very useful for my mob farms that are insufficient by 1.01%
@BeepirBypr Жыл бұрын
beepir you are the biggest minecraft nerd
@jacob_997 Жыл бұрын
@@jacob_997 😔
@BeepirBypr Жыл бұрын
You mean inefficient?
@Hietakissa Жыл бұрын
@@Hietakissa insufficient
@aklltv9598 Жыл бұрын
By 1%, not 1.01%.
@Periwinkleaccount Жыл бұрын
“Why are your tunnels 20-25° askew?” “Makes it easier to run from mobs”
@theoverseer393 Жыл бұрын
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.
@petersmythe6462 Жыл бұрын
diagonal lines are straight; you're thinking of 20-25 degrees away from a horizontal axis.
@palladianaltruist8047 Жыл бұрын
@@palladianaltruist8047 no big diff, his point still stands
i thik that reLLY is the best takeaway. sry, im just typig quickly with my two knuckles.
@cubicinfinity210 ай бұрын
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
@TheGoodMorty Жыл бұрын
It's always surprising to learn how many people find math interesting and think they don't.
@whitestonejazz Жыл бұрын
I actually got into math because of minecraft
@p1nball729 Жыл бұрын
@@whitestonejazz most people think math is just memorizing formulas and plugging numbers into them, because that's all that's taught in school
@cleverman383 Жыл бұрын
@@whitestonejazz Because public school math is the most boring and disgusting appropriation of what math actually is
@jadedesigns6171 Жыл бұрын
@@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)
@jarbarsi Жыл бұрын
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
@tsawy6 Жыл бұрын
not really chess geometry as the diagonal distance is still counted at the square root of two not as one
@olafim299 Жыл бұрын
@@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
@tsawy6 Жыл бұрын
@@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]
@random832 Жыл бұрын
@@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
@tsawy6 Жыл бұрын
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.
@PhilfreezeCH Жыл бұрын
As someone that thoroughly enjoys overcomplicating farms & avoiding typical "out of the box" tutorials, this content resonates extremely well with me. Sub'd !
@Zuchii Жыл бұрын
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 Жыл бұрын
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"
@_KK Жыл бұрын
Could you elaborate this, I don't quite understand
@owendeheer5893 Жыл бұрын
@@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
@_KK Жыл бұрын
@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
@owendeheer5893 Жыл бұрын
omaigosh. it's KK!
@dantesk1836 Жыл бұрын
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(?)!
@naturecomics Жыл бұрын
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?
@SteamShinobi Жыл бұрын
"Minecraft distance" is Chebyshev / chessboard distance.
@klobiforpresident2254 Жыл бұрын
@@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
@AlphaFX-kv4ud Жыл бұрын
@@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 Жыл бұрын
@@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).
@naturecomics Жыл бұрын
It's amazing how you innovate in areas we don't even think about
@TMinusRecords Жыл бұрын
great execution of a unique idea. your channel is going places, sir. (and now i'm gonna binge your other videos lol)
@pkalman2045 Жыл бұрын
I really like your energy and general curiosity. Thank you for lighting up my day
@dimaryk11 Жыл бұрын
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 )
@petervasil6159 Жыл бұрын
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.
@cetusdf3380 Жыл бұрын
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
@FQT_Keller-Ash Жыл бұрын
cool, i love these sorts of pathfinding farms and optimizations!
@thedenominator_ Жыл бұрын
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.
@Orberror404 Жыл бұрын
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.
@soninhodev7851 Жыл бұрын
That’s a really cool analysis!
@slicedlime Жыл бұрын
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 😅
@deegobooster Жыл бұрын
I loved all the analysis and math, and then finding an application for it all in making the farms fractionally more efficient
@theweeniemobile Жыл бұрын
Fascinating, this is some unique pi day content right here!
@andrewevenson2657 Жыл бұрын
This is genuinely the best Minecraft farm video I have seen in years. You earned yourself another sub!
@sgrey9181 Жыл бұрын
This stuff is really cool that I doubt most others think about. Keep it up
@rukus_1 Жыл бұрын
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 !
@YounesLayachi Жыл бұрын
amazing video man keep it up!!!
@FM_MC Жыл бұрын
you might know this already, but using the carpet ai_tracker module you can display the path finding of mobs!
@darkwise8628 Жыл бұрын
you're growing like crazy! Well-deserved!
