Is the gradient direction of a binary function unique at a point, or is there countless? Is it the normal direction of the point on the isoline?

Is the gradient direction of a binary function unique at a point, or is there countless? Is it the normal direction of the point on the isoline?

You can imagine a three-dimensional image of Z = f (x, y). Every (x, y) point has a Z mapping with it. You can imagine that it will be a surface. Then you can imagine a specific point on the surface, which is like standing on the hillside when you climb a mountain. If you walk flat on the hillside, then your height