Allam A. – Minecraft: The Far Lands Documentary – Part 2 – Cause of the Far Lands

The cause of the far lands was not discovered until January of 2015. shortly after the addition of customized worlds which enabled us to see the noise scales for the first time the farlands are caused by an integer overflow in the coordinates for two of the noise Maps used in generating Minecraft’s terrain

For all of the various Pearl and noise generators that exist within Minecraft a coordinate is initially calculated as a double by multiplying the block coordinate by the noise scale this value is then cast to a 32-bit integer which is rounded towards zero that is rounded down as positive and up if negative

If the value is larger than 2 to the 31 minus 1 the result of casting to an end is simply is simply 2 to 31 minus one the integer is then converted back to a double and subtracted from the original value to extract the fractional part of the

Noise coordinate in normal areas the fraction is always within the intended range of zero to one however when the noise coordinate is greater than 2 to the 31 the fraction will be much larger than one in Frac the in fact the fraction of the noise coordinate will be

How many units the noise coordinate is path to the 31 which is directly proportional to the number of blocks passed to start of the Farland as if that wasn’t enough the fraction value is then plugged into an equation which simplifies to 6X to the fifth minus 15x to the fourth plus 10x cubed

This formula is used for Quantic interpolation between 0 and 1. as it’s outputting that range is monotonous as monotonically increasing and it’s also between 0 and 1. however the function just blows up as the fraction value increases Beyond one which causes the noise values to become very large

The rest is essentially random being determined by the integer parts of the other two noise coordinate which in the case of the edge farlands as seen here are still within normal range essentially what curling noise does is it interpolates between the values at the four corners of a square or in the

Case of 3D Pearl noises the eight vertices of a cube and uses the quintic equation to interpolate between all the corners or vertices and the edges of the squares of the cubes would be the points or the noise coordinate their integers now the two main noise generators used in generating

Minecraft training is low in high noise are scaled so that one block is equivalent to 171.103 units of their highest octave and 2 to the 31 over 171.103 is wait for it about approximately 12 million five hundred fifty thousand eight hundred twenty four now the noise is also only calculated at

Blocks divisible by four on the x and z axes and box visible by 8 on the y-axis and it is linearly interpolated in between so this is why the far lands appears smoother and more natural looking and then you would expect than you would expect given the rest of the information

I just described and the sampling intervals on the y-axis being twice as large causes the tunnels to appear stretched vertically you may notice that the farlands look much more chaotic than the normal train generating up to them this is because there are 16 layers known as octaves of

Low and high noise and the octave that causes the far lands is actually the actually has the least effect when generating normal Terrain and the octave that has the most effect in normal is actually in normal training is actually the lowest octave whose coordinates increase by only 0.005221 approximately every block in

The case of low and high noise the higher octaves simply add detail to the noise map the noise also repeats every 256 units and the octaves are caused as the farlands increases by 117.13 every block once again so the smallest integer that that can be multiplied by to get a

Whole number divisible by 206 to 256 000 and sure enough The Edge farline structure can repeat every 256 000 blocks on the other axis and so sure enough The Edge Farland structure can repeat every 256 000 blocks on the other axis you may also notice these four block

Long artifacts at the beginning of the of the of the farlands and the Positive Directions these are also cause these are caused by the values of the noise at 12 500 828 being much larger than a 12 million five fifty thousand year 24 which in turns much larger than at 12 million five

Thousand year and 20. what’s more is that the noise generators use a random offset from 0 to 256. in most cases the random offset is enough to get the noise coordinate at 12 million five fifty thousand unit 24 for low and high noise over 2 to the 31 but

In some cases it might not be enough such as here where the far if that is the case then the far lands will actually start at 12 million five or fifty thousand eight or twenty five as we see right here if the random offset is just enough to

Get the noise coordinate at 12 million five hundred fifty thousand eight or twenty four over two to Thirty one then the initiation of the edge farlands will look rather smooth as it’s seen here if the off if the random and finally the random offset is enough to get the noise

Coordinate at 12 million 550 824 well over 2 to 31 as it usually is then the farlands will clearly start at 12 million five hundred fifty thousand eight hundred twenty one as the noise is once again only calculated at blocks where both the x coordinate and the Z coordinate are divisible by four

And and the noise is interpolated in between and the noise values at 12 million five fifty thousand eight or twenty four will be much larger than at 12 million 5000 even 20 because again with the quintic equation even even plugging in a value of a couple hundred we’re into the quintic equation we

Already give you a number on the order of a trillion that’s how quickly it will blow up after the noise coordinate starts overflowing also note that when there is a tip also note that whenever there is a tip of an art or in a tunnel or an artifact

