Fractals everywhere | Day 22

Each November Sydney erupts into gorgeous, light purple blossoms, courtesy of jacaranda trees. When this time of year comes around, whole streets and neighbourhoods start to resemble fantasy landscapes. However, even during winter the deciduous jacarandas can still be interesting. Today at lunch, struck by the intricate fractal-esque shape of its branches, I took a photo of a nearby jacaranda tree.

The general definition of a fractal goes somewhat like this:

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales.

Fractals are a mathematical concept, and the term itself was coined by mathematician Benoit Mandelbrot in 1975, using the Latin word fractus (to break). However, fractals were described my mathematicians long before that, and it’s no surprise, since they are also abundant in nature. For example, coastlines cannot have a well-defined length because they have fractal-like properties: depending on the level of detail at which you measure, more and more nooks will be discovered that increase the total length of the measurement. This is known as the coastline paradox. A snowflake is also an excellent example of a fractal.

Snowflake self-repetition | By Jasper NanceCC BY-NC-ND 2.0

And, of course, plants also exhibit countless variations on fractals — cauliflower is one, where each floret divides into smaller and smaller, yet similarly shaped florets. And so is the jacaranda — look closely at the self-repeating branch structure from the largest to the smallest of the tips, and you get a beautiful example of natural geometry. Turns out jacarandas are pretty in more ways than one.

Jacarandas at their best | By Ms ReflectionsCC BY-NC-ND 2.0

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