Nature is complex. It features a multitude of systems which, simple though they may be, are unpredictable in their behaviour, and seem not to be governed by the established deterministic laws of classical physics. For many years, scientists ignored such systems claiming that their unpredictability was a result of the limitations in the accuracy of measurements, or pure chance. Others even rejected them as unscientific. However, in the 1970s, a new theory evolved, which, if its supporters are right, explains the diversity we observe in nature and provides an accurate and scientific description of the unpredictable phenomena in question. This is known as “Chaos Theory”, and the purpose of this article is to provide an introduction to it together with fractals, the elaborate patterns which have become its emblem.