Terrain Generation

*See:* Open Problems

## Survival Mode

### Properties

One thing one may notice about the terrain in survival mode is that each level (that isn't part of some peak or trough) is bounded above and bounded below by contour levels of just one level up or down, that the contour levels change smoothly from slope to slope, that there might be directional artefacts, for sometimes the contour has long stretches that are parallel to the x or z axis, that when the slope changes in both directions, it usually changes only one block for x or for z, and if it does for both more than one block, it's only rarely and when it happens, the most common case is for it to change two blocks in x and two blocks in z, that islands in oceans are very rare, and also, that it attains a minimum of approximately 55 y and a maximum of approximately 88 y.  For all coordinates that are multiples of 250 in x and z, (e.g. x = -250, y = 500), the terrain height is exactly equal to 70. It could be that multiples of 125 or 50 are also constrained, but it requires a lot of data to corroborate, so far, it seems that for multiples of 125 they attain a maximum and minimum height of 13 more or less than 70 (especially when one of the values is 625 or -625, otherwise, the max or min is usually 9), whereas for multiples of 50, they attain a maximum and minimum height of 14more or less than 70 (i.e. so that there is the possibility but it would require a lot more evidence to find out.). For unknown reasons, it also seems that, when one component is a multiple of 250 and the other is a multiple of 125, then it might have as height values that are either 0, 4, or 9 more or less than 70 (and perhaps 8 since it happened once for a x = -625, z = 500, though 625 might be an exception, see above).

## Capture the Gems

All maps of capture the gems are circular islands, with a somewhat different algorithm, in that respect, from Survival Mode, the details, of which, remain an open problem. A theory is that it reduces linearly in height with respect to distance from the centre.

### Biome Changes

In the Oasis Map, the desert is found outside the region bounded by the river, and the forest is found within the region bounded by the river.

In the Riverdale Map and the Bulwark Map, the desert and the forest are divided by two lines one in the west and the other in the east, which shape is determined by a similar algorithm to the terrain generation and more precisely, the serpentine river of the Riverdale Map, though without the distinction between centre and sides (since in the separation river's algorithm, one has that near the centre, the river is less serpentine than in the sides). In particular, this algorithm is one dimensional in the sense that one can trace it rightwards or leftwards without ever seeing the separation between biomes moving in some u-turn in the opposite direction (it merely moves up and down, while staying in the rightwards or leftwards path). The specifics of which remain, however, an open problem.

## Invariance

### Total Invariance

Total invariance refers to the property that, across all servers, all feautures of a game mode remain invariant, across all servers and all games. This is true for battle royale and free for all, where everything except what's inside the boxes is invariant.

### Tree Invariance

Tree invariance refers to the property that across all servers, and across all games, the position of trees remains invariant, however, the height of the tree, the y of the bottom of the trunk and the top of the trunk are all variable. This is seen in every map of Voxiom. There are four sets of invariant trees, including, the set of trees that is found in the Oasis Map, the set of trees found in Free for All, the set of trees found in Battle Royale, and another set is the one found in Survival, the Riverdale Map and the Bulwark Map. In the case of the second set, it happens that it's related to maps which terrain is not invariant, such that sometimes, the place where a tree would be found is snow, sand or water instead of grass, and as such, the tree won't exist in that location. Tree Invariance is the reason behind the location of the leaf block that cannot break at a corner of the ruby gem tower.

### Terrain Invariance

Terrain invariance refers to the property that across all servers, and across all games, the terrain height and biome changes remain invariant. This is seen in all cases of total invariance and also in the Oasis Map.

## Algorithm

It might be using Perlin noise, OpenSimplex, or something else.

1. ↑ Though, this might be different if the ocean is actually a kind of biome and not just where the elevation is smaller than 65.
2. ↑ I checked it for 37 positions, 25 in one server, and 4 for each of the other servers.
3. ↑ the only apparent exception is when the terrain lowers down to level z = 11, that is when the desert confuses itself with the beach
4. ↑ For example, a tree found at: -29 x, 133 z in the Riverdale Map, will be found in the exact same position in the Bulwark Map, across all servers and across all games.