Visualizing Commutator of Two Vector Fields

differential-geometry multivariable-calculus

Solution 1:

In Gauge fields, knots and gravity by J. Baez and J. P. Muniain authors got the following two pictures to visualize commutator:
enter image description hereenter image description here

I hope it helps you.

Related

Intuition behind logarithm change of base
Expressing the trace of $A^2$ by trace of $A$
Holomorphic function $\varphi$ with fixed point $z_0$ such that $\varphi'(z_o)=1$ is linear?
Determine all functions satisfying $f\left ( f(x)^{2}y \right )=x^{3}f(xy)$
Independence of disjoint events
Calculate the radius of a circle given the chord length and height of a segment
Another beautiful integral (Part 2)
Inverse of regular value is a submanifold, Milnor's proof
If $E/F$ is algebraic and every $f\in F[X]$ has a root in $E$, why is $E$ algebraically closed? [duplicate]
No. of possible dense subsets of a metric space
Identity with Catalan numbers
Dimensions of vector spaces in an exact sequence