The beauty of chaos…

Humans tend to associate beauty with being well-ordered. If something is ordered, it typically follows a set of rules, patterns, or characteristics recognized by most people. But why the adjective ‘well’? ‘Well’ implies that lazy human minds can recognize it quickly, and once they do, they label it as “well” + “ordered”.

Numbers, art, drawings, nature — wherever you find patterns, sometimes it’s hard to figure out the exact logic. Other times, the logic is obvious, and the same thing keeps repeating.

1, 2, 3, 4, 5        

They’re just numbers, simple positive integers. Look at the beauty — you know what comes next, and the logic is clear.

2, 4, 6, 8, 10        

Multiples of 2. Not hard to spot the pattern, and the next number is obvious.

1, 2, 2, 1, 1, 2, 1, 2, 2, 1        

At first glance, you think, “Hmmm?” Then, “Ahhh…” You eventually spot a pattern — it’s the Kolakoski sequence.

2, 1, 3, 4, 7, 11, 18, 29, 47, 76        

Wow, great! Did you recognize the pattern? Personally, I was like, “WTF?” The pattern is L(n) = L(n ? 1) + L(n ? 2) for n ≥ 2, with L(0) = 2 and L(1) = 1 (Lucas numbers).

2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443        

Okay never mind we call it “Sylvester’s sequence” and the pattern is a(n + 1) = a(n)?a(n ? 1)? ? ?a(0) + 1 = a(n)2 ? a(n) + 1 for n ≥ 1, with a(0) = 2.

Lemme ask you a question, do you find that Sylvester’s sequence beautiful? Is it easy to see the logic behind them? Most of you might say no.

Okay, forget that. Look at the graph below:

Isn’t it beautiful? It’s orderly (since humans tend to associate order with beauty). And can you believe this graph represents Sylvester’s sequence? Yes, it does. If you were trying to grasp the logic just from the numbers, you might never figure it out. It seems like total chaos.

Now, let me show you something else:

How chaotic is this? It’s like a disordered thread. It represents part of the chaos geometric theorem. And believe it or not, when you zoom out and look at the chaos theorem’s graph:

It gives us Lorenz’s strange attractor plot, which illustrates the butterfly effect. In simple terms, it’s beautiful — like a butterfly. But all the lines inside are completely chaotic. The thing is, it’s not truly chaotic. There’s a deep, underlying logic, but our brains aren’t equipped to detect it. Unsure? Take a look:

Initially, the double-rod traces a predictable path that you can reverse. But give it 7 seconds, and it becomes harder to follow. Soon, it seems chaotic. Now think: is it real chaos, or are we just too lazy to understand the pattern? You may realize that every chaos in life has a hidden logic, which we, as external observers, find hard to decode.

I would say it’s okay not to decode everything or find the exact reasons behind the chaos. You can understand it to some extent, but not forever. Let the chaos be. Zoom out. Your eyes will eventually detect the butterfly effect, and in time, the chaos will complete its pattern. The more chaos, the more beauty in the butterfly effect. Every chaos has its unique beauty, though not everyone can see it. But if you have the patience and perspective, you’ll definitely find beauty in the chaos.

Life is chaos too, isn’t it? Like the double-rod pendulum (Fig. 4) — with ups and downs like a rollercoaster. These highs and lows make life seem chaotic. I say, let it flow and let the chaos unfold. You’ll eventually see its beauty.

The beauty of chaos…

Don’t try to find the start or end of chaos — just look at it and see how beautiful it is. You’ll definitely fall in love with it.