The Quadratic Family

This chapter discusses the dynamics of the quadratic functions Q_c(x) - x² + c. It discusses the construction of the classical Cantor middle-thirds set, or Cantor set for short. While this set may seem quite "pathological" at first, researchers will see that these kinds of sets arise over and over again in dynamics. The Cantor set is the most basic kind of fractal. One of the remarkable features of the Cantor set is the fact that there are many, many more points in K. In fact, K is an uncountable set. A set is uncountable if it is neither finite nor countable. To see that the Cantor set is uncountable, researchers make a brief digression into ternary expansions of real numbers.