Visualize the graph of a function is not easy (at least for me), without plotting the function.

It can be really hard to understand what y = x^2 * z^2 looks like.

So I obviously did an ICE compound with these most common graphs.

I couldn’t stop doing functions and playing with it, so I ended up with this list, all in the same compound:

x*z

x^2 + z^2

x^2 – z^2

x^2 * z^2

x^3 + z^3

sin(x)

cos(x) + cos(z) ^ 2

cos(x^2 + z^2)

sin(x^2 + z^2)

-1 / (x^2 + z^2)

|cos(x) + cos(z)| ^ (1/2)

cos(x) + cos(z)

| cos(x^2+z^2) | ^ (1/2)

|cos(x+z)| ^ (10/2)

cos( |x| + |z| ) * ( x + z )

cos( |x| + |z|) * (|x| + |z| )

cos( |x| + |z| )

|sin(x) * ( sin(x) + cos(z) )| ^ 0.2

sin(x^2) * cos(z^2)

Some are very common, others are not. It’s cool how many crazy patters you can get using these functions.

Hopefully this will work as a “educational” resource, so you can see what these functions look when applied to a 3d shape and understand how Sin, Cos, Absolute values, etc, can affect the function.

Here is what these equations look like when applied to a grid:

What’s even more cool in ICE is that after I had all the functions done, I could apply this as a force, a weightmap… basically anything that reads a 3d vector or a scalar.