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Miloslav Ciz 2023-12-07 00:48:04 +01:00
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@ -14,7 +14,7 @@ Using **[fractals](fractal.md)** (e.g. those in a form of [L-system](l_system.md
There are also other techniques such as [wave function](wave_function.md) collapse which is used especially in tile map generation. Here we basically have some constraints set (such as which tiles can be neighbors) and then consider the initial map a [superposition](superposition.md) of all possible maps that satisfy these constraints -- we then set a random tile (chosen from those with lowest [entropy](entropy.md), i.e. fewest possible options) to a random specific value and propagate the consequences of it to other tiles causing a cascading effect of collapsing the whole map into one of the possible solutions.
A good example to think of is generating procedural [textures](texture.md). This is generally done by first generating a basis image or multiple images, e.g. with **[noise](noise.md) functions** such as [Perlin noise](perlin_noise.md) (it gives us a grayscale image that looks a bit like clouds). We then further process this base image(s) and combine the results in various ways, for example we may use different transformations, [modulations](modulation.md), blending, adding color using [color ramps](color_ramp.md) etc. The whole texture is therefore described by a [graph](graph.md) in which nodes represent the operations we apply; this can literally be done visually in software like [Blender](blender.md) (see its [shader](shader.md) editor). The nice thing is that we can now for example generalize the texture to 3 dimensions, i.e. not only have a flat image, but have a whole volume of a texture that can extremely easily be mapped to 3D objects simply by intersecting it with their surfaces which will yield a completely smooth texturing without any seams; this is quite often used along with [raytracing](raytracing.md) -- we can texture an object by simply taking the coordinates of the ray hit as the 3D texture coordinates, it's that simple. Or we can animate a 2D texture by doing a moving cross section of 3D texture. We can also write the algorithm so that the generated texture has no seams if repeated side-by-side (by using modular "wrap-around" coordinates). We can also generate the texture at any arbitrary resolution as we have a continuous mathematical description of it; we may perform an infinite zoom into it if we want. As if that's not enough, we can also generate almost infinitely many slightly different versions of this texture by simply changing the [seed](seed.md) of [pseudorandom](pseudorandom.md) generator we use.
A good example to think of is generating procedural [textures](texture.md) -- similar techniques may also be used to create procedural terrain [heightmaps](heightmap.md) etc. This is generally done by first generating a basis image or multiple images, e.g. with **[noise](noise.md) functions** such as [Perlin noise](perlin_noise.md) (it gives us a grayscale image that looks a bit like clouds). We then further process this base image(s) and combine the results in various ways, for example we may use different transformations, [modulations](modulation.md), blending, adding color using [color ramps](color_ramp.md) etc. The whole texture is therefore described by a [graph](graph.md) in which nodes represent the operations we apply; this can literally be done visually in software like [Blender](blender.md) (see its [shader](shader.md) editor). The nice thing is that we can now for example generalize the texture to 3 dimensions, i.e. not only have a flat image, but have a whole volume of a texture that can extremely easily be mapped to 3D objects simply by intersecting it with their surfaces which will yield a completely smooth texturing without any seams; this is quite often used along with [raytracing](raytracing.md) -- we can texture an object by simply taking the coordinates of the ray hit as the 3D texture coordinates, it's that simple. Or we can animate a 2D texture by doing a moving cross section of 3D texture. We can also write the algorithm so that the generated texture has no seams if repeated side-by-side (by using modular "wrap-around" coordinates). We can also generate the texture at any arbitrary resolution as we have a continuous mathematical description of it; we may perform an infinite zoom into it if we want. As if that's not enough, we can also generate almost infinitely many slightly different versions of this texture by simply changing the [seed](seed.md) of [pseudorandom](pseudorandom.md) generator we use.
We use procedural generation mainly in two ways:
@ -23,6 +23,25 @@ We use procedural generation mainly in two ways:
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.
## Notable Techniques
The following are some techniques often used in procedural generation:
- **[noise](noise.md)**: Noise is often used as a basis for generation or for modulation, it can be seen as kind of "RNG taken to the next level" -- noise is greatly random but also usually has some structure, for example it may resemble smoke or water ripples. There are great many types of noise and algorithms for its generation; the simplest [white noise](white_noise.md) is actually not very useful, more common are various forms of fractal noise, often used noises are [Perlin noise](perlin_noise.md), [simplex noise](simplex_noise.md) etc., other ones are [Voronoi](voronoi.md) diagrams, midpoint displacement, spot noise, cosine noise, fault formation etcetc.
- **[random number generators](rng.md)**: To make random decisions we use random number generators -- here we actually don't have to have the best generators, we aren't dealing with "security" or anything critical, however the generator should at least have a great period so that it's not limited to just generating few different results, and its useful to be able to choose [probability distribution](probability_distribution.md).
- **[modulation](modulation.md)**: Using previously generated procedural data, for example noise, to somehow affect another data -- for example imagine we already have some basic procedural texture but want to make it more interesting by randomly displacing its individual pixels to warp it a little bit. If we use a simple random number generator for each pixel, the result will just look too chaotic, so it's better if we e.g. use two additional Perlin noise textures, which together say for each pixel by what distance and angle we'll displace the pixel. As Perlin noise is more continuous, gradual noise, then also the distortion will be kind of continuous and nice.
- **simulations resembling natural/biological phenomena**: E.g. [cellular automata](cellular_automaton.md), [particle systems](particle_system.md), ...
- **[fractals](fractal.md)**: Fractals can resemble nature, they create "content" on all scales and are very simple to define. Popular types of fractals are e.g. [L-systems](l_system.md) that draw fractals with [turtle graphics](turtle_graphics.md).
- **coloring**: To get colors from simple numeric values we may use e.g. color mapping of the values to some [palette](palette.md) or using three different arrays as [RGB](rgb.md) channels. We may also use [flood fill](flood_fill.md) and other things of course.
- **wave function collapse**: Analogy to quantum mechanics, often used for generating tile maps.
- **combining intermediate results**: For example when creating procedural textures we may actually create two separate textures and then somehow [blend](blending.md) them together to get a more interesting result.
- **wrap-around coordinates**: Wrap around (modular) coordinates help us make tiling data.
- **mathematical [functions](function.md)**: Nice structures can be generated just by combining basic mathematical functions such as [sine](sin.md), [cosine](cos.md), [square root](sqrt.md), minimum/maximum, [logarithm](log.md) etc. We take these functions and make an expression that transforms input coordinates (i.e. for example *x*, *y* and *time* for an animated picture) to the final generated value. The functions may be composed (put on input of other functions), added, multiplied etc.
- **higher [dimensionality](dimension.md)**: Equations used for procedural generation are often generalized to higher dimensions so that we can for example create smooth animation by taking the extra dimension as time.
- **[filters](filter.md)**: We may utilize traditional graphic filters such as Gaussian blur, [median](median.md) blur, general [convolution](convolution.md), color adjustments etc.
- **[stochastic](stochastic.md) models**: Stochastic mathematical models describe the generated result in terms of probabilities, which is convenient for us as we can take the model and just use random number generators to make decisions with given probabilities to obtain a specific result. For example [Markov chains](markov_chain.md) can be used to easily generate random procedural text by knowing probabilities with which any word is followed by another word, this may also be used to generate linear game levels etc. Similarly we may utilize various non-[deterministic](determinism.md) finite state automata, [decision trees](decision_tree.md) etc.
- ...
## Examples
Here are some cool [ASCII renderings](ascii_art.md) of procedurally generated pictures: