On the Generalized Taxicab Apollonian Sets

In this work, the concept of Apollonian set is explored in the framework of the generalized taxicab plane and named as the generalized taxicab Apollonian sets. It is determined that these sets do not conform to the properties of generalized taxicab circles; rather, the closed simple rectilinear figures are composed of line segments. By examining various configurations based on the positions of given points, the generalized taxicab Apollonian sets are systematically classified and characterized.