  Excitable media are ubiquitous in nature, and in such systems the local
excitation tends to self-organize in traveling waves, or in rotating
spiral-shaped patterns in two or three spatial dimensions. Examples include
waves during a pandemic or electrical scroll waves in the heart. Here we show
that such phenomena can be extended to a space of four or more dimensions and
propose that connections of excitable elements in a network setting can be
regarded as additional spatial dimensions. Numerical simulations are performed
in four dimensions using the FitzHugh-Nagumo model, showing that the vortices
rotate around a two-dimensional surface which we define as the superfilament.
Evolution equations are derived for general superfilaments of co-dimension two
in an N -dimensional space and their equilibrium configurations are proven to
be minimal surfaces. We suggest that biological excitable systems, such as the
heart or brain which have non-local connections can be regarded, at least
partially, as multidimensional excitable media and discuss further possible
studies in this direction.
