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With a Math node, we can do several different operations.

Let's take a look at some of the basic math operations.

These are mostly self explanatory, but there are some things to look out for.

The Math node takes one to three inputs, depending on the selected operation, and always has

a single output.

Perhaps the simplest of all operations is addition.

We all know what it is, but let's take a look at it in context.

Here we have a constant value of zero being fed into the first and second inputs.

On the top we can see the color representation of the value, and on the bottom we have a

plot of the value over the X axis.

If we start changing one of the inputs, we see the output value changing accordingly.

Now, looking at an example where we have a Noise Texture fed into one of the inputs,

we basically see the same thing, the output moves up and down based on the value we're

adding.

But something interesting happens when we feed it a linear gradient, such as the X channel

from a texture coordinate.

Here, the output seems to move side to side.

However, we know that we cannot shift values through space, as we cannot access values

from other points.

And if we highlight a point on the line, we can see that it is indeed moving up and down

according to the value being added.

This effect happens because with a linear gradient, there is no difference between shifting

up and down, and shifting left to right.

This is significant as it is the foundation of what allows us to move coordinate spaces

around.

We are calculating the values of a shifted gradient, from the original values themselves.

Note that this only works because we have an infinite gradient.

If we use a clamped gradient, such as the one output by the gradient node, initially

it looks the same, as we cannot see the values below zero or above one as colors, but if

we change the addition now, the horizontal shift only happens within the small region

where the values are not clamped.

So far we've only added a constant value to different inputs, which just offsets everything

up and down.

But nothing stops us from plugging varying values, like a noise and a gradient, into

both sockets to add them together.

Moving on to the other operations, subtraction is identical to addition, except that the

sign gets flipped.

So let's move on to multiplication.

Multiplication allows us to change the amplitude of a texture.

It's also interesting to note that on a linear gradient, we change the slope, which is equivalent

to a scaling operation, squashing the values together in space.

Division is the reciprocal of multiplication, meaning that it's the same as multiplying

by one over the value.

Moving on to the Power operation, applying this to a gradient, we get the typical power

curve.

Keep in mind that only the real part of the output is given, and the power of negative

values is set to zero except when the exponent is an integer.

Power is useful for smoothing, and for changing the distribution of things.

We'll explore some uses of the Power operation throughout the course.

Lastly, the Absolute operation, which takes a single input, simply flips the sign of any

negative values.

When applied to a linear gradient, this is especially useful for creating symmetry.