Can brain hemisphere activity/ dominance be inferred from the test subject's drawings? I'm aware that all tasks that a person undertakes involve both halves of the brain. At the same time, there are studies of people who have communication between brain halves severed or suppressed and they produce dramatically different drawings of the same object with different hands.

This makes me ask - is there some sort of a (non-FMRI) test that involves drawing or other activity and can:


Determine if one half of the brain is dominant at the given moment
Determine if communication between brain halves is fluctuating over multiple days
Determine if one half of the brain does not consistently function at the same level of activity?


I'm aware of this Ted talk: My stroke of insight, in which a neuroscientist describes the experience of having a stroke affect one half of her brain, dramatically altering her perception and ability to process real world information. For example she describes being unable to recognize digits in a phone number and "hunting" for the right digit by tracing its shape on the phone.

The images below were made using 100% input from one brain half and 0% from the other. I'm interested if different levels of activity in brain halves, like 100%/50% or 100%/80% or 60%/70% would also create noticeable differences in style.
You say you are "aware that all tasks that a person undertakes involve both halves of the brain". Then, On what kind of patients would this hypothetical test be suitable as healthy people use both hemisphere and split brain use just one hemisphere depending on the drawing hand ? 

If you refer to healthy patients I don't think such a test is possible.
For the moment left-brain/right-brain dominance is usually considered as a neuromyth.For example:
- this blog article http://www.psychologytoday.com/blog/brain-myths/201206/why-the-left-brain-right-brain-myth-will-probably-never-die
- or this paper http://www.nature.com/nrn/journal/v7/n5/full/nrn1907.html .

Maybe some tests (drawing or whatever) would correlate a bit with partial and short term hemispheric activation with desirable inter-individual differences. But aiming for a test bringing more than that is in my humble opinion vain hopes, as hemispheric dominance on healthy subjects has weak (or no) scientific ground.