Abstract: Fractals are many examples of the beautiful objects in mathematics. From the Mandelbrot set, to the Koch Snowflake, they give rise to objects that have very rich self-similar structure, forcing us to change our understanding of dimension.  In this talk we will discuss some constructions and computations for many classical fractals that arise from Iterated Function Systems.  We investigate versions of the Cantor set and make connections to generalized Fibonacci numbers, which are used to compute the dimension of the fractal.