Aristotle once said “In all things of nature there is something of the marvellous.” Living in a world brimming with technology, it is easy to forget the beauty and wonder of the world around us -unless it is accompanied by an Instagram filter, of course.
Despite the glorious diversity of the world we live in, we commonly see naturally occurring patterns. While early Greek philosophers were the first to investigate these shapes, the science behind these patterns still draws curiosity now in the 21st century. At the upcoming Manchester Science Festival an attempt to build the world’s largest fractal (the mathematical model behind some these patterns in nature) is taking place in the hope of enthusing and exciting the public about the wonders of maths.
What is a fractal?
How do trees grow? A single root divides into two branches which in turn each divide into two and so on and so forth. In the end the pattern made by a single twig is the same as the complex branches of a giant oak. So no matter at which scale you look at it, the patterns made by the branches are similar, and this self-similarity is mathematically termed a fractal.
These self-similar patterns are not only seen in trees, but also rivers and clouds, the cardiovascular system, broccoli – the list is endless. Since the 17th century the mathematics concept underlying these shapes has been investigated, with the mathematician Benoit Mandelbrot coining the term fractal in 1975. He defined a fractal as “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole”.
So – in a nutshell – fractals are infinite patterns made by repeating the same process over and over again to form structures which appear the same no matter which scale you look at them. They also happen to be an important and commonly occurring part of the world we live in!
The MegaMenger Project
The 8th annual Manchester Science Festival is set to run from 23rd October to 2nd
November. Showcasing a wide range of playful and imaginative projects to enthuse the public, one of this year’s star attraction events is the building of the MegaMenger. Scatted across twenty cities worldwide, a series of Menger Sponges will be displayed which will hopefully form the world’s largest 3D fractal – the MegaMenger!
How are Menger Sponges made?
Menger Sponges are fractal cubes named after their inventor Karl Menger. To form a Menger Sponge, you begin with a cube and divide it into 27 smaller cubes. Then you remove the smaller cube in the middle of each face and in the very centre of the cube. This is a level-1 Menger Sponge. By simply repeating the process of dividing each of these small cubes and removing central cubes, level-2, level-3 and so on cubes are formed.
In the MegaMenger project, each city will build a level-3 cube. These 3D fractals will be made of 20 cubes, each made of 20 smaller cubes that -you guessed it- are made of another 20 smaller cubes. The smallest cubes are simply made of 6 business cards. Using over a million business cards, the twenty level-3 Menger Sponges will form a distributed level-4 sponge – the largest ever made out of business cards.
How to get involved?
For a week starting from 20th October these fractals will begin to take shape across the world. Here at Manchester Science Festival on the Saturday and Sunday, 24th and 25th October, drop-in sessions are taking place at the Museum of Science & Industry so you can pop by to witness the build in action and find out more about the magic of fractals!
By visiting www.megamenger.com you can get more information about the enormous world record attempt and print off Menger cards so you can make your own 3D fractal.
• Manchester Science Festival. http://www.manchestersciencefestival.com/
• More about Fractals. http://fractalfoundation.org/resources/what-are-fractals/
October these fractals will begin to take shape across the world. Here and 25th October, drop-in sessions
Post by: Claire Wilson