Generators of SU(2)pic.twitter.com/7PcIVI6bWG
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SU(2) is kind of like rotations of two complex variables. In particular, they preserve the length of the vector. Two complex numbers have four real components, which live in R4. Since the length is constant, we only care about vectors in the 3-sphere...
The 3-sphere can be stereographically projected to R3, which is done here. Finally, some line and circles are added (all of which are circles in S3) to demonstrate the action of SU(2), which permutes them into each other.
