I thought I’d start with explaining what the header image to my blog actually is. It is a zoomed in image of a type of fractal called a Menger Sponge, generated by an excellent program called Mandelbulber and smoothed a little in Photoshop.
I shall leave an explanation of what a fractal actually is until a later post, except to say that generally they’re mathematical sets that tend to stay just as complex the closer you look at at a representation of them. Also they had a tendency to make an appearance on techno and dance music CD sleeves in the mid to late 90s. Of course this is a massive simplification of what they are, but I’m trying to keep the tone of this blog somewhere between pop-science and wading through obscure corners of the literature.
The Menger Sponge is a three dimensional version of the more commonly seen Sierpinski Carpet. As for the names, it’s easy to see that they follow the trend of <Discoverer’s Name> <Something everyone has heard of>. Looking at a Sierpinski carpet makes its name quite sensible.
It is calculated in a very simple manner. You start with a square, and divide it into 3 parts on each side, making 9 squares. You then cut out the square in the middle. The fun bit comes next. You then take all the squares that are still there, and do the same to them as you did to the original square. You can then repeat this to make smaller and small features forever, or until you get bored, whichever comes first.
A Menger Sponge takes this idea, but starts with a cube, and each side of the cube is treated in the same way as for the Sierpinski carpet, but the whole goes all the way through the cube, making lots of sub-cubes, which you do the same to. After a few hundred repetitions of this you end up with something like this:
Which you then colour in, smooth a bit and set at the top your blog with some writing on!
Land of Gregs 