What is a Fractal?

Today, I am going to talk about what can be called fractal. 

At first, I am going to talk about Fractal objects. 

The word fractal comes from the Latin word fractus, which means broken or fractured. A fractal is an object whose structure is repeated at different scales. That is, however much we approach or move away from the object, we will always observe the same structure. In fact, we are unable to affirm at what distance we are from the object, since we will always see it in the same way.

But, specially I am going to talk about fractal music. What is this? 

To make a clearer explanation, I am going to show you an example: 

John Cage, who was a composer, instrumentalist, philosopher, music theorist, poet, artist… He shows    the fractal structure with the battery cycles. Start with sixteen series of measures divided into five sentences of different length:

The first sentence has been associated with length four, we can repeat this structure four times:

At the same time, the second sentence has length three, so we will repeat the previous figure three times, then, the resultant will repeat two, given the length of the third, etc.

The result of the composition would be:

We can find this type of composition in authors as Sebastian Bach. 

I am going to talk about this, The German composes his musical pieces thinking about Fuga and Canon, which are musical elements that use the repetition of melodies in different scale or speed with or without counterpoint, but that are not exactly the same melody. The use of the canon and the escape is similar to the fractal nature but this term was not known in 1685 until 1975 when it was coined by the mathematician Benoît Mandelbrot.

Finally, I am going to give you a video, in which, you can listen this type of composition.