Fractal Geometry and its Correlation to the Efficiency of Biological Structures

Fractal geometry is a branch of mathematics that deals with, on a basic level, repeating geometric patterns that maintain the same level of complexity for any scale used to observe them. By observing the many facets of fractal geometry, including fractal dimension and points within fractal sets, we can draw comparisons to real-world phenomena. Fractal geometry appears in nature and biological systems where efficiency is needed, such as the surface area of the brain or lungs, or the branching patterns of leaves on a tree. This report examines the fractal geometry that exists within these biological systems, and how it relates to their overall output and efficiency. We will be gathering our information from print and online sources, from both mathematical and biological perspectives. From this project, we hope to gain a better understanding of the many ways mathematics permeates our universe, and how these correlations help to explain the seemingly infinite complexity of life