I thought I would write to you today about a concept called the Mandelbrot set because you might find it interesting.
This image belongs to a class of images called ‘fractals’. They are called fractals because when you enlarge them, you can see more detail – and when you enlarge that – you can see more detail. This is different to most shapes – which basically get more boring as you enlarge them. For example, if you enlarge the edge of a square – you will just see a straight line – and no matter how much you enlarge it – you will see just a straight line.
However, if you enlarge a part of the mandelbrot set, then you can see more and more detail which goes on for ever. So the set is infinitely detailed. Here is an example of a zoom into the set:
And if we make this bigger – we can see this:
and if we zoom into another portion of the set we see this.
Many years ago, it used to take a computer about 8 hours to calculate a view of the set. But with modern computers you can do it much quicker. The machine that I’m using to perform these calculations has 56 processors – the unit that performs the work within the machine – and so can calculate a view almost instantly.
If you’re interesting in trying it out for yourself, you can find a basic online viewer like this one:
I’ll cover the mathematics behind the set another time…
Hope you’re well anyways.