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<html>
<head>
<title>Generating terrain in Cuberite</title>
</head>
<body>
<h1>Generating terrain in Cuberite</h1>
<p>This article explains the principles behind the terrain generator in Cuberite. It is not strictly
specific to Cuberite, though, it can be viewed as a generic guide to various terrain-generating algorithms,
with specific implementation notes regarding Cuberite.</p>
<p>Contents:
<ul>
<li><a href="#preface">Preface: How it's done in real life</a></li>
<li><a href="#expectedprops">Expected properties</a></li>
<li><a href="#reversingflow">Reversing the flow</a></li>
<li><a href="#composablegen">The ComposableGenerator pipeline</a></li>
<li><a href="#coherentnoise">Using coherent noise</a></li>
<li><a href="#biomegen">Generating biomes</a></li>
<li><a href="#heightgen">Terrain height</a></li>
<li><a href="#compositiongen">Terrain composition</a></li>
<li><a href="#finishgen">Finishers</a></li>
<li><a href="#makefaster">Making it all faster</a></li>
<li><a href="#GPU">Executing on a GPU</a></li>
</ul>
</p>
<hr />
<a name="preface"><h2>Preface: How it's done in real life</h2></a>
<p>The nature has many complicated geological, physical and biological processes working on all scales from
microscopic to planet-wide scale, that have shaped the terrain into what we see today. The tectonic plates
collide, push mountain ranges up and ocean trenches down. Erosion dulls the sharp shapes. Plantlife takes
over to further change the overall look of the world.</p>
<p>Generally speaking, the processes take what's there and change it. Unlike computer generating, which
usually creates a finished terrain from scratch, or maybe with only a few iterations. It would be unfeasible
for software to emulate all the natural processes in enough detail to provide world generation for a game,
mainly because in the nature everything interacts with everything. If a mountain range rises, it changes the
way that the precipitation is carried by the wind to the lands beyond the mountains, thus changing the
erosion rate there and the vegetation type. </p>
<hr />
<a name="expectedprops"><h2>Expected properties</h2></a>
<p>For a MineCraft-like game terrain generator we need the generator to have several properties:
<ul>
<li>The generator must be able to generate terrain in small chunks. This means it must be possible to
generate each of the chunks separately, without dependencies on the neighboring chunks. Note that this
doesn't mean chunks cannot coordinate together, it means that "a tree in one chunk cannot ask if there's
a building in the neighbor chunk", simply because the neighbor chunk may not be generated yet.</li>
<li>The generated chunk needs to be the same if re-generated. This property is not exactly required, but it
makes available several techniques that wouldn't be possible otherwise.</li>
<li>The generator needs to be reasonably fast. For a server application this means at least some 20 chunks
per second for chunks close to each other, and 5 chunks per second for distant chunks. The reason for this
distinction will be discussed later.</li>
</ul>
</p>
<hr />
<a name="reversingflow"><h2>Reversing the flow</h2></a>
<p>As already mentioned, the nature works basically by generating raw terrain composition, then "applying"
erosion, vegetation and finally this leads to biomes being formed. Let's now try a somewhat inverse
approach: First generate biomes, then fit them with appropriate terrain, and finally cover in vegetation
and all the other stuff.</p>
<p>Splitting the parts like this suddenly makes it possible to create a generator with the required
properties. We can generate a reasonable biome map chunk-wise, independently of all the other data. Once we
have the biomes, we can compose the terrain for the chunk by using the biome data for the chunk, and
possibly even for neighboring chunks. Note that we're not breaking the first property, the biomes can be
generated separately so a neighboring chunk's biome map can be generated without the need for the entire
neighboring chunk to be present. Similarly, once we have the terrain composition for a chunk, we can
generate all the vegetation and structures in it, and those can again use the terrain composition in
neighboring chunks.</p>
<hr />
<a name="composablegen"><h2>The ComposableGenerator pipeline</h2></a>
<p>This leads us directly to the main pipeline that is used for generating terrain in Cuberite. For
technical reasons, the terrain composition step is further subdivided into Height generation and Composition
generation, and the structures are really called Finishers. For each chunk the generator generates, in this
sequence:
<ul>
<li>Biomes</li>
<li>Terrain height</li>
<li>Terrain composition</li>
<li>Finishers</li>
</ul>
</p>
<img src="img/biomes.jpg" />
<img src="img/terrainheight.jpg" />
<img src="img/terraincomposition.jpg" />
<img src="img/finishers.jpg" />
<p>The beautiful thing about this is that the individual components can be changed independently. You can
have 5 biome generators and 3 height generators and you can let the users mix'n'match.
