Abstract: “A fractal (fractus Latin for broken, uneven) is an object or quantity that displays self-similarity, i.e., for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size. The object need not exhibit exactly the same structure at all scales, but the same ”type” of structures must appear on all scales.”

 sources: http://mathworld.wolfram.com/Fractal.html and http://www.merriam-webster.com/dictionary/fractal

 

 

For our project we hope to illustrate what makes fractals so unique and how they are significant in computer science and mathematical concepts. We will begin by introducing the idea of scaling self-similar shapes and there associated length, area, volume, and measure to generalize the concept of non-integer based dimensionality .  After building intuition using self-similar shapes we will show how this can be generalized to non-self similar shapes as conceptualized by mathematician Benoit Mandelbrot. We will discuss the calculations of areas, landscapes, and real-life applications. To finish our project we provide an example in Maple of a fractal equation.