World’s Largest Fractal

1. MEGAMENGER is an international distributed fractal building event taking place in locations all around the globe. World’s Largest Fractal

2. 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!

3. A fractal is a shape which contains smaller copies of itself. It’s ‘self-similar’. No matter how far you zoom in on a fractal, you will see the same pattern over and over. What’s a Fractal?

4. Examples of Fractals: Sierpinski Triangle Images from Wikimedia Commons.

5. 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. Where’s the Mathematics?

6. Examples of Fractals: Mandelbrot Set Images from Wikimedia Commons.

7. Fractals can be generated using 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.

8. Examples of Fractals: Dragon Curve Images from Wikimedia Commons.

9. 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.

10. Examples of Fractals: Koch Snowflake Images from Wikimedia Commons.

11. What is a Menger Sponge? A Menger Sponge is a cube-shaped fractal made from twenty smaller cubes.

12. What is a Menger Sponge? This forms a cube with three holes through it. Twenty of those Menger cubes can be joined to make a bigger Menger Sponge, and so on.

13. If the process is repeated to infinity, you obtain a true fractal. Sadly, you cannot have infinite detail in physical reality. But we have printed the Menger pattern down to the pixel level.

14. 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! Menger Facts

15. 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. Menger Facts

16. If you cut a slice through a Menger Sponge at just the right angle, you get a beautiful pattern of six-pointed stars! Menger Facts Image by user Geometrian at FractalForums.com

17. Each Level 3 sponge measures around 1.5m/4.5ft tall, and weighs around 91kg/200lb. Menger Facts

18. Instead of making our Menger Sponge by cutting holes in an existing cube, we’re starting with small cubes and building them together. We’ve printed the cards with a picture of smaller and smaller cubes, so it looks like our cubes aren’t the smallest unit.

19. We’re building the internal structure from business cards. If we need six cards to make one cube, how many business cards do we need to make the Level 3 sponge?

20. Level 2 400 cubes Menger Facts Level 1 20 cubes Level 3 8,000 cubes Level 4 MEGAMENGER 160,000 cubes

21. Once we’ve built the internal structure, we cover the outside layer with printed cards. Overall we need around 1.3 million cards in all the worldwide locations. Menger Facts

22. Our Level 4 MEGAMENGER sponge will consist of Level 3, 2 and 1 cubes built in locations all around the world this week. Menger Facts

23. MEGAMENGER locations include: Menger Facts Manchester, UK Cambridge, UK Waterloo, Canada Auckland, New Zealand New York, USA San Francisco, USA Suzhou, China Tampere, Finland