what does "⨀" mean when used on complex numbers?

Question

So I was watching codeparade on youtube, when I saw that their "feather fractal" they created used the $\odot$ symbol in the context: $z\odot z$. When I searched it up, it said it is the "Hadamard product". The issue is that the Hadamard product is defined on matrices and vectors, not complex numbers.
I found out that you can represent complex numbers as matrices, so I thought that's how it worked, but I realized it's probably not so because there's no way to convert a matrix back into a complex number. I tried searching for a long time, but i didn't find anything that helps. thank you for the help! This is the video link and the feather fractal is shown at 5:18.