  We briefly present our version of noncommutative analysis over matrix
algebras, the algebra of biquaternions ($\mathbb B$) in particular. We
demonstrate that any $\mathbb B$-differentiable function gives rise to a null
shear-free congruence (NSFC) on the $\mathbb B$-vector space $\mathbb{C}\bf M$
and on its Minkowski subspace $\bf M$. Making use of the Kerr--Penrose
correspondence between NSFC and twistor functions, we obtain the general
solution to the equations of $\mathbb B$-differentiability and demonstrate that
the source of an NSFC is, generically, a world sheet of a string in $\mathbb
{C}\bf M$. Any singular point, caustic of an NSFC, is located on the complex
null cone of a point on the generating string. Further we describe symmetries
and associated gauge and spinor fields, with two electromagnetic types among
them. A number of familiar and novel examples of NSFC and their singular loci
are described. Finally, we describe a conservative algebraic dynamics of a set
of identical particles on the ``Unique Worldline'' and discuss the connections
of the theory with the Feynman--Wheeler concept of ``One-Electron Universe''
