Fractal Geometry

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Fractal Geometry

Fractal Geometry
Fractal geometry is a branch of mathematics having to do with fractals. Fractals are geometric figures, just like rectangles, circles and squares, but fractals have special properties that those figures do not have. In geometry two figures are similar if their corresponding angles are congruent in measure. Fractals are self-similar meaning that at every level the fractal image repeats itself. An example of self-similarity would be a triangle made up of triangles that are the same shape or are similar to the whole. Another important property of fractals is fractional dimensions. While in Euclidean geometry figures are either zero dimensional points, one dimensional lines, two dimensional planes, or three dimensional solids, in fractal geometry figures can have dimensions falling between these whole numbers, that is being made up of fractions. For example a fractal curve would have a dimension between one and two depending on how much space it takes up as it twists and curves. The more a flat fractal fills a plane the closer it is to being two-dimensional. As few things have basic shapes, fractal geometry provides for the complexities of these shapes and allows the study of them better then Euclidean geometry which is only successful in accommodating the needs of regular shapes.
Fractals are formed by iterative formation, meaning one would take a simple figure and operate on it in order to make it more complex, then take the resulting figure and repeat the same operation on it, making it even further complex. Algebraically fractals are the result of repetitions of nonlinear-equations. Using the dependent variable for the next independent variable a set of points is produced. When these points are graphed a complex image appears.
One does not have to try very hard in order t...

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