@PieterZijlstra Жыл бұрын
very interesting and informative video, thanks!
@nyanezt9636 Жыл бұрын
Not only does the spawning pad look cooler, it's also more efficient.
@Axodus Жыл бұрын
Love how you just notice something in minecraft and start a study about it. I do it sometimes as well, but with everyday stuff
@calvin5374 Жыл бұрын
Super cool stuff man, good job!
@NicoisLOST Жыл бұрын
Imagine if a farm was 0.5% away from reaching maximum efficiency...
@muffinman9018 Жыл бұрын
Such a great content! For the whole video I thought you have at least 100k views. Very underrated, keep going!
@Pipinder_ Жыл бұрын
You get your honorable spot in "might be useful later" playlist
@Windows__2000 Жыл бұрын
Wow this is really interesting! Super cool use of math tailored to minecraft!
@FloppyDonk Жыл бұрын
Wow the KZhead 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!
@gregwhite6998 Жыл бұрын
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
@andrewcpu Жыл бұрын
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.
@retu3510 Жыл бұрын
Thanks for sharing your parrot project at the end, I didn't know they were telling you the nuclear launch codes!
@maxinac Жыл бұрын
This is such a good example of why non-euclidean metrics are useful! This channel is everything I ever wanted ❤
@BurkeMcCabe Жыл бұрын
Woah ive been watching u for a while so this video is especially cool lol
@DashPum4 Жыл бұрын
This was phenomenal!
@michaelwarnecke3474 Жыл бұрын
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
@ShrekPNG Жыл бұрын
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.
@rigierish3807 Жыл бұрын
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.
@EebstertheGreat Жыл бұрын
this video snipes the sweetspot of my brain that has a weirdly vested interest in both math and minecraft
@ProbablyBarney Жыл бұрын
Sectors, segments, and arcs are the words you're looking for
@bruhmoment1835 Жыл бұрын
Well done!
@chinesecabbagefarmer Жыл бұрын
Oh my god I never knew you kept making videos. I'm still subscribed to RedstoneJazz lol
@introvertswag6494 Жыл бұрын
I wonder how this will shape the oldschool donut gold farms as these are freakishly hard to build without external tools.
@CivetKittyMC Жыл бұрын
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.
@ArchDennam Жыл бұрын
4:11 - For the eighth of a circle, I'd borrow from our lovely musician friends and say hemi-demi-semi-circle. 😂
@Carhill Жыл бұрын
great content
@chadchampion7985 Жыл бұрын
this is _revolutionary_ :)
@YounesLayachi Жыл бұрын
This knowledge will be applied to villager operated farms and bee farms, increasing productivity by 1% or more. 😊
@mrchampion7134 Жыл бұрын
This is awesome!
@Hlebuw3k Жыл бұрын
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)
@wheresmymuffins Жыл бұрын
Great video!
@leonantonov2577 Жыл бұрын
4:12 Reasonably sure that an eighth of a circle would be a hemidemisemicircle.
@roderik1990 Жыл бұрын
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?
@somniad Жыл бұрын
this is really cute and informative :>
@youvebeensubbedto8009 Жыл бұрын
This is cool, I like this content.
@bucketmann3443 Жыл бұрын
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
@lightguy250 Жыл бұрын
Nobody has commented this yet, but all of the digits of pi at the end are correct! Great job Chris!
@migsy15 ай бұрын
I don't know who you are but that was fun, thanks
@niconico6391 Жыл бұрын
As far as I can tell, the distance formula in this model is |x - y| + sqrt(2) min(x, y)
@addymant Жыл бұрын
very interesting video
@wollebay Жыл бұрын
2:55 this reminds me of Snell's Law, wonder if it'd apply here somehow
@1224chrisng Жыл бұрын
very interesting!
@daveguy_ Жыл бұрын
"there's no pi on this 4-func calculator" ... "oh yeah" *types it* my favorite reason I learned a bunch of pi
@DoctorPlasmaMC Жыл бұрын
Yo nice umbrella my guy
@dexlovesgames_dlg Жыл бұрын
you have a beautiful voice! also the minecraft stuff is cool
@shasha6704 Жыл бұрын
My head is spinning and I like it
@mikecroakphone Жыл бұрын
You remind me somewhat of SethBling, I remember really enjoying his content like this, digging into how the game works.
@xiphosura413 Жыл бұрын
@0:36 "sort of weirder diagonal" the word you are looking for is "oblique".