</p>
<hr />
<a name="coherentnoise"><h2>Using coherent noise for the generation</h2></a>
<p>For a great tutorial on coherent noise, see the <a href="http://libnoise.sourceforge.net/">LibNoise
documentation</a>.</p>
<p>Coherent noise is a type of noise that has three important properties that we can use to our advantage:
<ul>
<li>The noise is smooth</li>
<li>The noise is algorithmically generated, which means that the same data is generated when the same
parameters are given to the noise functions.</li>
<li>The noise can be seamlessly extended in any direction</li>
</ul></p>
<p>We'll be mostly using Perlin noise in this article. It is the easiest one to visualise and use and is one
of the most useful kinds of coherent noises. Here's an example of a Perlin noise generated in 2 dimensions:</p>
<img src="img/perlin.jpg" />
<p>It comes only naturally that such a 2D noise can be used as a terrain height map directly:</p>
<img src="img/perlinheightmap.jpg" />
<p>However, this is not the only use for this noise, and 2 dimensions is not the limit - this noise can be
generated for any number of dimensions.</p>
<hr />
<a name="biomegen"><h2>Generating biomes</h2></a>
<p>The easiest way to generate biomes is to not generate them at all - simply assign a single constant biome
to everywhere. And indeed there are times when this kind of "generator" is useful - for the MineCraft's Flat
world type, or for testing purposes, or for tematic maps. In Cuberite, this is exactly what the Constant
biome generator does.</p>
<p>Of course, there are more interesting test scenarios for which multiple biomes must be generated as easy
as possible. For these special needs, there's a CheckerBoard biome generator. As the name suggests, it
generates a grid of alternating biomes.</p>
<h3>Voronoi diagram</h3>
<p>Those two generators were more of a technicality, we need to make something more interesting if we're
going for a natural look. The Voronoi generator is the first step towards such a change. Recall that a
<a href="https://en.wikipedia.org/wiki/Voronoi_diagram">Voronoi diagram</a> is a construct that creates a
set of areas where each point in an area is closer to the appropriate seed of the area than the seeds of any
other area:</p>
<img src="img/voronoi.png" />
<p>To generate biomes using this approach, you select random "seeds", assign a biome to each one, and then
for each "column" of the world you find the seed that is the nearest to that column, and use that seed's
biome.</p>
<p>The overall shape of a Voronoi diagram is governed by the placement of the seeds. In extreme cases, a
seed could affect the entire diagram, which is what we don't want - we need our locality, so that we can
generate a chunk's worth of biome data. We also don't want the too much irregular diagrams that are produced
when the seeds are in small clusters. We need our seeds to come in random, yet somewhat uniform fashion.</p>
<p>Luckily, we have just the tool: Grid with jitter. Originally used in antialiasing techniques, they can be
successfully applied as a source of the seeds for a Voronoi diagram. Simply take a regular 2D grid of seeds
with the grid distance being N, and move each seed along the X and Y axis by a random distance, usually in
the range [-N / 2, +N / 2]:</p>
<img src="img/jittergrid.jpg" />
<p>Such a grid is the ideal seed source for a Voronoi biome generator, because not
only are the Voronoi cells "reasonable", but the seed placement's effect on the diagram is localized - each
pixel in the diagram depends on at most 4 x 4 seeds around it. In the following picture, the seed for the
