Hypercube Simulation of Electric Fish Potentials

We present a simulation of the electrosensory input of the weakly electric fish Apteronotus leptorhynchus. This fish senses its environment by producing a sinusoidal voltage difference between its body and tail sections, causing an electric field and a current distribution in the surrounding water. If an object is nearby which has different electrical conductivity from the surrounding water, the current distribution is disturbed on the skin of the fish. The fish senses this difference from the usual current distribution, and infers the presence and location of the object. Mathematically, the problem is to solve a potential equation in the domain exterior to the fish with Cauchy boundary conditions, in the presence of an induced dipole arising from the object, and extract the potential difference across the fish skin. We have created an unstructured triangular mesh covering the two-dimensional manifold of the fish skin, using the distributed Irregular Mesh Environment (DIME), then used the Boundary Element Method to solve for the potential derivative at the fish skin. The computational problem is the solution of a full set of simultaneous linear equations, where there is an equation for each node of the boundary mesh, typically about 100 - 200. We have used an NCUBE hypercube to calculate the matrix elements and solve these equations, once for each relative position of the fish and the test object. We present some early results from the simulation.