The VRayUVWRandomizer map allows applying random offset, rotation and scale to textures, assigned to a single object with different Face IDs or different objects. It can be used as a mapping source for VRayBitmap and VRayTriplanarTex texture nodes only.

In the image shown here, Randomize had its type set to By element.

Seed – Changes the randomization pattern when one or more of the randomization modes are used.

Randomize – Specifies a mode for randomization. Multiple modes can be combined.

By name – Generates a color index based on the name of the node that the texture is applied to. This allows the color to remain consistent if the object is merged into another scene, or X-Ref'd etc.;
By element – Assigns random colors based on element (e.g. teapot lid, etc.) IDs of the object;
By face ID – Considers the face IDs of the object when feeding the data (color or texture) to the material;
By instance ID – Assigns random colors based on InstanceID (works for Alembic instances, VRayInstancer source objects, VRayEnmesh, and Chaos Scatter);
By particle ID – Assigns random colors based on ParticleID (works for VRayInstancer source objects and Thinking Particles);
By render ID –  Assigns random colors based on RenderIDs;
By object ID – Considers the Object IDs of the object when feeding the data (color or texture) to the material;
By node handle – Each node in 3ds Max is assigned a unique number (a handle) when it is created. This option generates the color index based on that node ID. It is useful because the node handle survives through scene editing - e.g. if you add/remove other objects, or rename them, you still get the same colors.
Stochastic tiling – Changes the mapping based on the UV tile.

Tile blend – Edge blending between adjacent tiles when Stochastic tiling mode is used. See the example below.

Random flip U/V – Flips the texture on a random principle along the U or V axis.

Variance – The min and max range in which the scale, offset and rotation parameters are applied.

Step – Specifies the number of steps in which the variance interval is achieved. For example, if UV rotation is set from 0 to 360 with a Step of 5, the texture is rotated at an angle that is a multiple of 72 degrees (e.g. 72, 144, 216..).

U/V offset – Controls the position of the texture along the U or V axis.

UV rotation – Rotates the texture along the U or V axis.

U/V scale – Scales the texture along the U or V axis.

These parameters are the regular 3ds Max coordinates parameters as found in the general 3ds Max textures.

These parameters are the regular 3ds Max noise parameters as found in the general 3ds Max textures.