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Fractals 1 Introduce a simple idea of a fractal – something split up into infinitely small sections in a recursive way. Eg start with an equilateral triangle. The recursion is: take every straight line, divide it into 3 equal parts, construct a new equilateral triangle based just on the central section, erase the original central section. It goes something like this: It is worth noting that the perimeter of this shape becomes infinitely large although the shape itself is ‘contained’ – you could say it is infinitely wiggly! Students may like to try their own designs. Fractals were first studied by geographers trying to determine how long the coast of Great Britain was – as they used more and more detailed maps the coastline got longer and longer! Lots of interesting and curious results have been found, Eg (1): in each of these shapes, the length of the staircase diagonal is 2. As you keep going, the line gets closer and closer to the diagonal of the square. Therefore the diagonal of the square has length 2?? Eg (2) Again start with an equilateral triangle, this time divide it into 4 equilateral triangles and shade out the central one. Repeat….. Compare the result with Pascal’s Triangle, where all even numbers are shaded out…….. (continues down infinitely…)