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.
@@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)
@@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"
@@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
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(?)!
@@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).
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.
If we're familiar with L_p norms, then the L_(sqrt(2)) 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^(sqrt(2))/(1 - x^(sqrt(2))))^(1-sqrt(2)))^(1/sqrt(2)) 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. And it's not Manhattan because it's less restrictive. So the answer lies somewhere between L_2 (Euclidean) and L_1(Taxicab). And it turns out that L_(sqrt(2)) 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 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.
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
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
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 !
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.
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
Wow the RUclips 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!
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)
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
I was playing around with this metric and drew a picture as in 3:14 and got d(x, y) := (M - m) + sqrt(2)m = M + (sqrt(2) - 1)m where m = min(|x1-x2|, |y1-y2|) and M = max(|x1-x2|, |y1-y2|) The diagonal component forms a square with side lengths m, so the diagonal is sqrt(2)m, and the cardinal component is chebyshev minus the part covered by the square corresponding to the diagonal component, M - m This gives the same octagonal shape so I assumed it's equivalent to what you used, but I couldn't quite line things up when it comes to the part where we apply this to DashPum4's T-T I assume we're doing something like round(d(x,y))
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.
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!
π = ~2.8 for this circle if you use the equation 2πr There are ~96 blocks on the perimeter, and the diameter is 34 or 35, so Pi comes out to be around 2.8 It's actually a pretty big difference, even though this seems to be a pretty good approximation of a circle
Actually, if you use π=perimeter/diameter and use the zombie distance for diameter AND perimeter you get a different value than from the video (where he used the usual euclidean distance for the perimeter). For simplification let's take a radius of sqrt(2), then the zombie length of an edge is 1+(sqrt(2)-2)². Multiply that by 6 for the whole "circle" and divide by the diameter 2*sqrt(2) and you get 6*(sqrt(2)-1) which is roughly 2.49. That's close to what you get but not equal cause the video didn't show a perfect hexagon
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
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.
look it is 2 am in the morning and i just wanted to sleep...i suck in math now it is in my favourite video game...i love effeicent farms so much...im having a crisis...i think you did try to explain it to me but as soon as there are equations my brain goes on a field trip to neverland and doesnt want come back. that said i think it is neat that even people that clearly could do something "more of value" ( i dont think this is wasted time i just try to get my point across!!) are sitting here and thinking about math problems regarding minecraft farms..i know math is in every pc game dont hate me it s just mindboggling for me
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%.
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.
“Why are your tunnels 20-25° askew?”
“Makes it easier to run from mobs”
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).
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.
It's amazing how you innovate in areas we don't even think about
That’s a really cool analysis!
If we're familiar with L_p norms, then the L_(sqrt(2)) 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^(sqrt(2))/(1 - x^(sqrt(2))))^(1-sqrt(2)))^(1/sqrt(2)) 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. And it's not Manhattan because it's less restrictive. So the answer lies somewhere between L_2 (Euclidean) and L_1(Taxicab). And it turns out that L_(sqrt(2)) 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.
this video should've totally been 6:28 long for 2*pi
You get your honorable spot in "might be useful later" playlist
great execution of a unique idea. your channel is going places, sir. (and now i'm gonna binge your other videos lol)
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.
4:12 Reasonably sure that an eighth of a circle would be a hemidemisemicircle.
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 )
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.
Love how you just notice something in minecraft and start a study about it. I do it sometimes as well, but with everyday stuff
you might know this already, but using the carpet ai_tracker module you can display the path finding of mobs!
Super cool stuff man, good job!
Not only does the spawning pad look cooler, it's also more efficient.
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 😅
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
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
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.
@0:36 "sort of weirder diagonal" the word you are looking for is "oblique".
2:55 this reminds me of Snell's Law, wonder if it'd apply here somehow
this video snipes the sweetspot of my brain that has a weirdly vested interest in both math and minecraft
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 !
Sectors, segments, and arcs are the words you're looking for
4:11 - For the eighth of a circle, I'd borrow from our lovely musician friends and say hemi-demi-semi-circle. 😂
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.
I loved all the analysis and math, and then finding an application for it all in making the farms fractionally more efficient
cool, i love these sorts of pathfinding farms and optimizations!
This is such a good example of why non-euclidean metrics are useful! This channel is everything I ever wanted ❤
Thanks for sharing your parrot project at the end, I didn't know they were telling you the nuclear launch codes!
you're growing like crazy! Well-deserved!
"there's no pi on this 4-func calculator" ... "oh yeah" *types it*
my favorite reason I learned a bunch of pi
I really like your energy and general curiosity. Thank you for lighting up my day
Wow this is really interesting! Super cool use of math tailored to minecraft!
