MEGAMENGER
MEGAMENGER is an international distributed fractal building event taking place in locations all around the globe.
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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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MEGAMENGER
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.
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MEGAMENGER
Examples of
Fractals:
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Images from Wikimedia Commons.
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MEGAMENGER
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.
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Examples of
Fractals:
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Images from Wikimedia Commons.
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MEGAMENGER
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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MEGAMENGER
Examples of
Fractals:
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Images from Wikimedia Commons.
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MEGAMENGER
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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Examples of
Fractals:
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Images from Wikimedia Commons.
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MEGAMENGER
A Menger Sponge is a cube-shaped fractal made from twenty smaller cubes.
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MEGAMENGER
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.
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MEGAMENGER
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!
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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.
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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!
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Image by user Geometrian at
FractalForums.com
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MEGAMENGER
Each Level 3 sponge measures around
1.5m/4.5ft tall, and weighs around
91kg/200lb.
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MEGAMENGER
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 1
20 cubes
Level 2
400 cubes
Level 3
8,000 cubes
Level 4
MEGAMENGER
160,000 cubes
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MEGAMENGER
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.
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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.
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MEGAMENGER
MEGAMENGER locations include:
Manchester, UK
Cambridge, UK
Waterloo, Canada
Auckland, New Zealand
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New York, USA
San Francisco, USA
Suzhou, China
Tampere, Finland
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