How do I perform a GROWTH POLE THEORY/CONCEPT and what are its requirements?

Great question! Could you give some more details for a well targeted answer.

So the Growth pole as you know is only a theory, you literally cannot perform a theory, however, you can apply its concepts. For instance, you have a point which you identify as a growth pole, you can measure use the near and distance tools in either ArcMap or QGIS to measure the distance between the growth pole and other secondary growth poles. If you want to be a bit complicated, you can do a network analysis which would require that you have some streetlines data, and with that you can compute for travel time from growth poles to other areas and the shortest distance etc.