I've seen a lot of articles of spinors defined using representation theory, Clifford Algebras, etc. But i want to see (if its possible) how a spinor "looks like" and how it changes sign with a 2pi rotation or any aplication.
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If by spinor you mean an element of a Spin group, there are nice matrix representations for $\mathrm{Spin}(3)$ and $\mathrm{Spin}(4)$, occurring by quaternionic tricks. I believe these show an obvious sign change by a single rotation. – Randall Aug 18 '17 at 13:29
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Here you can see that a vector rotates an angle $\theta$ when the rotation matrix just has half the angle, i.e. $\theta/2$: https://math.stackexchange.com/questions/2336441/transformation-of-pauli-matrices/2340996#2340996 A spinor is transformed by the rotation matrix and is thus "rotated" half the angle, so it changes sign under a $2\pi$ rotation. – md2perpe Aug 19 '17 at 18:21
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Any quaternion is a spinor. – user48672 Sep 06 '17 at 14:02