In the early stages of the game, building can be a challenge as many sturdy building blocks require metal tools to obtain. However, there are a few building blocks that can be obtained with just stone tools.
More building blocks are obtainable with metal tools.
With just a Stone Knife, you are able to obtain Straw by breaking plant like blocks. This can be used to craft a very simple building material: Thatch. Thatch is a lightweight block that isn't affected by gravity, however players and other entities can pass right through it! It can also be crafted back into Straw if needed.
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Mud can be found on the ground, underneath rivers and lakes, or in patches in low elevation swampy environments. With a little bit of Straw, it can be crafted into Wet Mud Bricks.
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These can be placed on the ground in a dry location, and after a day they will harden into Mud Bricks.
These dried mud bricks can then be crafted into Mud Brick Blocks. They can also be made into Stairs, Slabs, or Walls, if so desired.
All different varieties of mud bricks.
Wattle and Daub is a versatile building and decoration block.
Wattle can be crafted and placed, however it is breakable and allows players and mobs to walk through it. It can be augmented with Daub, to make it solid.
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In order to make Wattle solid, it first must be woven, which requires adding sticks to the structure.
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Four sticks are required to weave wattle.
At any time, sticks can be added on each diagonal, as well as the top and bottom. Hold a single Stick in your hand and Right Click it to add a stick. Change what part of the wattle you're adding the stick to by selecting a different side of the face.
Adding sticks to wattle.
Using Daub on Woven Wattle creates a solid block.
It can then be stained by using dye on it.
Clay obtained from the ground can be crafted into clay blocks. When placed and dug again, they'll turn back into clay. While unattractive, they are easy to obtain.
Peat spawns in the world in patches along water bodies and is mineable with stone tools. Some plants will grow on it.
However, peat is quite flammable.