This is just a Julia set that I created. I was surprised at just how symmetric it is as well as showing clearly the fractal property of self-similarity.

This is just a Julia set that I created. I was surprised at just how symmetric it is as well as showing clearly the fractal property of self-similarity.

It looks both rotational and mirror symmetric in multiple axes – but is it? Is there a deep asymmetry – ie the latest iteration is always asymmetric but at larger scales it appears symetric. Can you tell from the formula and program?

I would not be surprised if this was not truly symmetric, but for sure it looks symmetric at the scales we can see. I don’t have the tools to really investigate this. I also don’t really have the will to find out what tools I would need!

It is a nice image and I am satisfied with that.