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Here’s all you need to know about fractals!
A mathematical art form, fractals are infinite geometric constructs that display similar patterns throughout, regardless of magnitude. The most popular example, and perhaps easiest to visualise, is the well-known (in the fractal world) Koch snowflake. This fractal curve is produced by starting with an equilateral triangle and then by following the infinite pattern of adding an equilateral triangle to each side of the shape. The beautiful snowflake design slowly appears.
As the name suggests, patterns like this are naturally occurring. Snowflakes are a clear example, but they can also be found in clouds, river networks, cauliflowers and systems of blood vessels in the human body!
The snowflake example is particularly interesting mathematically. As the diagram above demonstrates, the first iteration has 3x4 sides, the second 3x42, the third 3x43 as with each step every side of the previous shape is split into 4. After the nth iteration the shape would have 3x4n sides and therefore when the pattern is continued infinitely, the snowflake will have infinite sides and hence also infinite perimeter. Despite an infinite perimeter, the area of the snowflake remains finite, as there is a circle of some fixed perimeter that would always encompass it.
Aside from being visually appealing, it’s properties like these that make fractals so interesting. The pattern used to create a snowflake can be translated into solutions for real-world applications, such as a TV aerial to optimise the surface area with respect to volume.
A relatively new field, most of the study into musical fractals is simply to create art and news sounds. As studies develop, assuming they follow a similar trend to visual fractals, it will be interesting to see what applications and problems they solve!