Euclidean distance discriminants and Morse attractors

Our study concerns the Euclidean distance function in case of complex plane curves. We decompose the ED discriminant into 3 parts which are responsible for the 3 types of behavior of the Morse points, and we find the structure of each one. In particular we shed light on the ``atypical discriminant'' which is due to the loss of Morse points at infinity. We find formulas for the number of Morse singularities which abut to the corresponding 3 types of attractors when moving the centre of the distance function toward a point of the discriminant.