An Exploration of Fractals

Have you ever seen a cauliflower closely? If you observe it carefully, you will see that the smaller portions of it resemble the whole cauliflower. If you take a still smaller portion and magnify it, you will find that this too resembles the whole object. This is an example of a pattern which repeats itself, where each smaller portion is a scaled down copy of the larger portions. This leads us to the idea of self – similarity. In fact, we are now in a position to define a fractal. Fractals are self-similar objects. By self – similar we mean that smaller parts of the object are exact scaled down copies or replicas of the whole object. Nature is full of fractals. Broccoli, certain fern leaves, clouds etc manifest self-similarity and can be categorized as fractals. In this lesson we are going to construct and explore Fractals through simple geometric constructions.