left depicts the super-level sets of the positive and the negative parts of the first component of the vorticity field, while the figure on the right–the union of the six individual super-level sets–corresponds to the super-level set of the vorticity magnitude. Obtained from the Kida simulation.[]{data-label="fig:overview_figure"}](x.png "fig:"){width="40mm"}   ![An illustration of the difference between sparseness of the super-level sets of the individual components and the full vectorial super-level set. The figure on the left depicts the super-level sets of the positive and the negative parts of the first component of the vorticity field, while the figure on the right–the union of the six individual super-level sets–corresponds to the super-level set of the vorticity magnitude. Obtained from the Kida simulation.[]{data-label="fig:overview_figure"}](all.png "fig:"){width="40mm"}
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![image](game.jpg){width="180mm"}

Details can be found in [@BrFaGr18]; here we present the classes $Z_\alpha$ as well as the synopsis of the two main results encoded in the $Z_\alpha$-formalism. Henceforth, for a vector field $\pmb{f}$, the positive and the opposite of the negative parts of the components $f_i$ will be denoted by $f_i^\pm$, $i=1, 2, 3$.

For a positive exponent $\alpha$, and a selection of parameters $\lambda \in (0,1)$, $\delta \in (0,1)$ and $c_0>1$, the class of functions $Z_\alpha(\lambda, \delta; c_0)$ 