Java Edition hard limits

Floating point precision errors (X/Z: ±16,384–±2,147,483,519)
Many effects are noticeable after traveling millions of blocks away from the center of the map. The first effect that becomes evident is the jumpy or stuttering movement of the map, which is not directly related to the Far Lands themselves but instead to floating-point precision errors. In old versions of Minecraft, when the game renders the map around the player, there are two different versions that are generated, the rendering of the blocks themselves (i.e. entities, how much the block generates) and the visual aspect to the blocks (e.g. the hitbox, block pixels etc). In Java Edition Beta 1.7 and prior, the visual aspect of world rendering loses precision, resulting in the jumpy movement. The reason the world loses precision in the first place is that the rendering engine uses double-double precision, which determines the position of the world around the player. The rendering engine then uses a floating point integer to determine how far the already rendered blocks move around the player when they move. Unfortunately, this floating point integer cuts the double-double precision number in half, and thus the rendering engine doesn't have enough information to render the terrain correctly, and the information gets cut in half every time the player doubles their distance. Removing the floating text from the rendering engine fixes the stuttering movement.

This jumpy movement is notable even at an X/Z of ±16,384, becoming increasingly noticeable around ±524,288. The intensity of such glitches doubles every time the player passes a coordinate that is a power of two (e.g 2,097,152 or 4,194,304). After about X/Z 16,777,216, the hitbox is a full block off, which makes placing and destroying blocks almost impossible. The floating point precision errors are no longer noticeable past X/Z 2,147,483,519, as surface textures stop rendering and blocks no longer generate. At the center of the world, the world would be off by only $1/4194304$ (0.000000238...) blocks. Past the 32-bit limit, the world would be off by 256 blocks. For any position between n and 2n, where n is a power of 2, the world is offset by $n/8388608$ blocks, or $n/524288$ block pixels. The precision errors also affect entities like Redstone dust and ladders. If the player performs the "Spawn Chunk Glitch", then Redstone dust and ladders become noticeably stretched. They double in size for every exponent of 2 that the player travels from here on out. At X/Z: 268,435,456, Redstone dust is larger than one chunk and at X/Z: 1,073,741,824, Redstone dust is 128 blocks wide. If terrain were to theoretically generate out to the 64-bit limit (X/Z: ±9,223,372,036,854,775,807), then the hitbox would be over 2.2 trillion blocks off and redstone dust would be 2.2 trillion blocks wide as well.

Fake chunks (X/Z: >±32,000,000)
As the player journeys even deeper into the Far Lands, the effects worsen to the point where the game is unplayable. At X/Z ±32,000,000, blocks are treated as permanently nonexistent, and do not generate even though they may appear to. When Minecraft generates and loads chunks, it loads an empty version of the terrain, complete with grass, stone and water textures that cannot be walked on. This map generates out to the 32-bit integer limit. The game can load chunks only out to X/Z: ±32,000,000, causing a problem between the noise map and the chunk generator. To fix this problem, Minecraft removes the chunks generated beyond X/Z: >±32,000,000 and generates only the noise map. If the player tries to walk on this map, they fall into the void. This value is hard-coded in the source code of Minecraft, meaning that it cannot be changed without editing the source files. Because chunks technically do not generate beyond X/Z: ±32,000,000, things like trees, falling gravel, falling sand, mobs, grass, and other entities do not generate either. This can make the map relatively stable and crashes can be somewhat rare; however, crashes can happen on low-end computers. In rare cases, if the player performs the "ghost spawn glitch" that worked in versions between Alpha 1.1.0 and Beta 1.7.3, the player can cause trees and plants to generate beyond ±32,000,000.

World render limit (X/Z: ±268,435,456–±2,147,483,647)
At excessive X/Z positions (depends on the operating system and version, but usually occurs between X/Z: ±268,435,456 and ±2,147,483,647, and early versions such as Beta), world render glitches out, resulting in terrain that appears to flicker. This does happen at X/Z: <±268,435,456, but it becomes very noticeable at X/Z: >±268,435,456 and gets worse every power of 2 beyond that. This could most likely be that past X/Z: ±268,435,456 the Minecraft world is 32 blocks off, which is as large as 2 chunks, though it is unconfirmed.

