Voltage gradient in voltage difference across a resistor
An ideal resistor is indivisible, so you can't really talk about voltages inside the resistor.

A real resistor comprises some kind of resistive material: a carbon slug, a long wire, a thin metal or carbon film, for example. If you could trace a path from one terminal of the resistor, across this resistive material, to the other terminal of the resistor then you would indeed see a voltage gradient.

Having said that, you shouldn't assume that there is a linear gradient as you move across any physical dimension of the resistor.