How to automatically rearrange a path on a grid ?

Hello !

I have a grid and some planes with textures on it. In order to make a path, a path texture is assigned to some planes. However, I would like the path texture to change automatically depending of the path it self. For example, is a tile with a path texture can have a dot, a dead end in any direction, a straight line, a corner, a T join or a crossroad.

This is something very common that I've seen in thousands of games but I don't know how this principle is called.

How should I proceed ? Should I check every tick in the Update() if there is similar textures above, under, or on sides ? I'm looking for a method, or maybe an example for this.

Thanks in advance :)