@whtiequillBj Жыл бұрын
this video should've totally been 6:28 long for 2*pi
@dukecatfishjunior6291 Жыл бұрын
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.
@wingedcatgirl Жыл бұрын
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.
@RigoVids9 ай бұрын
cant wait for zombie pi day
@juniper8827 Жыл бұрын
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)
@Sawyernilsson Жыл бұрын
And went to the 69th digit (after the decimal). Nice
@thechosenone7849 Жыл бұрын
Math genius!
@What-is-a-handle-is-it-a-tag Жыл бұрын
"Today I was playing Minecraft and decided to calculate Pi." Also, making the title "... increasse by 1%" was zero click bait, nice!
@EnderMega Жыл бұрын
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.
@Dragenst Жыл бұрын
It is call "60 degree arc" nice video! 4:20
@aprobaralaprimera8108 Жыл бұрын
Cant wait for the guys at scicraft to hear about this and make more efficient farms with it
@alakazam482 Жыл бұрын
Look up the minihud mod, I think it might help you show the octagon shape
@James2210 Жыл бұрын
Hemidemisemicircle: one eighth of a circle
@ConsumerOfCringe Жыл бұрын
@Vsauce Michael this is pretty cool
@xtremhillblly2269 Жыл бұрын
matt parker might be a bit happy that his hand calculated pi's can be closer to minecraft's pi XDD
@ITS_MEEE333M Жыл бұрын
the relevant google search term would be "metric space" btw, or maybe "taxicab metric"
@wyboo2019 Жыл бұрын
Well now I need data. Test those 1% claims boi!
@Scott.E.H Жыл бұрын
Funny you measured the radius when talking about pi. People cant help but align with the more natural tau :P
@jek__ Жыл бұрын
Perhaps a tau day video is in order
@whitestonejazz Жыл бұрын
can we use the pi for zombies and use that to measure other numbers for a zombie?
@Spilt_Ice_Cream_Lover9 ай бұрын
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!
@addymant Жыл бұрын
Shows up on my feed on 3.31, lol.
@chuulover69420 Жыл бұрын
8th of a circle is a hemi-demi-semi-circle
@theapexsurvivor9538 Жыл бұрын
funny how i discovered this video on march 31st
@voidkat Жыл бұрын
As far as I'm aware, 1/8th of a circle would just be a sector!
@Kelvoraax Жыл бұрын
elaborate reason to flex the memorization of pi
@user-nu3kb8pe6g Жыл бұрын
Cool
@paradoxicalegg6112 Жыл бұрын
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!
Happy March 31st!
I'm confused..
@@SonifyBruh it was pi day yesterday, but pi day isn’t until the 31st for zombies.
He kinda did a march fools joke there
He means April 31st. Pi Day in Europe is 31/4, or April 31st
@@FewVidsJustComments Wrong, it's Nonnavimberter 4th
very useful for my mob farms that are insufficient by 1.01%
beepir you are the biggest minecraft nerd
@@jacob_997 😔
You mean inefficient?
@@Hietakissa insufficient
By 1%, not 1.01%.
“Why are your tunnels 20-25° askew?” “Makes it easier to run from mobs”
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.
diagonal lines are straight; you're thinking of 20-25 degrees away from a horizontal axis.
@@palladianaltruist8047 no big diff, his point still stands
move like a knight in chess
@@palladianaltruist8047 🤓☝ermmm technically ..............
i thik that reLLY is the best takeaway. sry, im just typig quickly with my two knuckles.
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
It's always surprising to learn how many people find math interesting and think they don't.
I actually got into math because of minecraft
@@whitestonejazz most people think math is just memorizing formulas and plugging numbers into them, because that's all that's taught in school
@@whitestonejazz Because public school math is the most boring and disgusting appropriation of what math actually is
@@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)
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
not really chess geometry as the diagonal distance is still counted at the square root of two not as one
@@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
@@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]
@@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
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.
As someone that thoroughly enjoys overcomplicating farms & avoiding typical "out of the box" tutorials, this content resonates extremely well with me. Sub'd !
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
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"
Could you elaborate this, I don't quite understand
@@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
@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
omaigosh. it's KK!
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(?)!
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?
"Minecraft distance" is Chebyshev / chessboard distance.
@@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
@@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).
@@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).
