The most interesting feature of this doodle is strong horizontal and verticle axes. You are thingking that is an error or typo, but I just looked it up and axes is the plural for axis.
The vertical central bar is not visually symmetrical, like the horizontal bar appears to be. I think this is because the small squares and circles in the vertical bar appear to be more of a field pattern than a linear pattern. While the diamonds in the other bar give a sense of horizontal movement and makes it appear even. This is interesting because there are also intermittent blackend areas around it. It's shorter length may be adding to this effect as well.
The central cross is the darkest part of the doodle, which is otherwise relatively equal in dark and light, is visually powerful. The image is neither random or rythmic. Because of it's dual nature, I find this image disturbing on some level I can't define. I keep looking at it though. There is something in the uncertainty that makes it compelling.
On the whole, do you prefer symmetry or asymmetry?