What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) [closed]

This wasn't the first, but it's definitely awesome:

A Proof of the Pythagorean Theorem (without words)

This is a proof of the Pythagorean theorem, and it uses no words!

For me it was the Times Table of $9$.

We are usually forced to memorize the multiplication tables in school. I remember looking at the table for $9$, and seeing that the digit in ten's place increased by one, while the digit in the one's place decreased by one.

$$ \begin{array}{r|r} \times & 9 \\ \hline 1 & 9 \\ 2 & 18 \\ 3 & 27 \\ 4 & 36 \\ 5 & 45 \\ 6 & 54 \\ 7 & 63 \\ 8 & 72 \\ 9 & 81 \\ 10 & 90 \end{array} $$

After this, I realized that I could always add $10$ and subtract $1$ to get the next result. For a $7$ year old, this was the greatest discovery ever made.

And that your hands could give you the answer immediately: $7 \times 9$ = hold down your $7$th finger, leaves $6$ fingers on left of held down finger, and $3$ on right: $63$.. works all the way up to $9\times10$, beautiful.

Whether this is 'simple' enough is debatable... the method to generate the Mandelbrot set is likely to be far too complicated for the book in question, but the mathematical expression that's at its heart couldn't be much simpler.

$z_{n+1} = {z_n}^2 + c$

After implementing the Mandelbrot set I learned about the Buddhabrot, which is basically a way of rendering the stages of the Mandelbrot algorithm, and after some considerable processing time I had a render:

Buddhabrot whole

I then tweaked my input parameters to 'zoom in' on a particular area, and when I saw the result my jaw hit the floor. This is when I saw the true beauty in mathematics beyond 'nice' results. Again, it's probably too advanced for your book because of the steps involved in creating the visual, but maybe it'd make for a nice final hurrah to inspire further exploration? It still boggles my mind to see such amazing results from something so simple.

enter image description here