In the book, gradient descent method and steepest descent method are different types. As seen in the figure, the direction of negative gradient and the steepest descent direction are different.
However, what I have known before is that negative gradient points in the steepest descent direction of a level set. Thus, I thought negative gradient $-\nabla f(x)$ must be $-\nabla f(x) = c \Delta x$ where $c$ is a constant. According to the figure as well as the context of the book, $-\nabla f(x)$ does not lies in the same direction of $\Delta x$ in general. Could you please explain that?