In the edge farlands as it’s seen right here it will always be at a coordinate on the other axis that is divisible by four similar similarly whenever a layer is one block thick in the corner farlands it can only be or when an artifact is even one block thick in the edge

Farlands it will only can only be at a y coordinate that’s divisible by eight an interesting artifact of the corner farlands is the diagonal lines that can be seen carved into the floors and ceilings of layers sometimes up on the top layer these can appear as cliffs like we see here

These all originate at the initiation of the corner of Farland and are caused by calculations using a grad function which takes two of the three noise coordinate fraction values and either adds one to the other or subtracts one from the other which two fractions are added or subtracted and

Whether they are added or subtracted is dependent on a random number from 0 to 15. which is determined using each of the internalized coordinates modules 256. in the corner farlands the X and V integer noise coordinates are always the same value that is 2 to 31 minus one

So it only depends on the Y noise coordinate basically now this is another thing I forgot to mention actually it’s the reason why the edge farlands appears striped is because the noise coordinate is always 2 to the 31 minus one on one axis but on the other axis

It varies because it’s doing normal range but the corner far length then the corner farlands both acts these integer noise coordinates are both always the same value which is what causes the relatively very flat Terrain now here’s a couple things I forgot to mention the noise and the edge farlands the

Noise values are roughly on the order of six times the fraction to the fifth power however in the corner farlands the quintic values on the x and z axes would be roughly multiplied together so when both the x and z coordinates are the same the noise values would actually

Be expected to be on the order of the fraction to the 10th power additionally when since the noise coordinate the integer noise coordinate is rounded towards zero when casting it will be rounded up in the negative so and so it will be decremented by the

Part of the code that makes it this is an added to make sure that the fraction is always positive however in the Negative Edge far length this causes the integer noise coordinate to wrap around from negative 2 to 31 all the way back around to positive 2 to the 31 minus 1.

And that right away puts the fraction at negative 4.295 billion approximately this is why you usually don’t see that as being diagonal lines in the in the other three quadrants of the corner Farland of course there are a couple here but there are just not as many

In the corner farlands on any given map there are two distinct regions the X side where the fraction on the x-axis is much larger than the fraction in the z-axis and the Z side where the fraction on the z-axis is much larger than on the x-axis everything else in the corner of

Firelands is is essentially an interpolation between the two and because in the middle the fractions are roughly the same so the terms relate so the terms related to them in the calculations have roughly equally effects but as you go toward the X side the the X fraction related terms

Way more and as we go toward the Z side the Z fraction in terms of the terms related to the Z fraction will have more weight the diagonal lines being caused by calculations of the fraction value Falls basically just from intuition because we know everywhere in the corner farlands

The integer noise coordinates are the same voltages are always coordinates are the same everywhere in the corner of farlands both to the real minus one now there is a certain way the quadrants are the four quadrants are all related to each other due to the noise partly due to the integerized coordinates also

Being positive 2 to 31 minus one and in all of the other quadrants as well so if we teleport to the Northeast quad in here you will see that it’s the side it’s pretty much exactly the same as that in the main quadrant but as we go toward the X side

In this quadrant it gradually become morphs into an inverse into an inversion of the X side of the main quadrant the reason for this is because if one fraction value sine is inverted its corresponding terms in the grad function will be inverted which will invert the signs of the graph

Function results if it is the larger one or have a negligible effect if it is a smaller one and one of the quintix which are multiplied together will also have to be inverted so when the lock still on the Z side over here we see that two signs are inverted

Which is why we get the mirror image but over here effectively only one sign is inverted in calculation which is why we get the inversion and indeed and if we teleport to the Northwest Quadrant we see that it is an exact inversion of the southeast quadrant and by that I

Mean that ever that if we switch if we switch which layers our air and which ones are solid from the southeast quadrant we get the Northwest Quadrant the southeast quadrant in this map is one of the thinnest corner of Harlan spawns I’ve seen which makes the Northwest one one of the thickest

And every Southwest here we go to the Southwest quiet here we see that it mirrors the X side of the main quadrant and and at the side is an inversion of that in the main quadrant another Seed where this inversion phenomenon is apparent is -3 quadruple

Four seven five oh eight five nine seven seven six three eight one you can see if we teleport if we’re in the positive quadrant if we teleport to the negative quadrant you will see that these areas of these oh that these taverns directly correspond to the negative quadrant directly correspond to the

Large Hills in the positive quadrant and if we head up to the top here we see that these low areas directly correspond to the floating island in the positive quadrant now note that the X side now note that the X side may not be exactly mirrors in

