The focus of this paper is a presentation of patterns that occur in the world in which we live and how they are explained in mathematics. The major pattern is that of the Fibonacci sequence, which was first discovered by Leonardo Pisano. A brief history of Leonardo (Fibonacci) will precede topics such as the equiangular spiral, naturally occurring patterns, the golden proportion and the golden ratio. Next is a short introduction to Blaise Pascal and how the Fibonacci sequence fits into his famous Pascal’s Triangle. Finally, fractals will be discussed along with background knowledge of Benoit Mandelbrot, the newest mathematician of his time.