>>13970932>>13970944>>13970978to further extend on that notion, the mathematical formalism of a field in physics can be two thing usually.
Vector fields: the one in your graph, where we assign a vector to each point in space, this could be 1D, 2D, 3D, like how different points of a river go at different speeds or how the magnetic fields exist around wires with electricity in them.
Scalar field: same idea as before, but instead of a vector we just assign a number to each point. For example you have a rectangular sheet of metal and you start heating it on the left side, this means that the first the atoms on the left get warmer before the atoms in the middle and right etc, get warmer. So if you look at first, you'll see a lot of bigger numbers on the left side and gradually smaller numbers going right. This is a scalar field. Or look at a map, each point on the map can be associated with a height, like mountains, valleys, etc. If we call our map the 'field' and the heights our numbers, then we have a scalar field again.
A scalar field is not as complicated as a vector field, as you can only represent numbers with it, there is no variation in direction (like with a vector).
If our vector field's every vector points in the same direction, then we just have a scalar field.
All of these can be described by a big timetable(this is how computers store data) or in simple cases just by functions.