requested point (blue) must be within the indicated circle. Even the second-nearest seed, which we will need
later, is inside that circle.</p>
<img src="img/jittergridlocality.jpg" />
<p>Calculating the jitter for each cell can be done easily by using a 2D Perlin noise for each coord. We
calculate the noise's value at [X, Z], which gives us a number in the range [-1; 1]. We then multiply the
number by N / 2, this gives us the required range of [-N / 2, +N / 2]. Adding this number to the X coord
gives us the seed's X position. We use another Perlin noise and the same calculation for the Z coord of the
seed.</p>
<p>Here's an example of a biome map generated using the Voronoi + jitter grid, as implemented by the Voronoi
biome generator in Cuberite:</p>
<img src="img/voronoijitterbiomes.png" />
<h3>Distorted Voronoi</h3>
<p>The biomes are starting to look interesting, but now they have straight-line borders, which looks rather
weird and the players will most likely notice very soon. We need to somehow distort the borders to make them
look more natural. By far the easiest way to achieve that is to use a little trick: When the generator is
asked for the biome at column [X, Z], instead of calculating the Voronoi biome for column [X, Z], we first
calculate a random offset for each coord, and add it to the coordinates. So the generator actually responds
with the biome for [X + rndX, Z + rndZ].</p>
<p>In order to keep the property that generating for the second time gives us the same result, we need the
"random offset" to be replicatable - same output for the same input. This is where we use yet another Perlin
noise - just like with the jitter for the Voronoi grid, we add a value from a separate noise to each
coordinate before sending the coordinates down to the Voronoi generator:</p>
<code>
DistortedVoronoiBiome(X, Z) := VoronoiBiome(X + PerlinX(X, Z), Z + PerlinZ(X, Z))
</code>
<p>The following image shows the effects of the change, as generated by Cuberite's DistortedVoronoi biome
generator. It is actually using the very same Voronoi map as the previous image, the only change has been
the addition of the distortion:</p>
<img src="img/distortedvoronoibiomes.png" />
<p>As you can see, this already looks reasonable enough, it could be considered natural biomes, if it
weren't for several drawbacks:
<ul>
<li>There's no way to limit the neighbors. A desert biome can neighbor a tundra biome. </li>
<li>All the biomes are considered equal. There's no way to make oceans larger. A mushroom biome is
generated right next to other land biomes.</li>
</ul></p>
<h3>Adding relativity</h3>
<p>Our next goal is to remove the first defect of the distorted Voronoi generator: unrelated biomes
generating next to each other. It is highly unlikely to find a jungle biome next to a desert biome, so we
want to have as few of those borders as possible. We could further improve on the selection of
biome-to-seed in the Voronoi generator. Or we can try a completely different idea altogether.</p>
<p>Recall how we talked about the nature, where the biomes are formed by the specific conditions of a place.
What if we could make a similar dependency, but without the terrain? It turns out this is possible rather
easily - instead of depending on the terrain, we choose two completely artificial measures. Let's call them
Temperature and Humidity. If we knew the temperature of the place, we know what set of biomes are possible
for such temperatures - we won't place deserts in the cold and tundra in the hot anymore. Similarly, the
humidity will help us sort out the desert vs jungle issue. But how do we get a temperature and humidity?