It's amazing how you innovate in areas we don't even think about
great execution of a unique idea. your channel is going places, sir. (and now i'm gonna binge your other videos lol)
I really like your energy and general curiosity. Thank you for lighting up my day
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 )
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.
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
cool, i love these sorts of pathfinding farms and optimizations!
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.
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.
That’s a really cool analysis!
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 😅
I loved all the analysis and math, and then finding an application for it all in making the farms fractionally more efficient
Fascinating, this is some unique pi day content right here!
This is genuinely the best Minecraft farm video I have seen in years. You earned yourself another sub!
This stuff is really cool that I doubt most others think about. Keep it up
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 !
amazing video man keep it up!!!
you might know this already, but using the carpet ai_tracker module you can display the path finding of mobs!
you're growing like crazy! Well-deserved!
very interesting and informative video, thanks!
Not only does the spawning pad look cooler, it's also more efficient.
Love how you just notice something in minecraft and start a study about it. I do it sometimes as well, but with everyday stuff
Super cool stuff man, good job!
Imagine if a farm was 0.5% away from reaching maximum efficiency...
Such a great content! For the whole video I thought you have at least 100k views. Very underrated, keep going!
You get your honorable spot in "might be useful later" playlist
Wow this is really interesting! Super cool use of math tailored to minecraft!
Wow the KZhead 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!
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
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.
Thanks for sharing your parrot project at the end, I didn't know they were telling you the nuclear launch codes!
This is such a good example of why non-euclidean metrics are useful! This channel is everything I ever wanted ❤
Woah ive been watching u for a while so this video is especially cool lol
This was phenomenal!
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
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.
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.
this video snipes the sweetspot of my brain that has a weirdly vested interest in both math and minecraft
Sectors, segments, and arcs are the words you're looking for
Well done!
Oh my god I never knew you kept making videos. I'm still subscribed to RedstoneJazz lol
I wonder how this will shape the oldschool donut gold farms as these are freakishly hard to build without external tools.
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.
4:11 - For the eighth of a circle, I'd borrow from our lovely musician friends and say hemi-demi-semi-circle. 😂
great content
this is _revolutionary_ :)
This knowledge will be applied to villager operated farms and bee farms, increasing productivity by 1% or more. 😊
This is awesome!
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)
Great video!
4:12 Reasonably sure that an eighth of a circle would be a hemidemisemicircle.
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?
this is really cute and informative :>
This is cool, I like this content.
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
Nobody has commented this yet, but all of the digits of pi at the end are correct! Great job Chris!
I don't know who you are but that was fun, thanks
As far as I can tell, the distance formula in this model is |x - y| + sqrt(2) min(x, y)
very interesting video
2:55 this reminds me of Snell's Law, wonder if it'd apply here somehow
very interesting!
"there's no pi on this 4-func calculator" ... "oh yeah" *types it* my favorite reason I learned a bunch of pi
Yo nice umbrella my guy
you have a beautiful voice! also the minecraft stuff is cool
My head is spinning and I like it
You remind me somewhat of SethBling, I remember really enjoying his content like this, digging into how the game works.
@0:36 "sort of weirder diagonal" the word you are looking for is "oblique".
this video should've totally been 6:28 long for 2*pi
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.
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.
cant wait for zombie pi day
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)
And went to the 69th digit (after the decimal). Nice
Math genius!
"Today I was playing Minecraft and decided to calculate Pi." Also, making the title "... increasse by 1%" was zero click bait, nice!
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.
It is call "60 degree arc" nice video! 4:20
Cant wait for the guys at scicraft to hear about this and make more efficient farms with it
Look up the minihud mod, I think it might help you show the octagon shape
Hemidemisemicircle: one eighth of a circle
@Vsauce Michael this is pretty cool
matt parker might be a bit happy that his hand calculated pi's can be closer to minecraft's pi XDD
the relevant google search term would be "metric space" btw, or maybe "taxicab metric"
Well now I need data. Test those 1% claims boi!
Funny you measured the radius when talking about pi. People cant help but align with the more natural tau :P
Perhaps a tau day video is in order
can we use the pi for zombies and use that to measure other numbers for a zombie?
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!
Shows up on my feed on 3.31, lol.
8th of a circle is a hemi-demi-semi-circle
funny how i discovered this video on march 31st
As far as I'm aware, 1/8th of a circle would just be a sector!
elaborate reason to flex the memorization of pi
Cool
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!