Patch 1.09 added in the option to customise the world design upon restarting a new world. This has since been greatly expanded on in Patch 1.1 Alpha.

After selecting restart world, the game offers a number of options to toggle:

Option Toggle Effect
FlatLand On Makes the entire world flat, the world is perfectly smooth all the way to the edge.
Off Normal function, flatland is disabled.
Elevation Ultra Low World depth is at its lowest, on flat land terrain is 2 blocks deep.
Low World depth is low, flat land terrain depth is 29 blocks deep.
Normal Standard world depth, flat land terrain depth is 49 blocks deep. (cannot be used with mountainous terrain)
High Highest world depth, flat land terrain depth is 69 blocks deep. (cannot be used with mountainous terrain)
Terrain Holland World terrain is very smooth; not as extreme as flat land.
Flatter Terrain is smooth, with small hills.
Normal Standard Setting, occasional large hills with moderate variation in world height.
Hilly Frequent large hills, lots of variation in world height.
Mountainous Mountains cover the map, can only be used with low or ultra low elevation.
Climate Temperate See Temperate
Tropical See Tropical
Desert See Desert
Alpine See Alpine
Caves None No caves underground
Small Small pockets of caves scattered around. Tiny caverns can be found at the bottom of the world
Medium Meduim-sized caves, sometimes pass very close to each other so only a small amount of digging is needed to find another. Medium sized caverns can be found at the bottom of the world.
Large Large caves wind through the ground, because of their size, large caves are often link to form even bigger cave systems. Large caverns at the bottom of the map are often linked by cave networks.
Insane Massive cave networks fill the landscape, most caves are linked to each other creating a huge web of tunnels throughout the world. Enormous caverns at the bottom of the map are almost always linked by tunnels.
Trees None No trees generated
Few Very small patches of trees in very small groups roughly 10-46 blocks away from each other.
Normal Small patches of trees in small groups roughly 7-38 blocks away from each other.
Many Large patches of trees in large groups roughly 7-29 blocks away from each other
Forests Very large patches of trees grouped together roughly 5-15 blocks away from each other
Island Mode On The edge of the map lowers to an 'ocean'; water spawners are place in every node at the edge flooding the area.
Off Edge of the map is normal terrain generation.
World Seed Player The world seed is unique to the player's gamertag, if a player resets their world with the same settings as they had in the previous world, the world wil be identical.
Random The world seed is random, resetting with identical settings will produce a different world.
Manual World seed is by choice, if the player likes a particular world seed they can enter the number and get the world they want.

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