By Gemma Penson - Computer Science Student @ Trinity Hall, Cambridge

At school, students are often taught about predictable phenomena such as chemical reactions, eclipses, and gravity. When modelling scenarios in school, a system of equations, each involving a set of variables, can often be used to gain insight into that scenario. For example, equations involving the variables acceleration, velocity, and distance can be used to predict the time it would take for a ball to hit the ground. If any of the variables were to change, one could predict reasonably how it could affect the outcome.

Predictability is seldom this simple in reality, with chaos theory being the exploration of phenomena that are near to impossible to predict or control such as the stock market, the weather, human brain states and even how milk swirls in your morning cup of tea. Chaos is the science of surprises, of the nonlinear and the unpredictable. It explores the transitions between order and disorder, which often occur in surprising ways.

Chaotic phenomena are facts or situations where there is no discernible regularity or order. They are often described using fractal mathematics, where a factual is an infinitely complex never-ending pattern. They are created by iterating a simple process in an ongoing feedback loop and are self-similar, which means that their properties are preserved with respect to scaling in space or time. One class of fractals is the Mandelbrot set - a set of non-real (complex) numbers that creates some of the most famous images in mathematics.

Fractals are the picture of chaos! They exist between our familiar dimensions but are perceived by everyone on a daily basis. This is because the laws of nature repeat fractals on different scales. For example, trees are natural fractals as each tree branch, from the trunk to the tips, is a copy of the one that came be