The Gestalt principle of proximity states that objects that appear to be close to each other would be perceived as forming groups.
The overarching principle of perceptual organisation is the Figure/Ground. In proximity, the Ground (the background information or white space) acts as a separator that distinguishes the edges of the Figures, and the further the distance between edges the more dissimilar the Figures are perceived.
An overpowering principle
Proximity is a powerful perceptual organising principle, and can overpower other principles. Even if objects have different properties, e.g. different colour or different shape, as long as they are close to each other, they will be perceived as groups.
Consider the following scatter graph. The pseudo-dataset is distinguished by four categorical groups as encoded by the retinal variables of colour hue and shape. Specifically, the four groups are encoded as red circles, red diamonds, blue circles and blue diamonds:
What information do you perceive from the above scatter plot? Can you perceive any discernible patterns? Probably none.
The above scatter plot is designed so that every coordinate is equidistant from its neighbour. In other words, because proximity is a constant there so no perceivable pattern, regardless the colours or shapes.
Now consider the same scatter graph but with a wide aspect ratio. The wider aspect ratio reduces the distance between rows and increases the distance between columns. As a result, our perception is distorted to perceive columnar groupings:
The groupings are formed because of the proximity between rows regardless if the data is a random collection of red circles, red diamonds, blue circles and blue diamonds. That is to say, proximity trumps other Gelstalt principles of perceptual organisation like the principle of similarity. The other lesson is the we really need to be careful with imposing too wide or too tall aspect ratios in scatter plots.
Here is an example of what can happen if you are not well versed in Gestalt theory – remember that the proximity in data is more powerful than the similarity in data: