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. Vector fields 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:

1.(+x,+y)F(x, y) = + x i + y j

2.(+x,-y)F(x, y) = + x i – y j

3.(-x,+y)F(x, y) = – x i + y j

4.(-x,-y)F(x, y) = – x i – y j

5.(+y,+x)F(x, y) = + y i + x j

6.(+y,-x)F(x, y) = + y i – x j

7.(-y,+x)F(x, y) = – y i + x j

8.(-y,-x)F(x, y) = – y i – x j


About Dimitrios Kalemis

I am a systems engineer specializing in Microsoft products and technologies. I am also an author. Please visit my blog to see the blog posts I have written, the books I have written and the applications I have created. I definitely recommend my blog posts under the category "Management", all my books and all my applications. I believe that you will find them interesting and useful. I am in the process of writing more blog posts and books, so please visit my blog from time to time to see what I come up with next. I am also active on other sites; links to those you can find in the "About me" page of my blog.
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