What we call a pixel art can be best described as a crossover of digital painting and the traditional art of tapestry
Dubious.
You start with a grid and you fill its cells with square patches of color
I start with a blank canvas, the same as when I paint traditionally. I don't consider the grid until I'm pixel-pushing toward the end of the image.
A specific role that a colored cell plays in the final image is determined by its relation with other cells. With the adjacent ones, in the first line. It means that the image is never a simple sum of its colored cells. Rather, it is an organic composition where the grid position of the colored cell determines its specific role in the image taken as a whole. For example, a cell with a certain color that is surrounded by lighter cells gives a shadow effect. Surrounded by darker cells, the same cell with the same color results in a highlight, etc.
I didn't follow any of this.
The capacity of the single cell to influence the whole image - or at least adjacent cells - is made possible by the size of the cell. Obviously, the minimal size of the cell should not go bellow the naked eye visibility. Otherwise, a single cell color change would not have any effect on the image. The minimal "brush" size of our digital painter would have to grow in order that he be able to control the effect of a single color placement gesture. That would, however, transform our grid art into an ordinary form of digital painting - one that we normally do in Gimp or Photoshop. The grid art would lose its proper essence and it would cease to be what it is.
I think you're a little concerned with the visibility of squares. As Ryumaru and Carnivac have pointed out (and Pix3m proved with an image), this is a strict and contemporary definition. In the days of CRT monitors, the pixels were blurred, which affected the medium and how the artists created images (e.g. dithering was a much more useful technique.) Likewise, "hi-res" pixel art that "loses" the grid is fine too (see: Panda, Elk, etc.) The bit about losing its "proper essence" and ceasing to be "what it is" is especially nebulous.
That said, two minimal conditions must be fulfilled in order to call something a grid art:
- The image has to be a) grid-structured and b) a minimal patch of color should be a square that fits exactly the size of the grid cell.
- A single grid cell must be visible to the naked eye.
I've seen pixel art that uses a triangular grid, an offset-brick pattern, and non-square rectangles (either tall or long).
We do not want our art to be defined by something as volatile as screen technology.
I think it's defined by its medium of expression. We can't divorce pixel art from its dependence upon and history with the computer. It is true that there is a tradition of grid-based art (beadwork of the Native Americans, dyed inlays on colonial American furniture, mosaic pattern from the Islamic Golden Age, etc.), but it would be simplistic to reduce pixel art to just this impulse. That would reduce pixel art to just the 'tapestry' mindset you described earlier, with no regard for the importance of the 'digital' or 'painting' aspects that you yourself say are foundational.