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We collect a number of elementary constructions of $\mathbb Z_2$ harmonic$1$-forms, and of families of these objects. These examples show that thebranching set $\Sigma$ of a $\mathbb Z_2$ harmonic 1-form may exhibit thefollowing features: i) $\Sigma$ may be a non-trivial link; ii) $\Sigma$ may bea multiple cover; iii) $\Sigma$ may be immersed, and appear as a limit ofsmoothly embedded branching loci; iv) there are families of $\mathbb Z_2$harmonic $1$-forms whose branching sets $\Sigma$ have tangent cones filling outa positive dimensional space, even modulo isometries.

New examples of Z/2 harmonic 1-forms and their deformations