Once again, the Perlin noise comes to the rescue. We can use a simple 2D Perlin noise as the temperature
map, and another one as the humidity map.</p>
<p>What we need next is a decision of what biome to generate in certain temperature and humidity
combinations. The fastest way for a computer is to have a 2D array, where the temperature is one dimension
and humidity the other, and the values in the array specify the biome to generate:</p>
<img src="img/temperaturehumiditydecisionsimple.jpg" />
<p>We can even "misuse" the above diagram to include the hill variants of the biomes and have those hills
neighbor each other properly, simply by declaring some of the decision diagram's parts as hills:</p>
<img src="img/temperaturehumiditydecisionhills.jpg" />
<p>The problem with this approach is that there are biomes that should not depend on temperature or
humidity, they generate across all of their values. Biomes like Oceans, Rivers and Mushroom. We could
either add them somewhere into the decision diagram, or we can make the generator use a multi-step decision:
<ul>
<li>Decide whether the point is in the ocean, land or mushroom</li>
<li>If it's land, decide if it's real land or river.</li>
<li>If it's real land, use a TemperatureHumidity approach to generate land-biomes</li>
</ul>
</p>
<p>This is the approach implemented in Cuberite's MultiStepMap biome generator. It generates biome maps like
this:</p>
<img src="img/multistepmapbiomes.png" />
<p>To decide whether the point is in the ocean, land or mushroom, the generator first chooses seeds in a grid
that will be later fed to a DistortedVoronoi algorithm, the seeds get the "ocean" and "land" values. Then it
considers all the "ocean" seeds that are surrounded by 8 other "ocean" seeds and turns a random few of them
into "mushroom". This special seed processing makes the mushroom biomes mostly surrounded by ocean. The
following image shows an example seeds grid that the generator might consider, only the two framed cells are
allowed to change into mushroom. L = land, O = ocean:</p>
<img src="img/multistepmapgrid.jpg" />
<p>Next, the generator calculates the DistortedVoronoi for the seeds. For the areas that are calculated as
mushroom, the distance to the nearest-seed is used to further shrink the mushroom biome and then to
distinguish between mushroom and mushroom-shore (image depicts a Voronoi cell for illustration purposes, it
works similarly with DistortedVoronoi). O = ocean, M = mushroom, MS = mushroom shore:</p>
<img src="img/multistepmapdistance.jpg" />
<a name="perlinrivers">
<p>The rivers are added only to the areas that have been previously marked as land. A simple 2D Perlin noise
is used as the base, where its value is between 0 and a configured threshold value, a river is created. This
creates the rivers in a closed-loop-like shapes, occasionally splitting two branches off:</p>
<img src="img/perlinrivers1.jpg" />
<img src="img/perlinrivers2.jpg" />
<img src="img/perlinrivers3.jpg" />
</a>
<p>For the leftover land biomes, the two Perlin noises, representing temperature and humidity, are used to
generate the biomes, as described earlier. Additionally, the temperature map is used to turn the Ocean biome
into FrozenOcean, and the River biome into FrozenRiver, wherever the temperature drops below a threshold.</p>
<h3>Two-level Voronoi</h3>
<p>The 1.7 MineCraft update brought a completely new terrain generation, which has sparked renewed interest
in the biome generation. A new, potentially simpler way of generating biomes was found, the two-level
DistortedVoronoi generator.</p>
<p>The main idea behind it all is that we create large areas of similar biomes. There are several groups of
related biomes that can be generated near each other: Desert biomes, Ice biomes, Forest biomes, Mesa biomes.
Technically, the Ocean biomes were added as yet another group, so that the oceans will generate in
approximately the size of the larger areas, too.</p>
<p>For each column a DistortedVoronoi is used to select, which large area to use. This in turn results in
the list of biomes from which to choose. Another DistortedVoronoi, this time with a smaller grid size, is
used to select one biome out of that list. Additionally, the smaller DistortedVoronoi calculates not only
the nearest seed's distance, but also the distance to the second-nearest seed; the ratio between these two
is used as an indicator whether the column is in the "inside" or on the "outskirt" of the smaller Voronoi
cell. This allows us to give certain biomes an "edge" biome - the Mushroom biome has a MushroomShore edge,
the ExtremeHills biome have an ExtremeHillsEdge biome on the edge, etc.</p>
<p>The images below illustrate the process with regular Voronoi diagrams, for clarity purposes. The real
generator uses distortion before querying the small areas.</p>
<img src="img/twolevellargeareas.jpg" /><br />
<img src="img/twolevelsmallgrid.jpg" /><br />
<img src="img/twolevelsmallareas.jpg" /><br />
<p>The following image shows an example output of a TwoLevel biome generator in Cuberite:</p>
<img src="img/twolevelbiomes.png" />
<p>Note that rivers are currently not implemented in this generator in Cuberite, but they could be added
using the same approach as in MultiStepMap - by using a thresholded 2D Perlin noise.</p>
<hr />
<a name="heightgen"><h2>Terrain height</h2></a>
<p>As with biomes, the easiest way to generate terrain height is not generating at all - assigning a constant
height value to all columns. This is again useful either for internal tests, and for worlds like MineCraft's
Flat world.</p>
<p>For a somewhat more realistic landscape, we will employ the good old 2D Perlin noise. We can use it
directly as a heightmap - each value we get from the noise is stretched into the desired range (usually from
