Simple space-filling curve Here are six iterations of Hilbert space-filling curve.

Isn't there a simpler space-filling curve?
For example $16$ iterations of this curve:


Isn't it also a space-filling curve?

*

*If it is not then why?

*If it is then why they (mathematicians) did not use the simplest possible curve? Or what are advantages of Hilbert curve over mine?



The images you provided don't lead to the construction of a space-filling curve. This is due to the fact that if you take $\{f_n\}$ to be the sequence of functions defining the iterations that you have provided, normally we'd call $f:= \lim_{n\rightarrow \infty} f_n$ our resulting space-filling curve. However, in this case this limit doesn't exist (so $f$ isn't well-defined).
