Random terrain

Introduction

Procedurally generated terrain, often refered to as randomly generated terrain, is a terrain that is created via script rather than by hand. This gives the ability to have a game that is a completely different experience every time as well as uses alot less work.

The basic algorithm

The most basic algorithm is to place bricks of random size in random positions across your baseplate. To do this we will set up a simple for loop that instances a new, anchored part every time.

for i=1,200 do
    local a=Instance.new("Part",workspace)--creates new part in workspace
    a.Anchored=true

Next we will set the size to a random amount. For this we will use the function math.random()

    a.Size=Vector3.new(math.random(1,20),math.random(1,20),math.random(1,20))

This will set the Size to a random amount between 1 and 20 for the X,Y and Z size. Now for the last step of our algorithm, use CFrame to place the brick in a random spot. We will easily just place the X and Z axis using math.random() yet for the Y axis, we'll have to do something special. Being that we want all the bricks to stay on the ground, we want their base to be at 0. Now since the Position of a brick in roblox uses the center of the brick, we'll have to divide the Y size in half, so that it sits just perfectly on 0. So it would be :

    a.CFrame=CFrame.new(math.random(-100,100),a.Size.Y/2,math.random(-100,100))
end -- for the for loop

The basic algorithm

Heightmap

A heightmap shows different elevations across the whole map. For making a basic one, we will just have a script in the base of our map. This way we can specify the size of the map we want and where it will be positioned, easily. To start, we will define three variables.

Xlength=10
Zlength=10
par=script.Parent

Xlength and Zlength will be the dimensions ( in parts ) that will be used whereas par shows the base, which is what our math is based on. Now, how we will create all the bricks is similar to last time, only now it will use two for loops.

for x=1,Xlength do
for z=1,Zlength do
    local a=Instance.new("Part",workspace)
    a.Anchored=true

By setting it up this way, it'll start from a corner and go all the way to the edge, then go back to that corner and do the same thing just one up until the map is complete. Now the sizing of the brick will be a little bit more unique than last time. Now we will only use math.random() on the Y axis, the other two we will divide the par.Size by their equivalent Xlength or Zlength. This will insure that it will sit perfectly on our base, but only if the formFactor is set to Custom

    a.formFactor="Custom"
    a.Size=Vector3.new(par.Size.X/Xlength,math.random(1,20),par.Size.Z/Zlength)

Now we will do the tricky part, positioning it with CFrame. There are 3 basic steps to getting the CFrame perfect. Step 1 will be very similar to the first example. The Y axis will be done exactly the same way, however the other 2 axis are going to have to be done by doing

size.X*x and size.Z*z
    a.CFrame=CFrame.new(x*a.Size.X,a.Size.Y/2,z*a.Size.Z)

This is done because now it'll take the for loop x and z values, and multiply them by the size to get it to scale. Next we're gonna add the position of the part, and also subtract half of the size on the X and the Z.

    a.CFrame=a.CFrame+Vector3.new((par.Position.X-par.Size.X/2),par.Position.Y,(par.Position.Z-par.Size.Z/2))

The reason we also subtract half of the X and half of the Z is because then it will make it offset from the corner, instead of the middle of the base. Now if you run it like this, you'll notice that it still comes off the base a little bit. This is because the bricks aren't being moved by the corner as well, but by the middle of them. We will fix this in the third and final step, subtracting half of the x and z size of the brick being placed.

    a.CFrame=a.CFrame-Vector3.new(a.Size.X/2,0,a.Size.Z/2);
end end -- an end for each for loop

Coloring the bricks

Now in case you sadly haven't noticed, the bricks are alil dull and all completely grey. So

to change this we will make a simple function named color.

randomly picked

For this method, we'll use a table full of strings, that will be the names of the colors. Then the function will pick a random color out of the table and use it. Here is the function

colors={"Bright red","Really black","White"}
function color(part)
    part.BrickColor=BrickColor.new(colors[math.random(1,#colors)])
end

Now all you have to do to use this function is somewhere in the script put

color(a)

and it will run.

Based on height

Now we will base are function off of the height of the brick. It will be basically the same thing, with one real difference. Now we will have acouple conditionals and the color(a) will have to go after the brick is sized.

colors={"Bright red","Really black","White"}
function color(part)
    part.BrickColor=BrickColor.new(colors[1])
    if part.Size.Y>3 then
        part.BrickColor=BrickColor.new(colors[2])
    end
    if part.Size.Y>7 then
        part.BrickColor=BrickColor.new(colors[3])
    end
end

Using weighted values

In scripting terminology, weighted means numbers adjusted to seem more proportional towards what you want.

Mountains

In case we wanted to make sure a mountain came out of our script, we can easily just use a variable ( rand ) to hold the highest point we reach and add that to every number. Now to maintain it being random, we will also add a random number between -2 and 2. Then after we have that number, we'll check if the random number between -2 and 2 is greater than 0 and add it to our variable rand.

rand=0

for x=1,Xlength do
for z=1,Zlength do 
    local a=part:clone() 
    local random_factor=math.random(-2,2)
    a.Size=Vector3.new(par.Size.X/Xlength,rand+random_factor,par.Size.Z/Zlength)
    if random_factor>0 then
        rand=rand+random_factor
   end

Lake

Now to make a lake, we won't need random_factor or rand. All that will be needed is a little bit of math to add in the weighted factors. Just try

    a.Size=Vector3.new(par.Size.X/Xlength,math.random(-2,2)+math.abs(x-Xlength/2)+math.abs(z-Zlength),par.Size.Z/Zlength)

Now this works because it will subtract half of the number of bricks from x, putting x in the middle, then taking the absolute value of that and adding it with the same thing for Z.