Fractals and the Lorenz Attractor are just two examples of systems related to chaos theory. The state of a deterministic system is determined by its previous state and the rules of the system, its governing equations BUT the state of a random system is independent of its previous state. That's why it's paradoxical that a deterministic system should seem to behave like a random system. Yet, while the exact equations show unpredictable behavior of a particular state of a chaotic system, other descriptions of the system, such as fractals and strange attractors, portray the essence of the system and the underlying order of its strange behavior. In the next section, the logistic map illustrates such alternate descriptions.
Some chaotic systems have remarkably simple governing rules.
For mathematical simplicity, it's hard to beat the logistic map. Yet it has a rich and varied set of outcomes and a wide range of applications. Along with the constant c, each value of the evolving quantity Q determines the succeeding value, Qnext. That's the simple part. The actual sequence of Q values in any one case can be orderly or chaotic.