Particle Distance to Some Particular Point
The particles are colored differently within a certain distance to a given point P0. Emission Shader. In the user ortho view is the cylinder with a particle system. The white torus has that same point P0 as center. Image above.
Cycles Material Nodes calculating distance and employing color ramp. Image above.
Click image above to see larger image.
The OP has asked about Textures Controlling Particles Systems.
This is a quick piece of information for further research. The two columns are of the Particle Texture Settings which are visible only in Blender Internal Render Mode. Cycles will [not] show the same info, yet will be influenced by the textures as well. You can switch back and forth as [interesting] as this might seem. The three yellow arrows emphasize Texture Panel Purpose, Mapping, and Influence areas. This is not a tutorial on the topic. I use two columns for the same settings out of edit convenience and readability convenience.
With a more complicated frame change handler and Python anything is possible. Same comment for BAN - Blender Animation Nodes.