Spawn chunk glitch (X/Z: ±524,288–X/Z: ±1,073,741,824)
Using single player commands for Minecraft Beta 1.7.3, when the player teleports to 524,288 on only one axis and keeps their position along the other axis near zero, the player can allow the chunk they originally spawned in to re-appear. If done enough times, once the player reaches X/Z: 33,554,432, trees and entities can reappear inside the Far Lands, even though vegetation and entities are not supposed to generate out this far because of the block limit at X/Z: 32,000,000. However, because of the block render limit at X/Z: 2,147,483,519, the maximum distance that trees and entities can spawn at is X/Z: 1,073,741,824. If the player does happen to generate natural terrain beyond X/Z: 32,000,000, then any trees or other entities that spawn begin to decay but the image remains frozen in place. For example: a flower generated in the fake chunks drops the flower item as if it has decayed, but the flower still appears in place, unable to be removed. It does this infinitely and causes countless entities to begin spawning, causing lag spikes.

32-bit limit (X/Z: >±2,147,483,647)
At X/Z: ±2,147,483,519, blocks are no longer rendered, giving way to an empty sky. At X/Z: ±2,147,483,647 (maximum 32-bit integer), the game is likely to crash or the player gets stuck. However, chunks still generate along with clouds. Fast graphics clouds are however insanely stretched. It is very dangerous to reach X/Z ±4,294,967,296 or higher, as the chances of crashing (assuming the player has 64-bit Java) are extremely high, and get higher the further the player goes.

Cloud render limit (X/Z: ±25,769,803,000–±25,769,804,000)
Between X/Z: ±25,769,803,000 and X/Z: ±25,769,804,000 clouds stop rendering (Varies between maps, but they disappear somewhere in between these distances. Does not apply for fast graphics clouds). Beyond here, only the sky, sun, moon and void remain.

Chunk overwrite limit (X/Z: >±34,359,738,368)
If one makes it to X/Z: ±34,359,738,368 (235), away from spawn, chunks start getting overwritten. As a result, this is the end of chunk generation in Minecraft. As soon as this limit is approached, the game freezes and crashes, resulting in an Out of memory screen. However, in some cases, the player may be able to move past this limit for a few seconds before Minecraft crashes. A chunk is 16 × 16 blocks, so it is likely due to the fact that Minecraft 's chunk generation is also 32-bit, as 2,147,483,648 × 16 = 34,359,738,368.

Stripe Lands (X/Z: >±9,007,199,254,740,992)
(This limit is theoretical.) Minecraft: Java Edition uses 64-bit floating point precision for entity positions and other calculations. Most of the time, only 52 bits are dedicated to the fraction; therefore, after 2^53 blocks out, precision breaks to consider only every second block, and so on. These are purely conjectural, however, as nobody has managed to get terrain to render out this far (without modifying source files)

64-bit integer limit (X/Z: >±9,223,372,036,854,775,807)
The highest signed value for 64-bit machines is X/Z ±9,223,372,036,854,775,807. However, despite this being the limit any machine can go, it may not be possible (through in-game methods) to go near this point, since the vast majority of people experience instant client freeze, followed by the client crashing. In some cases, it is possible to teleport to it however this is difficult. The only way that this can work with a high consistency is if one uses Cheat Engine to edit a players position to be at this limit. If one manages to make it this far, the only things that exist are the Sun and the sky, as shown by one user that managed to actually be out this far.

Previously, there was a theory that at this distance there would be no sun, the sky would be pitch black and the clouds would glow oddly. This has since been debunked as false.

<64-bit floating point limit (X/Z: >±1.797693134862315907729305190789 x 10^308)
On August 1, 2018, a YouTube user named "Aura Gunner" made a video showing the player teleporting to 1.797693134862315907729305190789 x 10^308 (past 21024) on the X-axis. Because 1.797693134862315907729305190789 x 10^308 is the maximum 64-bit floating-point integer, it caused the player's X coordinate to roll over to read "Infinity". It is impossible to go further since this is the physical limit at which Java can render, and the game always crashes at this distance. It is possible to get this far, however, Cheat Engine must be used to edit the coordinates in a way that allows continuous teleportation.

Vertical effects (Y: <&minus;2,147,483,647)
In Beta 1.7.3, as the player falls below Y=&minus;2,147,483,647, the darkness of being in the void disappears. Instead of darkness, the void now looks like an empty world. It has a sky, a sun, and a moon, and they are all visible depending on the time of day. Despite this, the player still receives damage from the void.

Map editors
When viewing the Far Lands in a 3D Minecraft map editor, the player encounters errors. In MCEdit, the selection cubes start to distort and the map distorts when viewing. In addition, when the player rotates their view around a selected area, blocks are not lined up right and change how poorly lined up they are at random, making the whole world seem to shake.