Join the Mandelbrot set

Hi Alex

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:

http://math.hws.edu/eck/js/mandelbrot/MB.html

I’ll cover the mathematics behind the set another time…

Hope you’re well anyways.

Love, Dad.

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