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procgen.md

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 # Procedural Generation
 
-Procedural generation (procgen) refers to creation of data, such as [art](art.md) assets in [games](game.md) or test data for data processing software, by using [algorithms](algorithm.md) and mathematical formulas rather than creating the data manually or measuring it in the real world (e.g. by taking photographs). This can be used for example for automatic generation of [textures](texture.md), texts, [music](music.md), game levels or 3D models but also practically anything else, e.g. test [databases](database.md), animations or even computer programs. Such data are also called *synthetic*. Procedural art currently doesn't reach qualities and creativity of a skilled human artist, but it can be [good enough](good_enough.md) or even necessary (e.g. for creating extremely large worlds), it may be preferred e.g. for its extreme save of storage memory, it can help add detail to human work, be a good filler, a substitute, an addition to or a basis for manually created art. Procedural generation has many advantages such as saving space (instead of large data we only store small code of the algorithm that generates it), saving time (once we have an algorithm we can generate a lot data extremely quickly), increasing resolution practically to infinity or extending data to more dimensions (e.g. [3D textures](3d_texture.md)). Procedural generation can also be used as a helper and guidance, e.g. an artist may use a procedurally generated game level as a starting point and fine tune it manually, or vice versa, procedural algorithm may create a level by algorithmically assembling manually created building blocks.
+Procedural generation (procgen, not to be confused with [procedural programming](imperative.md)) refers to creation of data, such as [art](art.md) assets in [games](game.md) or test data for data processing software, by using [algorithms](algorithm.md) and mathematical formulas rather than creating it manually or measuring it in the real world (e.g. by taking photographs). This can be used for example for automatic generation of [textures](texture.md), texts, [music](music.md), game levels or 3D models but also practically anything else, e.g. test [databases](database.md), animations or even computer programs. Such data are also called *synthetic*. Procedural art currently doesn't reach artistic qualities of a skilled human artist, but it can be [good enough](good_enough.md) or even necessary (e.g. for creating extremely large worlds), it may be preferred e.g. for its extreme save of storage memory, it can help add detail to human work, be a good filler, a substitute, an addition to or a basis for manually created art. Procedural generation has many advantages such as saving space (instead of large data we only store small code of the algorithm that generates it), saving artist's time (once we have an algorithm we can generate a lot data extremely quickly), parametrization (we can tweak parameters of the algorithm to control the result or create animation, often in real-time), increasing resolution practically to infinity or extending data to more dimensions (e.g. [3D textures](3d_texture.md)). Procedural generation can also be used as a helper and guidance, e.g. an artist may use a procedurally generated game level as a starting point and fine tune it manually, or vice versa, procedural algorithm may create a level by algorithmically assembling manually created building blocks.
 
 As neural [AI](ai.md) approaches human level of creativity, we may see computers actually replacing many artists in near future, however it is debatable whether AI generated content should be called procedural generation as AI models are quite different from the traditional hand-made algorithms -- AI art is still seen as a separate approach than procedural generation. For this we'll only be considering the traditional approach from now on.
 
-[Minecraft](minecraft.md) (or [Minetest](minetest.md)) is a popular example of a game in which the world is generated procedurally, which allows it to have near-infinite worlds -- size of such a world is in practice limited only by ranges of [data types](data_type.md) rather than available storage memory. [Roguelikes](roguelike.md) also heavily utilize procgen. However this is nothing new, an old game Daggerfall was known for its extremely vast procedurally generated world. Some amount of procedural generation can be seen probably in most mainstream games, e.g. clouds, vegetation or NPCs are often made procedurally.
+[Minecraft](minecraft.md) (or [Minetest](minetest.md)) is a popular example of a game in which the world is generated procedurally, which allows it to have near-infinite worlds -- size of such a world is in practice limited only by ranges of [data types](data_type.md) rather than available memory. [Roguelikes](roguelike.md) also heavily utilize procgen. However this is nothing new, for example the old game called Daggerfall was known for its extremely vast procedurally generated world, and even much older games used this approach. Some amount of procedural generation can be seen probably in most mainstream games, e.g. clouds, vegetation or NPCs are often made procedurally.
 
 For its extreme save of space procedural generation is extremely popular in [demoscene](demo.md) where programmers try to create as small programs as possible. German programmers made a full fledged 3D shooter called [.kkrieger](kkrieger.md) that fits into just 96 kB! It was thanks to heavy use of procedural generation for the whole game content. [Bytebeat](bytebeat.md) is a simple method of generating procedural "8bit" music, it is used e.g. in [Anarch](anarch.md). Procedural generation is generally popular in indie game dev thanks to offering a way of generating huge amounts of content quickly and without having to pay artists.
 
@@ -19,7 +19,7 @@ A good example to think of is generating procedural [textures](texture.md). This
 We use procedural generation mainly in two ways:
 
 - **offline/explicit**: We pre-generate the data before we run the program, i.e. we let the algorithm create our art, save it to a file and then use it as we would use traditionally created art.
-- **realtime/implicit**: We generate the data on the fly and only parts of it that we currently need. For example with a procedural texture mapped onto a 3D model, we would compute the texture pixels ([texels](texel.md)) when we're actually drawing them: this has the advantage of giving an infinite resolution of the texture because no matter how close-up we view the model, we can always compute exactly the pixels we need. This would typically be implemented inside a fragment/pixel [shader](shader.md) program. This is also used in the voxel games that generate the world only in the area the player currently occupies.
+- **realtime/implicit**: We generate the data on the fly and only parts of it that we currently need (this of course requires an algorithm that is able to generate any part of the data independently of its other parts; for example for a procedural texture each pixel's color should only be determined by its coordinates). For example with a procedural texture mapped onto a 3D model, we would only compute the texture pixels ([texels](texel.md)) that we are actually drawing: this has the advantage of giving an infinite resolution of the texture because no matter how close-up we view the model, we can always compute exactly the pixels we need. This would typically be implemented inside a fragment/pixel [shader](shader.md) program. This is also used in the voxel games that generate the world only in the area the player currently occupies.
 
 Indeed we may also do something "in between", e.g. generate procedural assets into temporary files or RAM [caches](cache.md) at run time and depending on the situation, for example when purely realtime generation of such assets would be too slow.