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
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
amazing video man keep it up!!!
Nobody has commented this yet, but all of the digits of pi at the end are correct! Great job Chris!
Fascinating, this is some unique pi day content right here!
"Today I was playing Minecraft and decided to calculate Pi."
Also, making the title "... increasse by 1%" was zero click bait, nice!
Wow the RUclips 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!
As far as I can tell, the distance formula in this model is |x - y| + sqrt(2) min(x, y)
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)
This knowledge will be applied to villager operated farms and bee farms, increasing productivity by 1% or more. 😊
very interesting and informative video, thanks!
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
Woah ive been watching u for a while so this video is especially cool lol
As far as I'm aware, 1/8th of a circle would just be a sector!
Imagine if a farm was 0.5% away from reaching maximum efficiency...
It is call "60 degree arc" nice video! 4:20
I was playing around with this metric and drew a picture as in 3:14 and got d(x, y) := (M - m) + sqrt(2)m = M + (sqrt(2) - 1)m
where m = min(|x1-x2|, |y1-y2|)
and M = max(|x1-x2|, |y1-y2|)
The diagonal component forms a square with side lengths m, so the diagonal is sqrt(2)m,
and the cardinal component is chebyshev minus the part covered by the square corresponding to the diagonal component, M - m
This gives the same octagonal shape so I assumed it's equivalent to what you used, but I couldn't quite line things up when it comes to the part where we apply this to DashPum4's T-T
I assume we're doing something like round(d(x,y))
Such a great content! For the whole video I thought you have at least 100k views. Very underrated, keep going!
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.
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!
You remind me somewhat of SethBling, I remember really enjoying his content like this, digging into how the game works.
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.
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!
Oh my god I never knew you kept making videos. I'm still subscribed to RedstoneJazz lol
the relevant google search term would be "metric space" btw, or maybe "taxicab metric"
matt parker might be a bit happy that his hand calculated pi's can be closer to minecraft's pi XDD
@Vsauce Michael this is pretty cool
Hemidemisemicircle: one eighth of a circle
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.
After paying close attention to the blocks the piglin walked on, it follows the "8-directional" format
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
π = ~2.8 for this circle if you use the equation 2πr
There are ~96 blocks on the perimeter, and the diameter is 34 or 35, so Pi comes out to be around 2.8
It's actually a pretty big difference, even though this seems to be a pretty good approximation of a circle
that's a good point
Actually, if you use π=perimeter/diameter and use the zombie distance for diameter AND perimeter you get a different value than from the video (where he used the usual euclidean distance for the perimeter). For simplification let's take a radius of sqrt(2), then the zombie length of an edge is 1+(sqrt(2)-2)². Multiply that by 6 for the whole "circle" and divide by the diameter 2*sqrt(2) and you get 6*(sqrt(2)-1) which is roughly 2.49. That's close to what you get but not equal cause the video didn't show a perfect hexagon
I don't even care about the farm I just clicked the video bc the title was too good
This was phenomenal!
Cant wait for the guys at scicraft to hear about this and make more efficient farms with it
they live in a world where circles are octagons, truly terrifying
I don't know who you are but that was fun, thanks
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
Now we need a "Zombie circle" generator
This might do the trick www.desmos.com/calculator/f2orycqevk
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.
4:11 demisemihemicircle!
elaborate reason to flex the memorization of pi
funny how i discovered this video on march 31st
this is really cute and informative :>
Ayo my man worked out the MC metric 🤔😎🗿
The end of the video makes me think "NEEERRRRRDD" XD
:) my high school had a pi day competition each year. Student with the most digits memorized got to eat the first slice of pie
@@whitestonejazz That sounds both fun and hilariously pointless lol
My head is spinning and I like it
cant wait for zombie pi day
Remember redstone jazz?
I do.
And now I'm sad.
I feel similarly sometimes
Well now I need data. Test those 1% claims boi!
Yo nice umbrella my guy
you have a beautiful voice! also the minecraft stuff is cool
it's not that they can only can go in 8 directions. it's that they follow the pathfinding waypoints that happen to always be adjacent blocks
this is _revolutionary_ :)
Shows up on my feed on 3.31, lol.
look it is 2 am in the morning and i just wanted to sleep...i suck in math now it is in my favourite video game...i love effeicent farms so much...im having a crisis...i think you did try to explain it to me but as soon as there are equations my brain goes on a field trip to neverland and doesnt want come back. that said i think it is neat that even people that clearly could do something "more of value" ( i dont think this is wasted time i just try to get my point across!!) are sitting here and thinking about math problems regarding minecraft farms..i know math is in every pc game dont hate me it s just mindboggling for me