Have you ever contemplated the fact that simple rules give rise to complex objects? Consider that nature is complex, irregular, and seemingly random – so what if it could be described by simple mathematical rules? Until the early 20^{th} century, describing a system using a set of mathematical rules was a successful practice in the realm of physics, but when the same concept was applied to biology and nature, the systems seemed to be too complex to describe with equations. Recognizing this shortcoming, a man called Alan Turing aimed to reconcile the disparity.

Shortly before his untimely death, Turing published a paper containing equations that could describe how identical cells seemingly become different – a process known as morphogenesis.

Around this same time, Russian-born Vladimir Belousov was unwittingly contributing towards a similar goal. Belousov sought to mimic glucose absorption in the body. Part of the experiment involved mixing two solutions together; upon doing so, a very strange and unheard of thing happened: the mixture turned yellow, then to clear and back to yellow again. The mixture was oscillating between two colors, seemingly mixing and unmixing over and over again. Ironically, without any knowledge of Turing’s work, Belousov’s research served to confirm the predictions of Turing’s equations.

A few decades later, meteorologist Edward Lorenz began researching ways to predict the weather using the same simple equations that describe air currents. In the process, he stumbled upon the fact that small changes in the initial starting point of air currents led to wildly different outcomes. This became known as the butterfly effect, also known as “the hallmark of chaotic systems.” Lorenz’s findings begged the question, “Does the flap of a butterfly’s wings in Brazil start a tornado in Texas?”

Together, the contributions of Turing, Belousov, Lorenz, and others led to the development of the notion of chaos. Chaos tells us that even if a system can be completely described by simple equations, this does not mean that the system will not behave unpredictably and with some degree of randomness. Systems behave chaotically when equations used to describe them have a property called **feedback** – *which is precisely what can be seen in the following video*. Feedback occurs when the input for each step in the process is provided by the output of the step preceding it.

Polish national Benoit Mandelbrot developed the mathematical language for feedback; he called it fractals. Check out the next video of what is known as “the Mandelbrot set”. It demonstrates how using the math equation pictured below can generate a repetitive image on an infinite scale.

In the equation, a number is plugged into ‘z’ – the outcome is that number times itself plus a constant, which is then fed back into the other side of the equation over and over again. This is the way we see complex patterns repeated again and again in nature.

In this way, evolution can be viewed as a chaotic system. When organisms reproduce, nature provides feedback on the variations that come through in the offspring. Evolution then selects for or against these tiny changes, ultimately amplifying those retained traits over time, eventually yielding very complex life forms from simple beginnings!

Contrary to the way it sounds, there is order in chaos. Scientists use mathematic equations as tools by which to organize and understand this order, and in this way, they can develop concepts that were always present in nature that mankind had yet to conceive of.