If you think of it in terms of energy, where energy is defined as some quantity you want to minimise, then it becomes apparent.
Define the energy as the distance of an atom of data to other atoms of the same subject (row) plus the distance of the data to other atoms of the same abstract property (column). Then choose a model; this defines your atoms. You could call the selection of the model a discretisation because all models become 1s and 0s eventually. If you choose a model where atoms occupy pixels exclusively (only 1 atom per pixel) and the XY coordinates of each atom is the variable, I think you’ll find that feeding it into most optimisers (such as a Monte Carlo simulation) will result in something very closely resembling a grid of cells.
If you choose a different 2D model/discretisation, such as hexagons, you’ll find an abstractly similar result if not a little unfamiliar.
If you chose a higher dimension space for your model/discretisation (3D+), then you may find something uniquely interesting, but good luck mapping it to a solution which is compatible with our traditional 2D UIs.
If you think of it in terms of energy, where energy is defined as some quantity you want to minimise, then it becomes apparent.
Define the energy as the distance of an atom of data to other atoms of the same subject (row) plus the distance of the data to other atoms of the same abstract property (column). Then choose a model; this defines your atoms. You could call the selection of the model a discretisation because all models become 1s and 0s eventually. If you choose a model where atoms occupy pixels exclusively (only 1 atom per pixel) and the XY coordinates of each atom is the variable, I think you’ll find that feeding it into most optimisers (such as a Monte Carlo simulation) will result in something very closely resembling a grid of cells.
If you choose a different 2D model/discretisation, such as hexagons, you’ll find an abstractly similar result if not a little unfamiliar.
If you chose a higher dimension space for your model/discretisation (3D+), then you may find something uniquely interesting, but good luck mapping it to a solution which is compatible with our traditional 2D UIs.