40 to 120 blocks for regular MineCraft worlds) and used as the height value. However, this doesn't play too
well with the biomes we've just generated. If the biome says "ocean" and the Perlin noise says "mountain",
the end result will be unpleasant.</p>
<p>So we want a height generator that is biome-aware. The easiest way of doing this is to have a separate
generator for each biome. Simply use the biome map to select which generator to use, then ask the appropriate
generator for the height value. Again, this doesn't work too well - imagine an ExtremeHills biome right next
to an Ocean biome. If no extra care is taken, the border between these two will be a high wall. The following
image shows a 2D representation (for simplification purposes) of the problem:</p>
<img src="img/biomeheights.jpg" />
<p>This requires some further processing. What we need is for the terrain height to be dependent not only on
the immediate biome for that column, but also on the close surroundings of the column. This is exactly the
kind of task that averaging is designed for. If we take the area of 9x9 biomes centered around the queried
column, generate height for each of the biomes therein, sum them up and divide by 81 (the number of biomes
summed), we will be effectively making a 9-long running average over the terrain, and all the borders will
suddenly become smooth. The following image shows the situation from the previous paragraph after applying
the averaging process: </p>
<img src="img/biomeheightsavg.jpg" />
<p>The approach used in Cuberite's Biomal generator is based on this idea, with two slight modifications.
Instead of using a separate generator for each biome, one generator is used with a different set of input
parameters for each biomes. These input parameters modify the overall amplitude and frequency of the Perlin
noise that the generator produces, thus modifying the final terrain with regards to biomes. Additionally, the
averaging process is weighted - columns closer to the queried column get a more powerful weight in the sum
than the columns further away. The following image shows the output of Cuberite's Biomal terrain height
generator (each block type represents a different biome - ocean in the front (stone), plains and ice plains
behind it (lapis, whitewool), extreme hills back right (soulsand), desert hills back left (mossy
cobble)):</p>
<a name="biomalheights"><img src="img/biomalheights.jpg" /></a>
<p>One key observation about this whole approach is that in order for it to work, the biomes must be
available for columns outside the currently generated chunk, otherwise the columns at the chunk's edge would
not be able to properly average their height. This requirement can be fulfilled only by biome generators that
adhere to the second <a href="#expectedproperties">Expected property</a> - that re-generating will produce
the same data. If the biome generator returned different data for the same chunk each time it was invoked, it
would become impossible to apply the averaging.</p>
<p>(TODO: height with variations (N/A in MCS yet)</p>
<hr />
<a name="compositiongen"><h2>Terrain composition</h2></a>
<p>As with the other generators, the composition generator category has its easy and debugging items, too.
There's the "special" composition of "all the blocks are the same type", which fills the entire column, from
the bottom to the height, with a single blocktype. This generator is useful when testing the generators in
the other categories, to speed up the generation by leaving out unnecessary calculations. Another special
compositor is a similar one, that fills all blocks with the same type, but the type varies for each biome.
This way it's easy to see the generated biomes and possibly the heights for those biomes, as shown in the
previous section on the <a href="#biomalheights">height averaging screenshot</a>.</p>
<p>For a natural look, we need to put together a more complicated algorithm. The standard set forth in
MineCraft is that the top of the world is covered in grass, then there are a few blocks of dirt and finally
stone. This basic layout is then varied for different biomes - deserts have sand and sandstone instead of the
grass and dirt layer. Mushroom biomes have mycelium in place of the grass. This per-biome dependency is
trivial to implement - when compositing, simply use the appropriate layout for the column's biome.</p>
<p>The next change concerns oceans. The generated heightmap doesn't include any waterlevel indication
whatsoever. So it's up to the terrain compositor to actually decide where to place water. We do this by
configuration - simply have a value in the config file specifying the sealevel height. The compositor then
has to add water above any column which has a height lower than that. Additionally, the water needs to
override per-biome layout selection - we don't want grass blocks to generate under water when the terrain
height in the plains biome drops below the sealevel accidentally.</p>
<p>The final feature in the compositor is the decision between multiple composition layouts within a single
biome. A megataiga biome contains patches of non-grass dirt and podzol blocks, and the ocean floor can be
made of dirt, gravel, sand or clay. A simple 2D Perlin noise can be used to select the layout to use for a
specific column - simply threshold the noise's value by as many thresholds as there are layout variations,
and use the layout corresponding to the threshold:</p>
<img src="img/perlincompositor1.jpg" />
<img src="img/perlincompositor2.jpg" />
<img src="img/perlincompositor3.jpg" />
<h3>Nether composition</h3>
<p>So far we've been discussing only the Overworld generator. But MineCraft contains more than that. The
Nether has a completely different look and feel, and quite different processes are required to generate that.
