect" farm someone comes up with this tiny optimization

[@ITS_MEEE333M]

matt parker might be a bit happy that his hand calculated pi's can be closer to minecraft's pi XDD

[@aprobaralaprimera8108]

It is call "60 degree arc" nice video! 4:20

[@juniper8827]

cant wait for zombie pi day

[@bucketmann3443]

This is cool, I like this content.

[@michaelwarnecke3474]

This was phenomenal!

[@alakazam482]

Cant wait for the guys at scicraft to hear about this and make more efficient farms with it

[@shasha6704]

you have a beautiful voice! also the minecraft stuff is cool

[@ConsumerOfCringe]

Hemidemisemicircle: one eighth of a circle

[@xiphosura413]

You remind me somewhat of SethBling, I remember really enjoying his content like this, digging into how the game works.

[@EnderMega]

"Today I was playing Minecraft and decided to calculate Pi." Also, making the title "... increasse by 1%" was zero click bait, nice!

[@addymant]

As far as I can tell, the distance formula in this model is |x - y| + sqrt(2) min(x, y)

[@whtiequillBj]

@0:36 "sort of weirder diagonal" the word you are looking for is "oblique".

[@RigoVids]

The taxicab analogy forgets one aspect, that being that the distance covered still takes time. The mobs walk the same distance across diagonals, meaning it may be slightly less efficient to have the mobs travel along the diagonals.

[@user-nu3kb8pe6g]

elaborate reason to flex the memorization of pi

[@wingedcatgirl]

That is... a lot more pi than I have memorized! Though you happened to pause for a sec right after the last number I know.

[@YounesLayachi]

this is _revolutionary_ :)

[@xtremhillblly2269]

@Vsauce Michael this is pretty cool

[@mikecroakphone]

My head is spinning and I like it

[@lexiette8343]

they live in a world where circles are octagons, truly terrifying

[@dexlovesgames_dlg]

Yo nice umbrella my guy

[@Scott.E.H]

Well now I need data. Test those 1% claims boi!

[@ryansullivan3085]

I don't know how I haven't noticed that zombies only walked in 8 directions. I've been playing this damn game since before zombies were even added!

[@addymant]

By the way, I got a different value of pi than you. Area of an octagon I believe is 2 sqrt(2) r^2 (where r is the major radius), which lines up pretty nicely with πr^2, so π = 2 sqrt2 ≈ 2.83 So I guess I'll see you on Feb 83rd!

[@jek__]

Funny you measured the radius when talking about pi. People cant help but align with the more natural tau :P

[@whitestonejazz]

Perhaps a tau day video is in order

[@migsy1]

Nobody has commented this yet, but all of the digits of pi at the end are correct! Great job Chris!

[@chinesecabbagefarmer]

Well done!

[@leonantonov2577]

Great video!

[@wyboo2019]

the relevant google search term would be "metric space" btw, or maybe "taxicab metric"

[@chadchampion7985]

great content

[@voidkat]

funny how i discovered this video on march 31st

[@Kelvoraax]

As far as I'm aware, 1/8th of a circle would just be a sector!

[@chuulover69420]

Shows up on my feed on 3.31, lol.

[@RockylarsYT]

We do see the Zombie Pigman walk a 2 block long diagonal or just half diagonal in the beginning though, so they can go in 16 directions.

[@captainpolio867]

After paying close attention to the blocks the piglin walked on, it follows the "8-directional" format

[@somniad]

Does it turn out to be practically true that zombies take the same time to move along a diagonal as straight, or do they actually take longer by a factor of sqrt(2), or is it something weirder?

[@niconico6391]

I don't know who you are but that was fun, thanks

[@kit0134]

4:11 demisemihemicircle!

[@Bloopy]

I don't even care about the farm I just clicked the video bc the title was too good

[@Hlebuw3k]

This is awesome!

[@Dragenst]

really enjoyed the video! what you're reffering to is also more formally denoted as "Manhattan Distance" (might give better search results idk) I researched a lot on this topic when doing distance functions for a crosshair builder I was working on while in college. also, I love to see people finding out these sorts of things that are genuinely interesting; It's something I wouldn't expect to see in a Minecraft video. color me pleasantly surprised and satisfied.

[@theapexsurvivor9538]

8th of a circle is a hemi-demi-semi-circle

[@wollebay]

very interesting video

[@basicallyluci8048]

how is there people like mumbo or etho, or the guys from scicraft.. but this gorgeous man with a medieval clock as his beds footend is discovering sh*t that ive never seen before no hate, all love this blows my mind