world’s largest fractal
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MEGA MENGER is an international distributed fractal building event taking place in locations all around the globe. World’s Largest Fractal. - PowerPoint PPT PresentationTRANSCRIPT
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
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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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Examples ofFractals:
MandelbrotSet
Images from Wikimedia Commons.
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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
Images from Wikimedia Commons.
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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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Examples ofFractals:
KochSnowflake
Images from Wikimedia Commons.
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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