abstract: The construction of the Mandelbrot set for a family of coquaternionic quadratics will be used as an opportunity to discuss dynamical systems in the context of coquaternions. In particular, we will emphasize the differences from the well known complex dynamics (and also from the dynamics in the quaternions). The richness revealed by the studies already carried out, but also the challenges posed - namely the need for a new concept of attractivity - will be the main topic of this talk.