Why do these complex patterns emerge from a simple iteration?

Question

I was playing around with some simple turtle code a few months ago and found a very neat and complex pattern emerging from a simple code. I also noticed that changing the $x$ to $x2^n$ where $n$ is any whole number also made some neat patterns, as well as to $x^3n$, yet not to $x^2n$. Is there any reason for these emerging patterns?