Recall that MineCraft's Nether is 128 blocks high, with bedrock both at the top and the bottom. Between these
two, the terrain looks more like a cavern than a surface. Not surprisingly, the Nether doesn't need a
complicated height generator, it can use the flat height. However, the terrain composition must take an
altogether different approach.</p>
<p>The very first idea is to use the Perlin noise, but generate it in 3D, rather than 2D. Then, for each
block, evaluate the noise value, if below 0, make it air, if not, make it netherrack.
<p>To make it so that the bedrock at the top and at the bottom is never revealed, we can add a value
increasing the more the Y coord gets towards the bottom or the top. This way the thresholding then guarantees
that there will be no air anywhere near the bedrock.</p>
<p>(TODO)</p>
<hr />
<a name="finishgen"><h2>Finishers</h2></a>
<p>Finishers are a vast category of various additions to the terrain generator. They range from very easy
ones, such as generating snow on top of the terrain in cold biomes, through medium ones, such as growing
patches of flowers, complicated ones, such as placing trees and generating caves, all the way to very
complicated ones such as villages and nether fortresses. There is no formal distinction between all these
"categories", the only thing they have in common is that they take a chunk of blocks and modify it in some
way.</p>
<h3>Snow</h3>
<p>Snow is probably the easiest of the finishers. It generates a block of snow on top of each block that is
on top of the terrain and is not marked as non-snowable. It checks the chunk's heightmap to determine the top
block, then checks whether the block supports snow on its top. Rails, levers and tall grass don't support
snow, for example.</p>
<h3>Ice</h3>
<p>Another example of an easy finisher. This scans through the world and turn each water block on the surface
into an ice block if the biome is cold. This means that any water block that is under any kind of other
block, such as under a tree's leaves, will still stay water. Thus an additional improvement could be made by
scanning down from the surface block through blocks that we deem as non-surface, such as leaves, torches,
ladders, fences etc. Note that Cuberite currently implements only the easy solution.</p>
<h3>Bottom lava</h3>
<p>Most worlds in MineCraft have lava lakes at their bottom. Generating these is pretty straightforward: Use
the user-configured depth and replace all the air blocks below this depth with lava blocks. Note however,
that this makes this generator dependent on the order in which the finishers are applied. If the mineshafts
generate before bottom lava, the mineshafts that are below the lava level will get filled with lava. On the
other hand, if bottom lava is generated before the mineshafts, it is possible for a mineshaft to "drill
through" a lake of lava. Cuberite doesn't try to solve this and instead lets the admin choose whichever they
prefer.</p>
<h3>Specific foliage</h3>
<p>There are generators for specific kinds of foliage. The dead bushes in the desert biome and lilypads in
the swamp biome both share the same generating pattern. They are both specific to a single biome and they
both require a specific block underneath them in order to generate. Their implementation is simple: pick
several random columns in the chunk. If the column is of the correct biome and has the correct top block,
add the foliage block on top.</p>
<p>In order to generate the same set of coordinates when the chunk is re-generated, we use the Perlin noise's
basis functions (the ones providing the random values for Perlin cell vertices). These basically work as a
hash function for the coorinates - the same input coordinates generate the same output value. We use the
chunk's coordinates as two of the coords, and the iteration number as the third coordinate, to generate a
random number. We then check the biome and the top block at those coordinates, if they allow, we generate the
foliage block on top.</p>
<p>Another example of specific foliage is the tall grass in the plains biome. There are quite a lot of these
tall grass blocks, it would be inefficient to generate them using the random-coords approach described above.
