The things that I am going discuss here are linked to one another in a strange and beautiful kind of way.
I am sure most of you know what Ferns are. A Fern is a vascular plant that belongs to the group of plants called pteridophytes. Here, we are interested in a Fern leaf. Most of us recognize Ferns through their bright green, large, quasi-symmetrical, tapering, decorated leaves.
A Firn on the other hand is a type of ice that is formed after moderate solidification of falling fresh snow. Snow falls in the form of snowflakes, which also happen to be beautifully decorated symmetrical structures.
Some of you may have already guessed the link between the two (Of course, not the similarity in the way they are spelt). If not, let me give a clue. A Fern leaf and a Firn Snowflake can be virtually created by a mathematical logical process called an Iterated Function System, which comes under Fractal geometry. To introduce a fractal in simple terms, I could say the following
“You start with a simple object, or a pattern, or a shape. You introduce a simple reiterating transformation process that performs repeatedly on the object/shape you have started with (could be done infinite number of times). The transformation could include change in scale and rotation etc. However, the set of changes remains the same each time you perform it on the previous resultant object/shape. The object you had started with grows (in a counterintuitive kind of way) and becomes various exotic realistic and not so realistic shapes/objects that we may or may not come across”.
I hope that the description makes at least some kind of sense. Fractal fern leaves and Koch snow flake (later Firn) are extensively used as good communicating examples for Fractal geometry and if you search you will find plenty of examples on the internet. My reason for writing this article is to introduce a third example that comes from Carnatic classical music.
The word ‘Furn’ might be unknown to many. Let me introduce that here. In Indian-carnatic classical music, the art of percussion involves a playing pattern that is commonly referred to as “Furn(s)”. A furn is an extremely fast paced, intricate set of percussion notes. A Furn is too fast to be spelled out in letters hence is represented by an abstract sound (Zrrr…………).
An example of a Furn could be: In AditaaLa, chaturashra nade, we play 4 maatras per akshara. This is called a Nade paaTHa. If we increase it to 8 maatras per akshara, then it becomes an Urutu. The doubling of an urutu leads to a Furn, which then contains 16 maatras per akshara. Let us for the time being, assume that a comfortable speed would be one akshara per second. Then, within a second, if we play a Furn, it should contain 16 notes. Uttering/playing 16 notes within one second is pretty fast. Normally, 8 aksharas (1 aavartha) of AditaaLa will be complete within 6 seconds, making the Furn faster than fast.
Let us assume that a pattern of 8 aksharas and 1 maatre per akshara (AditaaLa) is our basic unit (also called an Initiator). One can imagine this to be an octagon. Let the process of splitting into half (dividing by 2) be our reiterating process of transformation (also called a Generator). One can imagine this to be a staircase with two steps replacing the sides of our octagon. The single akshara (which had 1 maatra) is referred to as our ‘base element’ (side of the octagon), which will undergo the process of transformation.
If the process of splitting is done 4 times, that is to say, 1 becomes 2, 2 becomes 4, 4 becomes 8, and 8 becomes 16, we arrive at a Furn. Theoretically speaking, we could go on forever and create Furns of a Furn, Furns of Furns of a Furn and so on. It is human limitation that stops us at 16 maatras per akshara. Although my knowledge of Fractal geometry is very limited, I think, the creation of a Furn in classical percussion could fit into an Iterated Function System and can be a rudimentary example of a Fractal. It would be nice to see what an AditaaLa would look like, if we could convert that into a Fractal image.
Ferns are living organisms. Snowflakes that become firn ice are physical objects. A furn in classical percussion is a sound wave created by a physical object. I don’t know why they were named as they are named. They sound similar, don’t they?