Some Fractals in the Botanic Gardens

Continuing the series of posts inspired by nature. This time I will be talking about my discoveries at the Royal Botanic Gardens in Edinburgh. Today, I will be talking a little bit about fractals in nature.


In mathematics, a fractal is an abstract concept that is used to describe objects or phenomena which can be found in nature. Therefore, there is no surprise that I have found some examples in the Botanic Gardens. Generally speaking, fractals commonly show a similar pattern repeated at increasingly small scales. Thinking about my previous post on symmetry, fractals are also known as expanding symmetry or evolving symmetry. If the pattern replicated is exactly the same at every scale, then we have a self-similar pattern. But this isn’t the case all the time.

The example I saw recently is represented by ferns. The Glasshouse in the Royal Botanic Gardens in Edinburgh has a special room just for ferns and I have spent a lot of time studying their shapes and patterns. Ferns have been used as examples to understand this mathematical concept for a long time. Everything starts from the fern’s features. I am not a biologist, so I will try to explain as clear as possible. The “leaf” looks like a small version of a “branch”, which is a small version of the whole plant. It looks very interesting and every time I see one it makes me think that mathematics is just the language that helps us understand nature.


Moreover, in mathematics there is something called the Barnsley Fern, a fractal named after a British mathematician. It actually looks very similar to a common species of fern known by the common name black spleenwort. This is a typical example of a self-similar pattern. Barnsley’s method of creating (computer code) this pattern has been used since then by a number of mathematicians and artists to represent other similar objects and patterns from nature.

What other examples of fractals found in nature do you know? Let me know in the comment box bellow.


Hope you enjoy this post. More nature related posts are coming soon. Let me know what you’ve been up to in the past month. Have a great day. You can find me on Facebook,  Tumblr,  Google+,  Twitter   and  Instagram. I will try to post there as often as possible.

Lots of love and don’t forget that maths is everywhere! Enjoy!

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