This article illustrates the basic features of chaotic systems and demonstrates some of the differences between chaotic and nonchaotic systems. To facilitate the explanation of advanced mathematical ideas, this presentation is couched in terms of the interactions within two families: the Limit family and the Scroll family. A nonchaotic model of the Limit family leads to repetitive sequences of affection and hostility between husband and wife. The Scroll family model demonstrates the dynamics of a truly chaotic system; it leads to alternating episodes of mutual endearment and mutual aversion between mother and daughter. Problems of measurement that would accompany the use of these models are mentioned.