The Amazing Fractals- And My Weird Connection With Them

Art of a fractal

When I was younger, I used to have this one nightmare where the scenes of the dream suddenly used to start zooming in, and it would get stuck in a loop. The loop used to seem never-ending. Something with an infinite perimeter in a limited area. Dear nerdy readers, does something click? Yes, fractals! Fractals are a mathematical concept, but I have stories to tell from my life that are not even remotely related to mathematics but are somehow connected to fractals.

You know about paradoxes? we call an seemingly absurd concept a paradox. Similarly, in mathematics, we call a conclusion so unexpected that it is difficult to accept even though every step in the reasoning is valid a paradox. Fractals are a paradox -insightful as the exponential constant, yet as simple as the number- one.

My childhood nightmares stopped at some point, and I completely forgot about them. Fast forward a decade- on one late night I was scrolling through my phone. Ironically, I came across this video named "Top 10 Things That Keep Me Awake at Night". In the video on number 5, I learned about fractals. All those nightmare memories came back, and turned out there was a compartment in my brain that I didn't remember at all till that night. This time the feeling about fractals wasn't as horrifying as before, it was different and somewhat a happy feeling. 

Fractals have a characteristic that is named self-similarity. This means as we look closer and closer into a fractal, we can see the replica of the whole thing. Fractals are also recursive, regardless of scale. Fractals are in our nature- branches of trees, animal circulatory systems, snowflakes, lightning and electricity, plants and leaves, geographic terrain and river systems, clouds, crystals, etc. 

During this fractal-obsessed time of my life, I met this friend of a friend of mine. As I got to know her more, I came to know that she loves two things- 1. Skyscrapers and 2. Snowflakes. The word "snowflakes" made me smile so wide. I lectured her about fractals for a long time. This is how I bonded over a geometrical pattern with one of the closest friends I have had to this date. 

Macro image of a snowflake 

There is a famous fractal pattern called the Koch snowflake. It is a fractal because it has the patter
n of dividing a side into 3 equal segments, drawing an equilateral triangle in the center segment. This way when you “zoom in” to each side it has the same pattern. However, the Koch snowflake isn’t a real snowflake. In a real snowflake, each of the branches contains some self- similarity but the pattern doesn’t continue on forever. So, it isn’t a fractal but it has fractal geometry in it.

I won't bore you here with all the facts and stuff. I still don't know why I used to have those particular weird nightmares as a child. There is a book in my TBR list for years named The Fractal Brain Theory written by Wai Tsang that I'm looking forward to read. Also long ago I read this book named Turtles All The Way Down by John Green where the main character girl was a clinically anxious patient and used to kept getting thought spirals and get stuck there. These scattered things make me think about how fractal is not just a mathematical paradox; it's around us, it's within us.