Systems of two iterated functions over skew field of quaternions

Systems of linear iterated functions $f_0(z)=qz+a$, $f_1(z)=qz+b$ over the field of complex numbers have been investigated since 1985 (Barnsley and Harrington). Much attention is paid to the question of the connectedness of their attractors. We consider systems of iterated functions $f_0(z)=qzp+a$, $f_1(z)=qzp+b$ over the skew field of quaternions. We simplify the form of such systems and study the structure of their attractors.