## Visualizing eight elementary vector fields

I used Wolfram Alpha to draw eight vector fields that fascinate me, albeit or because of their simplicity. In Wolfram Alpha, I entered (x,y) and the engine plotted the integral curves for the corresponding vector field. Then I entered (x,-y) and the engine plotted the corresponding integral curves for that corresponding vector field. And so on. You can tell that it is not the vector fields that are depicted here, but their integral curves. This is because, in the plots above, each arrow has the same length as the others. If the actual vector field was plotted, each arrow’s length would be equal or proportional to the magnitude of the vector field function F(x, y) at that point. In the case of all eight vector fields studied here, the magnitude of the arrows would be greater as x and y increase. Specifically, in all cases, the magnitude of each arrow is sqrt((f1(x,y))^2 + (f2(x,y))^2) = sqrt(x^2+y^2).

Update, September 11, 2014: Using Kevin Mehall‘s awesome Vector Field Online Graphing, I was able to depict the above vector fields with great ease. Here they are:

# F(x, y) = – y i – x j 