Abstract
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, twigs and 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 pretty pictures. 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.
Faculty Sponsors
Dr. Ricardo Carrera, Dr. Evan Haskell
Project Type
Event
Location
Alvin Sherman Library
Start Date
4-3-2009 12:00 AM
End Date
4-3-2009 12:00 AM
What is a Fractal?
Alvin Sherman Library
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, twigs and 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 pretty pictures. 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.
