Starting with a fixed triangle \(A_0B_0C_0\) in the complex plane, and a sequence of complex numbers \((t_n)_{n\ge 0}\) , define the sequence of Kasner triangles \((A_nB_nC_n)_{n\ge 0}\) (named after E. Kasner (1878–1955)), where the points \(A_{n+1}\) , \(B_{n+1}\) , \(C_{n+1}\) are “dividing” the segments \([A_nB_n]\) , \([B_nC_n]\) , \([C_nA_n]\) in the ratio \(t_n:1-t_n\) , respectively. When \(t_n\in (0,1)\) , \(n\ge 0\) , such triangles are called nested (the points of the next iteration are on the sides of the current one), and many results involving real weights and polygons have been studied (see, e.g., [12, 14], or [17]). In this paper we derive exact formulae for the general terms and we study the dynamic geometry of these Kasner iterations, extending results involving a fixed real, or complex parameter [4].