Math - Intuitive Curl

On this page we try to show an intuitive understanding of what Curl is for a Vector Field. 

We use the idea of water, fluid, or a gas that is flowing thru or circulating around in the X-Y Plane.  

How much Rotation or Circulation occurs around point (a, b)?  

Note: CE3 and CE4 have an extra minus sign.  If V1 is negative along E3 and V2 is negative along E4,  then  by including the minus sign the circulation along E3 and E4 will add to the total circulation.  

Below are two examples of vector fields and their curls. 
Desmos 2D Plotting was used to plot the vector field and CalcPlot3D was used to plot the Curl.
Scaling factors were used to make the plots clear. 

Below we see that along the X-Axis Curl is generally positive (counterclockwise). 
Along the Y-axis, the Curl  is generally negative (clockwise).

Below we see that along the positive Y-Axis the Curl is positive (counter clockwise).
Along the negative Y-Axis the Curl is negative (clockwise).