Allegedly, fractals have been known about since about the 17th century by the mathematician and philosopher Gottfried Leibniz. It was known by the late 19th century that fractals were recursive and that they were continuous but not always differentiable discovered by Georg Cantor, Felix Klein, and Henri Poincare. In 1904 Helge von Koch started making figures that represented the ideas of fractals (which can be viewed at http://en.wikipedia.org/wiki/File:Von_Koch_curve.gif). Later that century, around 1918, at about the same time, two French mathematicians Pierre Fatou and Gaston Julia, came up with how fractals map the complex numbers. By 1975, the name "fractal" was finally coined for these figures. The name is derived from the Latin fractus meaning "broken" or "fractured." The name fractal was coined by Benoit Mandelbrot. Although naming these objects fractals, debate is still had over these objects. Many people do not know how to formally define a fractal and what its name should encompass, but Mandelbrot was known for saying that fractals are "beautiful, damn hard, and increasingly useful. That's fractals!" Now the general consensus on what a fractal is, is infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions.
Fractals have been defined as many things, not just geometric objects. Among other things, fractals can also describe processes of time. Fractals have been studied in images, structures and sounds, and also found in nature, technology, art, and law. My area of interest comes from fractals in nature. Fractals in nature show extended, but finite, scale ranges. These fractals are being studied heavily and are helping in many ways. One such way is leaves, based on the fractals of leaves it can be determined how much carbon is in a given tree. Wikipedia.org gives the following extensive list of fractals in nature...
- river networks
- fault lines
- mountain ranges
- lightning bolts
- Mountain Goat Horns
- Animal coloration patterns
- Broccoli and Cauliflower
- Heart rates
- Blood vessels and pulmonary vessels
- Ocean waves
- Soil pores
- Psychological subjective perception
My information was either previously known information or found from http://en.wikipedia.org/wiki/Fractal.