What is a Fractal?

What is a Fractal?

What are fractals? Mathematicians like to make simple models to understand and advance the world around us. Common geometric objects, unfortunately, are often too simple to model the world we live in. A line as a model for a river, or a cone as a model for a mountain could be overly simplistic. Many objects in nature, such as broccoli, twigsand the venous and arterial system of a child‘s kidneys, exhibit a self-similar structure whose geometry can be modeled using ―fractals.‖ Fractals are much more than just prettypictures. Fractals have many interesting and seemingly paradoxical properties. Such as a bounded curve of infinite length or a planar figure that contains no area. In addition, some fractals exhibit a broad array of symmetry which can be explained, and depicted, by a variety of dihedral and rotational groups. While the aesthetic appeal of fractals is captivating, the true beauty is in the mathematical theory behind them. In this presentation we will examine the mathematical theory behind fractals and depict a variety of real world applications.