I said in my previous post that I would talk more in-depth about my option choices this semester and the first of these is Fractals and Chaos. If you haven’t come across the word before, as I hadn’t before I started the module, fractals are essentially an infinitely repeating pattern. They are visible throughout nature from the appearance of a romanesco broccoli to the structure of snowflakes, ferns and crystals. The main feature that makes something a fractal is self-similarity: if you zoom in on one part of a fractal, the same structure is visible, just smaller and smaller.
This mountain range may looks realistic but it is a fractal landscape. It has been created by a computer using the concepts of fractals.
In the course we looked at the mathematics involved in producing fractals. Iteration is used to create fractals, which is the process of repeatedly reevaluating a function over and over with slight differences each time. Julia sets are an example of a fractal which usually involves the iteration of a complex polynomial. The module was made up of a mixture of lectures and workshops. In the lectures we learnt the theory and in the workshops we put the theory into practice using R and C programming to create fractals.
We ran and edited R scripts to create julia sets similar to this in our workshops.
The chaos part of Fractals and Chaos refers to iterations which, with small differences in initial conditions lead to very different results, ending in chaos. Which is what you would expect chaos to look like.
Bifurcation is an example of chaos and the butterfly effect in action. What starts out as the line in the graph splitting into two quickly turns into chaos.
This was definitely a module to choose for people interested in pure maths and computing or those looking to improve their R programming skills. I have a report to write on the things learnt in workshops and lectures due in January, but I’ve already taken out some books from the library and I think it might be quite interesting to write about.
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Nice blog Kira! I studied complex fractals as part of my Maths undergrad (and also wrote a blog on it too!), and would be really interested to hear more about how that is applied or studied within physics!
Thanks Jess! All the books I found on fractals and chaos were in the maths section of the library and focused on the pure maths so I’ve probably covered some of the things you studied 🙂 In the computing workshops it was mostly about understanding the code used to produce julia sets, mandelbrot sets etc. Later on we got to link bifurcation to the behaviour of an LCR circuit which is a physics application of complex analysis but I might look into more examples in physics when I write my report because I’m not sure of any others right now.