Nature is filled with beauty – and mathematics!
Let’s start with a little riddle. What do lightning, trees and snowflakes have in common?
They’re all fractals!
Nature is filled with fractals – they’re everywhere. A fractal can be thought of as a never-ending complex pattern that repeats itself at different scales. Fractals, found all around us, are a key mathematical theory. We all have an innate ability to recognise and detect patterns – for some it even soothes us.
The term ‘fractal geometry’ was coined by Benoit Mandelbrot (the father of fractals). Mandelbrot was fascinated by 19th century mathematicians and was inspired by their work. His inspiration paid off as he was able to bring these theories into the 21st century and engrave his name in maths history. He is even a popular TED speaker!
Fractals can be found in maths and nature. Mathematical fractals, such as the Mandlebrot Set – named after Benoit Mandlebrot, are formed by calculating a simple equation thousands of times. These fractals are infinitely complex, and simply beautiful!
In nature we can see fractals everywhere at every scale. During a storm the last thing we might be thinking about is maths and patterns, but they are there. Lightning creates chaotic and jagged lines as pent up electrical energy is discharged from electrically charged clouds down to Earth. Fractals can be observed by looking carefully at one part of a lightning bolt, and seeing its appearance is the same as the lightning strike as a whole.
Another example of a fractal in nature can be seen in trees. For example, let’s look at a big old oak tree. Imagine looking at a whole oak tree, then looking at one of its branches and you would see it splits in a similar way to the previous branch and so on. Each branch of the tree is a repeated shape of itself as a smaller tree.
Fractals can be both difficult to define and understand. However, despite their complexity, they can be created or defined by the simplest shapes. An oak tree’s branches can be simply described as a repetition of the letter ‘Y’.
One of the most famous and impressive fractals in nature is the snowflake. Snowflakes were one of the earliest fractals to be identified and described. Everyone knows that no two snowflakes are the same, but it should be noted that every snowflake does have the same pattern, always reproduced again and again. If you had a microscope and zoomed in on a snowflake crystal before it melted, you would see that the fractal pattern is a near-identical copy of the whole snowflake – it’s just been reduced in size and scale.
Mandelbrot is recognised for helping bridge the gap between nature, art and mathematics. He has helped to show how these disciplines have a strong interconnected relationship. The exploration of fractals in nature has also helped many other fields including research into climate change and even the trajectory of meteorites. It begs the question – what can’t maths do?
Fractals are an incredibly interesting, yet complex illustration of how we can see maths in nature during our everyday life.
So, look around and enjoy maths in all of its beauty.
ORIGO Education is focused on making mathematics meaningful and enjoyable. ORIGO Education’s Think Tanks provide ready-to-use opportunities for Year 1–6 students to apply learning, foster thinking skills, and increase procedural fluency.