Well, the nicest ones are two dimensions and one dimension, which sort of (not really) exist as subsets of 3D. So a single variable is one-dimensional. Then you

Well, the nicest ones are two dimensions and one dimension, which sort of (not really) exist as subsets of 3D. So a single variable is one-dimensional. Then you could have a gradient, say: https://en.wikipedia.org/wiki/Spatial_gradient https://en.wikipedia.org/wiki/Spatial_gradient And you could have a gradient (of colors if you like, or salinity or force of whatever) along a line, one dimension, or on a plane, two dimensions, or in space, three dimensions. By extension, just adding components to vectors and iterating over the components when you do stuff with them, you can apply the same logic about higher dimensions. This makes people thin and unhealthy and serves no purpose, but seems to have a compulsive appeal for a certain kind of mind. You can't always reliably extend some idea to different numbers of dimensions, because the interactions between components can get complicated, sometimes a thing that's valid for certain numbers of dimensions is not in fact valid for other numbers of dimensions, like maybe you have to have a odd number of dimensions to prevent positives and negatives cancelling out or something. Like many people, I knew this stuff for about a month once but forgot the specifics. But a tesseract is kind of fun to look at. https://en.wikipedia.org/wiki/Tesseract https://en.wikipedia.org/wiki/Tesseract This is like the next step in the sequence dot, line, square, cube. The animation is a "projection into 3 dimensions", like how the shadow of a cube on a piece of paper is in two dimensions. It can't be shown in four dimensions, due to four dimensions being complete fiction. (It's squirming like that because it's rotating, but the axis it's rotating around is at some 4D angle.)