Visualizations of ordinal numbers

Question

I find this picture of the ordinal numbers up to $\omega^\omega$ rather hard to grasp:

I wonder if the following might be a more compelling way to visualize ordinal numbers up to $\omega^\omega$:

My questions are:

1. (Where) has this way of visualization been suggested before?

2. How far can it been generalized by repeating the indicated step in a transfinite way?

The "indicated step" is: rotating the picture by 90° counter-clockwise.