  We construct supersymmetric Lagrangians for the recently constructed
off-shell worldline N=3 supermultiplet $Y_I/(i D_I X)$ for I=1,2,3, where $Y_I$
and $X$ are standard, Salam-Strathdee superfields: $Y_I$ fermionic and $X$
bosonic. Already the Lagrangian bilinear in component fields exhibits a total
of thirteen free parameters, seven of which specify Zeeman-like coupling to
external (magnetic) fluxes. All but special subsets of this parameter space
describe aperiodic oscillatory response, some of which are controlled by the
"golden ratio," $\varphi\approx1.61803$. We also show that all of these
Lagrangians admit an $N=3\to 4$ supersymmetry extension, while a subset admits
two inequivalent such extensions.
