"Why, oh why, didn't I take the blue pill?"
- Cypher, Matrix (1999)

Fractal, oh boy, this is something mind-bogglingly arresting (as I believe nearly completely all of math is!) Just the term, for a start, is funny, coined in 1975 from the Latin fractus ...
Fractal is a geometric object that can look extremely self-similar at different levels of magnification. True fractals possess infinite detail, and so on ...

Mind-bogglingly, I said it.

The concept of fractals has been applied in science, technology and computer-generated art. Where exactly, would you inquire:
- The fractal antenna for communication devices as GSM phone for instance has been proven to be a very effective antenna for miniaturization techniques and is likely to have a very promising future,
- or may I point you to a paper by Benoît Mandelbrot, the pioneer of fractals, titled How Long Is the Coast of Britain?,
- or do look at this picture of a park, arranged and tessellated in a neat fractal manner.


It's to note that no object or phenomena in nature can be a true fractal, since a true fractal possesses infinite granularity. And since our tehcnology and most of our endeavours can be regarded as mimicking the nature, we can conclude that human products as well as those of nature can at best display fractal-like properties across a limited range of scale.
Such approximate fractals are easily found in nature: in clouds, snowflakes, mountains, river networks, and systems of blood vessels.
Let us think of broccoli the cabbage for example. I think there is more to broccoli than bunch of vitamin C, soluble fibre and anticancer compounds. For me it is the very fine natural fractals of the fleshy heads, pinched on a fork, that I marvel at first for quite some time before devouring it. And devouring such natural beauty is fun, and yummy.

If I give a though now about my life thus far, I readily recognize a lot of fractality in my past: of studying, initiating and developing the personal relationships and so on.
Feeling the same way all over again? - Does that feeling ever get over you? It gets over me. But I don't see it anymore as being stuck somewhere. No I don't, I see it more as the zooming in-and-out effect. Yes, that's what it is. Life is a fractal. Life has no true ultimate destination. It is a road, a winding road that goes down from the door where it began. And, as Bilbo, you may follow, if you can, or you may not. I chose life, I chose to follow. I choose zooming-in over zooming-out any time!
Oh, by the way, "Feelin' the Same Way All Over Again" is one of my favourite songs (actually, together with "Take My Hand" they top anything for me). Please, do listen it here: to Jones' here and to Dido's here.

Now let me show you an example of a fractal: The Koch Snowlake. The picture below shows the first few iterations of the flake, generated by adding smaller and smaller triangles. To get a true fractal, infinite number of iterations would be necessary.



With each new iteration n the perimeter l_n - i.e. the length of the flake's boundary - grows. It grows and it grows to infinity:



At the same time the area



however remains finite:



Here the area of the intial triangle is denoted by P₀.
This game of finite versus infinite over different dimensions is my all time favorite property of fractals.

And for you and you only, with sugar on top,
the Koch snowflake in rainbow colors:

RELEASE NOTES:

Left it in the main hall of the faculty at the very FRI BookCrossing Zone (click here and scroll down for more information).