Thank you for the fast reply, my problem was in my own code - now it works. However, one question remains: in standard examples like your each member of the list is prepared independently. If the next member list[[k+1]] =ListPoitPlot3D[...F[k+1}...] and F we compute by the inductive definition: F[k+1] from F the standard way makes a lot of extra work because it repeats the previous work. For sin there is no problem but if F is complex - is there some way to find =ListPoitPlot3D[...F[i+1}...]  from F directly? Of course, I always can store the list of F values and reduce the time, but imagine that F occupy the great memory and list is long. I can store one value list but not the whole list. My question is how to avoid the remembering the whole list in the animation - is there some modification of Animate[list...] which requires only sequential using of the list?