Application of Fractals

APPLICATION OF FRACTALS TO MATERIALS SCIENCE Introduction The term “Fractals” refers to the mathematical concept of how vastly different objects can be described using the same mathematical relationships. For example, the coastline of a continent viewed from space will have readily visible distinct attributes such as bays, peninsulas, and relatively straight sections. If we now observe a coastline from an airliner flying at 35,000 feet, we will notice far more detail than an astronaut on the International Space Station. But, in general, the exact same attributes will be seen: bays, peninsulas, and straight sections. Now imagine flying over a beach at 1000 feet. The generic features will still look exactly the same even though the size or scale of these attributes are far smaller than the two previous examples. If we then wanted to represent the coastline using a mathematical curve fitting technique such as spline functions, we could apply exactly the same method for all three scenarios. This demonstrates the concept of fractals. There are fundamental physical phenomenon resulting from both the processing and application of materials that result in similar scaling behavior as described in the previous example. We will discuss four different materialsrelated phenomenon and further point out how they can be examined using fractals. Specifically we will discuss the use of fractals in examining thin film deposition processes, fracture mechanics, optical properties of materials, and electrochemical deposition processes. Our intent is to demonstrate the types of materials/processes that can benefit from fractal analysis and as a result, provoke further thought on other physical processes that could benefit from similar approaches.