The southwest quadrant and the Z side may actually not be exactly here in the Northeast quadrant like we actually see in this seed like you’ll see right here if you remember in this seed in the seed we never had to float the floating islands weren’t actually this

High on the Z side and this seed in the main quadrant yet over here they are for some reason and that’s actually this and that actually happens when the noise value at that layer as in as the as that one fraction value gets larger than much larger than the

Other one that is going towards zero okay yeah there’s also some Far lands in the nether which look identical to the overworlds except with nether features and in the Sky Dimension note that the Sky Dimension farlands look much more stretch horizontally than the Overworld and never as far lands and the reason

For this is because in the Sky Dimension the noise is actually sampled every eight blocks is actually sampled every eight blocks along the x and z axes rather than every four and ever and it is sampled every four blocks on the y-axis rather than every eight so basically the horizontal and vertical

Sample always sampling intervals are switched note that this is basic note that this is identical to the shape of the end far lands and layer versions which we’ll show later in the video in older versions of the game at 32 million the game will no longer bother

To run the world and everything and every block after this was essentially a ghost block which you could which you could not interact with and that would have no clipping in fact this limit is what would become the world border we have today there is a statement floating around

That the terrain no longer generates after this point but but with and only air blocks of detections of the surrounding train generate but what actually happens is the terrain does generate but it is considered air by functions in the game’s code that that you have blocks in the world

There is there’s also there’s also a wrong Theory going around that this is a Java limitation when in reality it was a boundary intentionally defined in the game’s code most likely to most likely to allow the complete avoidance of the original far land which would just

Appear as a stone wall at 2 to the 25 with nothing beyond that that’s really not that interesting it is is also incorrect to say that block physics and lighting stopped working at this point because what’s actually happening is that they would function all the way out to the 32-bit

Integer limit but the game just doesn’t bother to or to run block physics or lightning past this point because again they’re intensely coded to only operate within this limit also note that for whatever reason the faith chunks can call the law of lag and then if and with entities and lighting

And all that stuff ruled out the only pot we pause for explanation is that the game is searching for a valid block to spawn animals or something I can’t find any intangible blocks are considered air however this limit can be easily modded out allowing trees and entities and lighting

Everything’s all here out to the 32-bit integer limit remember the tidbit earlier about the noise octaves well it turns out that for every every addition there is another set of farlands for every additional Octave of low and high noise the last of which does not overflow until over 411 billion blocks out

However if we teleport to 25 millimeter 1000 648 on both axes we see no visit there is no visible effect as the as the noise values of the first octave by this point are already much larger than than those the second octave would be just after it overflows because

The noise values of this of the second octave here are comparable to the first octave at the beginning those are the first octave at the beginning of the farlands however there are however there are some visible manifestations if we teleport to negative 25 million 10748 and one of this you will see

That there are some small shifts in the edge far landed strips of terrain and tunnels at that at that exact point and that’s again because of the fraction of the second octave going straight from like a normal value to minus 4.295 billion or unlike on the positive end

Where it just starts in the hundreds it just starts off in like 100. and in the Steve Gargamel whose corner farlands look pretty average except for the plateaus being blockier than usual due to the due to the grad functions for that noise down there on that I’m at level 120 coming

Out in such a way that’s the various terms cancel out if we if we head to 29 million 145 800 on both axes you will see that the plateau is actually end in this diagonal line that is actually different from the usual diagonal to the point farlands you see it’s actually a mathematical

Curve okay this is actually a visible manifestation of the second octave Corner Farland the far lands look different in early in-depth versions than the original instead of build the farlands were just a stone wall at 33 million 554 432 if chunks Beyond just completely filled with stone and that was it

The farlands became much more familiar in the March 27th 2010 build however these farlands as seen in the world generation of the instead of April 15 2010 build using the modern beta Bond look considerably different from the later Farland in general these farlands appear to kind of denser than the later Farland

The look of the farlands would change throughout the INF Dev builds which was reflective of the fact that the terrain algorithm was still very much a work in progress at that point in general The Edge Farland would just appear sort of kind of flatter and thicker and the in the corner farlands

Would also have thinner layers which appeared more densely packed you may notice that that the early instead of farlands can actually start at 12 million 550 000 822 or 12 million five fifty thousand eight hundred twenty three like we see here while in later versions the only

Possible for the far lands to either start at 12 million 550 821 or 12 million 550 000 825. that’s because instead of being sampled every four blocks in the X and z-axis the noise in these versions was actually sampled every block on all three axes

Like on the V side here we see that the farlands also start 12 million five thousand unit 23. as well