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With version 1.13, the Update Aquatic, Minecraft introduced coral blocks into the game, most prominently found in naturally generated coral reefs in warm ocean biomes, where they build elaborate tree-like structures.

However, what I haven't found so far is a proper reference as to how exactly the coral block structures in a coral reef generate. The Wiki on coral reefs and coral blocks seems to be rather scarce on that information. Though, the world generation aspects of Minecraft are often deciphered quite accurately and I wouldn't consider this a matter all too different or more complicated than tree growth. Or at least for someone to have made an analysis of the different structures that can be generated in a coral reef, yet googling on the issue wasn't all too successful.

So, is there already some analysis of the exact coral generation algorithm or at least some proper reference, even if home-made, showing the various distinct structures that are generated from coral blocks as part of a reef?

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    To close voters: This question asks "how does this behave in the game", not "find me a list" or "why does it do that". It's on-topic. Sep 11, 2018 at 8:34

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In lack of an analysis of the actual generation algorithm, I just went to a coral reef and made a few observations, which I'll try and form into somewhat of an analysis of the possible coral structures. But note that this is purely emprical and likely incomplete.

First of all, the structures seem to fall into three distinct general categories. They are only ever generated from a single kind of coral block, but they can of course generate into each other, forming more elaborate constructions.

Vertical

Those are most similar to trees. They originate from a single vertical stem of various height (~1-3), from which branches can grow out in all 4 directions. The growth is diagonally upward in vertical segments of varying height (up to 4, rarely even 5), however, the first segment growing away from the stem seems to always be just a single block. The number of segments in each branch (and thus the diameter of the structure) can reach up to 3, rarely even 4 blocks, making the whole thing on average 5-7 blocks wide in x and z. Some of the 4 directions might be missing branches entirely, though.

enter image description here

Horizontal

Those work in a similar way of a central source block and branches going out. However, the branches go out more horizontally (though, still diagonally upwards) and into the same direction. From the central block there can be up to 3 branches (from the block itself and 1 block diagonally upwards to the left and right each) going into a common direction. The branches themselves are again made of segments, this time horizontal, of varying length (up to 5, maybe more?). Sometimes the first of those segments can even be vertical (2 blocks, maybe more?), giving the whole branch a more circular curve. And rarely, the side braches can be offset to the side by 2 blocks away from the source block rather than just 1, it still seems to be the same general structure, though.

enter image description here

Spherical

Those form kind of a hollow sphere, or to be more precise, a box with the edges missing. The individual side planes can thereby be of varying width along each dimension, from 2 to 4, giving the whole structure a size of (4-6)³. There will be random blocks missing throughout and often the bottom part might be entirely missing, too, making it more dome-like. But it doesn't seem to happen that an entire side or the whole top is missing, beyond the individual block holes.

enter image description here

As to the seeding pattern of the structures, it's hard to say much from general observations. They seem to be generated at a frequency that roughly gives each individual coral structure a perimeter of just about its own size, with some areas clumping them a little more for the structures to penetrate each other more, and other areas where they have a little more "breathing room".

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