WORLD’S LARGEST FRACTAL MEGAMENGER is an international distributed fractal building event taking place in locations all around the globe. This is one of our main build sites, where we’ll be building a fractal called a Menger Sponge. This will join with other Menger Sponges around the world to form one giant, planet-spanning fractal!

Where’s the Mathematics?

You might be wondering where mathematics comes into this - but fractals are objects studied carefully by mathematicians. Modern science research involves all sorts of fractals.

Fractals can be generated using Sierpinski Triangle Dragon Curve iterative processes - the same process is repeated over and over again but on finer and finer scales. They naturally appear within dynamical systems theory, a hugely important area of maths which studies what future states follow from current states according to given evolution rules.

Researchers at Queen Mary University of London use fractals to study the movement of bodies in complicated systems. These concepts have applications to everything from the chaotic motion of molecules in fluids to the movement of foraging animals. Koch Snowflake Mandelbrot Set Fractals and fractal processes are also used by computer game What’s a Fractal? programmers to generate complex and detailed objects such as trees, without having to specify the position A fractal is a shape which contains There are many different types of of every leaf. Understanding fractals smaller copies of itself. It’s ‘self-similar’. fractal - like those shown here. Others, can also help us understand processes No matter how far you zoom in on a like the Menger Sponge we’re building, from nature. fractal, you will see the same pattern are 3-dimensional and can be built over and over. as a model.

www.megamenger.com @megamenger What is a Menger Sponge?

A Menger Sponge If the process is a cube-shaped is repeated fractal made to infinity, you from twenty obtain a true smaller cubes. fractal.

Sadly, you This forms a cannot have cube with three infinite detail in holes through it. physical reality.

Twenty of those But we have Menger cubes printed the can be joined to Menger pattern make a bigger down to the Menger Sponge, pixel level. and so on. Menger Facts!

A Menger Sponge can be made by removing each central section all the way down. At each step the volume is reduced by 25.925%. This means that when you’ve removed infinitely many pieces, the remaining volume must be zero!

However, the surface area is increased each time you remove a section. This means that a true Menger Sponge has no volume but infinite surface area! If you wanted to paint it, you’d never have enough paint to get into all the fiddly corners.

Image credit: User Geometrian at FractalForums.com The Sierpinski Carpet is a 2D If you cut a slice through a Menger Sponge at Six-pointed star of a version of a Menger Sponge just the right angle, you get a beautiful pattern sliced Menger Sponge of six-pointed stars!

www.megamenger.com @megamenger HOW TO BUILD A MENGER SPONGE

Make Square Units Join the Square Units into a Cube

If you place two rectangular cards across You can build the cards into a cube, always leaving the tabs outside, and each other at right angles, the area where always placing a tabbed end of a rectangle against a non-tabbed side. they overlap in the middle is square. If you then fold the sides in you will get a square Six square units joined together using the flaps become a Menger Sponge! with tabs!

1 1 2

3 4 2

5 6

3

One cube unit complete!

www.megamenger.com @megamenger Level 3 Menger Sponges

Each Level 3 sponge We’re building the internal Once we’ve built the Overall we need around measures around structure from business internal structure, we 1.3 million cards in all the 1.5m/4.5ft tall, and weighs cards. If we need six cover the outside layer worldwide locations. around 91kg/200lb. cards to make one cube, with printed cards. how many business cards do we need to make the Level 3 sponge?

Instead of making our Menger Sponge by cutting holes in an existing cube, we’re starting with small cubes and building MEGAMENGER them together. We’ve printed the cards with a picture of smaller and smaller cubes, so it looks like our cubes aren’t Level 3 Menger Sponges the smallest unit. Around the World You should be able to see the builders constructing small cubes - these will make up our sponge. Each cube is joined together to form a frame of 20 cubes, called a Level 1 These Level 3 Menger Sponges are being built in locations Menger sponge. Then, 20 of these are joined to create a all around the world - some of the main build sites are listed Level 2 sponge consisting of 400 cubes. Then, we take 20 below. When we’re all finished, we’ll have 20 Level 3 sponges, Level 2 sponges and join them together to make a Level 3 which will make one giant distributed Level 4 Menger Sponge Menger Sponge. - bigger than anyone’s built before!

London, UK Suzhou, China Level 4 Manchester, UK Waterloo, Canada Level 1 Level 2 Level 3 Auckland, New Zealand 20 Cubes 400 Cubes 8000 Cubes 160000 New York, USA Cubes San Francisco, USA Tampere, Finland

www.megamenger.com @megamenger