Instead, we will use a 2D Perlin noise again, with a threshold defining where to put the grass and where
not.</p>
<h3>Small foliage</h3>
<p>For the flowers, grass, mushrooms in caves etc. we want to use a slightly different algorithm. These
foliage blocks are customarily generated in small "clumps" - there are several blocks of the same type near
together. To generate these, we first select random coords, using the coord hash functions, for a center of a
clump. Then we select the type of block to generate. Finally, we loop over adding a random (coord hash)
number to the clump center coords to get the block where to generate the foliage block:</p>
<img src="img/smallfoliageclumps.jpg" />
<p>In order to make the clump more "round" and "centered", we want the offsets to be closer to the clump
center more often. This is done using a thing called Gaussian function distribution. Instead of having each
random number generate with the same probability, we want higher probability for the numbers around zero,
like this:</p>
<img src="img/gaussprobability.jpg" />
<p>Instead of doing complicated calculations to match this shape exactly, we will use a much easier shape.
By adding together two random numbers in the same range, we get the probability distribution that has a
"roof" shape, enough for our needs:</p>
<img src="img/roofprobability.jpg" />
<p>(For the curious, there is a proof that adding together infinitely many uniform-distributed random numbers
produces random numbers with the Gaussian distribution.)</p>
<p>This scheme can be used to produce clumps of flowers, when we select the 2D coords of the clump center on
the top surface of the terrain. We simply generate the 2D coords of the foliage blocks and use the terrain
height to find the third coord. If we want to generate clumps of mushrooms in the caves, however, we need to
generate the clump center coords in 3D and either use 3 offsets for the mushrooms, or use 2 offsets plus
searching for the closest opening Y-wise in the terrain.</p>
<p>Note that the clumps generated by this scheme may overlap several chunks. Therefore it's crucial to
actually check the surrounding chunks if their clumps overlap into the currently generated chunk, and apply
those as well, otherwise there will be visible cuts in the foliage along the chunks borders.</p>
<h3>Springs</h3>
<p>Water and lava springs are essential for making the underground quite a lot more interesting. They are
rather easy to generate, but a bit more difficult to get right. Generating simply means that a few random
locations (obtained by our familiar coord hashing) are checked and if the block type in there is stone. Then
we see all the horizontal neighbors of the block, plus the block underneath. If all of them except one are
stone, and the one left is air, our block is suitable for turning into a spring. If there were more air
neighbors, the spring would look somewhat unnatural; if there were no air neighbors, the spring won't flow
anywhere, so it would be rather useless.</p>
<p>The difficult part about springs is the amount of them to generate. There should be a few springs on the
surface, perhaps a bit more in the mountaineous biomes. There should be quite a few more springs underground,
but there should definitely be more water springs than lava springs in the upper levels of the terrain, while
there should be more lava springs and almost no water springs near the bottom. To accomodate this, the
Cuberite team has made a tool that scanned through MineCraft's terrain and counted the amount of both types
of springs in relation to their height. Two curves have been found for the distribution of each type of the
spring:</p>
<img src="img/vanilla_springs_huge.png" />
<p>Cuberite uses an approximation of the above curves to choose the height at which to generate the
spring.</p>
<!--
<h3>Caves</h3>
<p>Caves are definitely one of the main things people notice about MineCraft terrain. There are quite a lot
of different algorithms available to generate terrain with caves.
-->
<hr />
<a name="makefaster"><h2>Making it all faster</h2></a>
<p>(TODO)</p>
<a name="GPU"><h2>Executing on a GPU</h2></a>
<p>Much of the terain generation consists of doing the same thing for every single column or block in a chunk. This
sort of computation is much faster on a GPU as GPUs are massively parallel. High end GPUs can execute up to 30,000
threads simultaneously, which would allow them to generate every block in half a chunk in parallel or every column
in over 100 chunks in parallel. A naive comparison suggests that a 800MHz GPU with 15,000 threads can execute parallel
code 250 times faster than a 3GHz CPU with 128 bit SIMD. Obviously we want to harness that power.</p>
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