The animate, animatecurve, animate3d, and seq commands are convenient, but as the animations we write become more elaborate, we will sometimes want more control over how the frames are produced. A loop allows that. Also, when the structure of each frame is an intricate one, although we may be able to use seq cleverly to create the frames, a loop can clarify the code. We will use loops to create a sequence of frames, then use display to display them in order. In this chapter, we will also see how to use Maple to find derivatives for functions of one and of several variables. We will encounter a convenient line-drawing procedure from the plottools package, and we’ll create animations for generating solids and surfaces of revolution and for demonstrating Newton’s method.