The vector function is a combination of trig and exponentiation (mixing up x and y to keep things interesting across the plane). These animated GIFs show a zoom in toward the origin.
I'm especially fond of this chromatic-circle vector field mode - the vector length controls the circle radius, while the angle is interpreted as hue color:
Here's the same function, field, and zoom, using a simple line representation of each vector (drawn from tail at evaluated point):
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