How can I randomize a numerical value for a node? Is there any one node, or combination of nodes that can achieve this effect?
Object Info Node's Random Output
I just discovered there is an Input node that can output a random value:
Input -> Object Info
However, it only works for Material Shader nodes.
Here is the Blender wiki description of this node:
Information about the object instance. This can be useful to give some variation to a single material assigned to multiple instances, either manually controlled through the object index, based on the object location, or randomized for each instance. For example a Noise texture can give random colors or a Color ramp can give a range of colors to be randomly picked from.
Note that this node only works for material shading nodes; it does nothing for lamp and world shading nodes.
Location: Location of the object in world space.
Object: Index Object pass index, same as in the Object Index pass.transformed.
Material Index: Material pass index, same as in the Material Index pass.
Random: Random number unique to a single object instance.