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This is one of the things that datapacks are designed for, a standard feature in vanilla Minecraft. You can either download an existing datapack from a site like [Modrinth](https://modrinth.com/datapacks), or you can write your own. A datapack is stored inside the folder for each world, so it only applies to one world at a time. If you want to use the same pack for multiple worlds, use symbolic links.

Datapacks are versioned, and each release of Minecraft specifies the datapack format version that it accepts. There are breaking changes between each version, but not everything is changed every time it's updated, so in many cases, you can continue using a datapack in an older format version than the one Minecraft specifies. This means that you need to ensure that the datapack your world is using is compatible every time you update the game. If the new version of Minecraft requires a new datapack format, it'll tell you before loading up the world, though, so there shouldn't be any problems with damaging your world because you forgot about the datapack.

The [full specification for datapacks](https://minecraft.wiki/w/Data_pack) is on the unofficial Minecraft wiki, as well as a more [general tutorial on creating them](https://minecraft.wiki/w/Tutorials/Creating_a_data_pack). For more details, explanations or possibilities with datapacks, look at the wiki.

For Minecraft 1.21.1, the datapack should be placed in `.minecraft/saves/<MY_WORLD>/datapacks/`, and look like this:

```
 - MyHeightLimitIncreaserPack
   - data
     - minecraft
       - dimension_type
         - overworld.json
   - pack.mcmeta
```

`pack.mcmeta` describes the data pack, and should contain:
```
{
  "pack": {
    "pack_format": 48,
    "description": "Increases the world height"
  }
}
```

`overworld.json` overrides the properties for the overworld type (the main dimension). You'll need to name it appropriately if you want it to apply to the nether, end dimension or a custom dimension instead. For a world with y ∈ [-256, 1024], it should contain:

```
{
  "min_y": -256,
  "height": 1280,
}
```

When existing chunks are extended, the new space that didn't exist before, will use the default biome, `plains`.

World generation will remain the same as before, however, if you extend the world further down (by lowering `min_y`), all new chunks will now generate at a lower level, which can create a rather nasty connection to existing chunks. 

The dead space below bedrock will not be updated for existing chunks. If you're in creative, you can use a mod like World Edit to fill out that space, but it's tedious and won't give you a natural underground.