Fractal Geometry is a branching field of mathematics developed by French mathematician Benoit B. Mandelbrot in the 1970's. Fractals are defined as a geometric shape that is complex and detailed in structure at any level of magnification. Also, many fractals consist of portions identical to the whole, scaled down. The significance of Mandelbrot's discovery is with its approach to the definition of dimensions. According to Mandelbrot, dimensions could be much more abstract, and rather then whole numbers, be fractions, because a fractal's size must be measured with exponents, resulting in fraction results. Fractal geometry's significance is becoming exceedingly more important in today's world, both in their groundbreaking scientific advantages and in their beauty as art form. Fractals play an important role in science because of their nature; many natural landscapes, landforms and other phenomenon are fractal by nature, so to define their dimension in terms of whole numbers would be inaccurate. Fractals can also be used to create digitized computer art, and to compress still and video computer images. Fractals have two major properties: Fractional dimension, self-similarity. Fractional dimension is necessary for fractions because of their self-similarity property. The dimension of the fractal is a function of the number of similar copies of the figure. This can be expressed as n = d squared, where n is the number of copies and d is the dimension. For example, if there were 4 similar copies in the figure, the square root of 4 would equal the dimension. In this picture of the Sierpinski Triangle, every triangle in the fractal is similar to the whole. Another example of a fractal is the snowflake model, which is an equilateral triangle with smaller equilateral triangles continuously constructed on the progressively smaller sides, creating a figure that would theoretically have an infinite perimeter and an infinite # of vertices, but a non-infinite area. Fractals are often formed by a process called iteration. This is a simple process of taking a simple geometric figure, changing it to make it more complicated by adding similar figures within it, and continuously applying this process, thereby creating a fractal. Fractals have several specific uses, in science and art. Fractals can explain a pattern to something previously thought to be random. As far as the earth, fractals can be used to capture the huge details and irregularity of clouds and landscapes. Also, fractals are a very useful tool for landscapers attempting to draw realistic natural objects. For example, in science fiction films to create the backdrop the producers could start with basic shapes and iterate them over and over to accomplish what they are looking for. Also, fractals can be used to describe, predict and model the evolution of different types of ecosystems, which in turn are greatly useful in determining the spread of things such as acid rain and pollution. Fractal geometry's uses aren't limited to biology, however. Fractals can also be used to distinguish and characterize metals, because a metal surface's fractal dimension is a measure of the metal's strength. Besides these specific uses, fractals can also be used in describing astronomy, meteorology, economics, and in the study of galaxy clusters. Thus, fractals are very intricate and essential branch of geometry that has growing uses realistically, and popularity for their beauty. The discovery of fractals in a sense opened a new world to us, and began to explain some phenomenon previously unexplainable.