World’s Largest Fractal

MEGAMENGER

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MEGAMENGER is an international distributed fractal building event

taking place in locations all around the globe.

World’s Largest Fractal

MEGAMENGER


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!

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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?

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Examples ofFractals:

SierpinskiTriangle

Images from Wikimedia Commons.

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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?

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MandelbrotSet


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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.

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Examples ofFractals: Dragon

Curve


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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.

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KochSnowflake


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A Menger Sponge is a cube-shaped

fractal made from twenty

smaller cubes.

What is a MengerSponge?

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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.

What is a MengerSponge?

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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.

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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

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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

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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

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Each Level 3 sponge measures around 1.5m/4.5ft tall, and weighs around

91kg/200lb.

Menger Facts

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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.

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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?

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Level 2

400 cubes

Menger Facts

Level 1

20 cubes

Level 4MEGAMENGER

160,000 cubes

Level 3

8,000 cubes

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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

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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

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MEGAMENGER locations include:

Menger Facts

Manchester, UK

Cambridge, UK

Waterloo, Canada

Auckland, New Zealand

New York, USA

San Francisco, USA

Suzhou, China

Tampere, Finland

World’s Largest Fractal

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