Transcript MEGAMENGER
MEGAMENGER World’s Largest Fractal MEGAMENGER is an international distributed fractal building event taking place in locations all around the globe. Supported by Resources by 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! Supported by Resources by MEGAMENGER What’s a Fractal? 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. Supported by Resources by MEGAMENGER Examples of Fractals: Sierpinski Triangle Resources by Supported by Images from Wikimedia Commons. MEGAMENGER 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. Supported by Resources by MEGAMENGER Examples of Fractals: Mandelbrot Set Resources by Supported by Images from Wikimedia Commons. 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. Supported by Resources by MEGAMENGER Examples of Fractals: Dragon Curve Resources by Supported by Images from Wikimedia Commons. 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. Supported by Resources by MEGAMENGER Examples of Fractals: Koch Snowflake Resources by Supported by Images from Wikimedia Commons. MEGAMENGER What is a Menger Sponge? A Menger Sponge is a cube-shaped fractal made from twenty smaller cubes. Supported by Resources by MEGAMENGER 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. Supported by Resources by MEGAMENGER 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. Supported by Resources by MEGAMENGER 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! Supported by Resources by MEGAMENGER Menger Facts 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. Supported by Resources by MEGAMENGER Menger Facts If you cut a slice through a Menger Sponge at just the right angle, you get a beautiful pattern of six-pointed stars! Supported by Image by user Geometrian at FractalForums.com Resources by MEGAMENGER Menger Facts Each Level 3 sponge measures around 1.5m/4.5ft tall, and weighs around 91kg/200lb. Supported by Resources by 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. Supported by Resources by MEGAMENGER 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? Supported by Resources by MEGAMENGER Menger Facts Level 1 20 cubes Supported by Level 2 400 cubes Level 3 8,000 cubes Level 4 MEGAMENGER 160,000 cubes Resources by MEGAMENGER Menger Facts 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. Supported by Resources by MEGAMENGER Menger Facts Our Level 4 MEGAMENGER sponge will consist of Level 3, 2 and 1 cubes built in locations all around the world this week. Supported by Resources by MEGAMENGER Menger Facts MEGAMENGER locations include: Manchester, UK New York, USA Cambridge, UK San Francisco, USA Waterloo, Canada Auckland, New Zealand Supported by Suzhou, China Tampere, Finland Resources by