Amphiphiles are molecules with hydrophobic tails and hydrophilic heads. When dispersed in solvents, they self assemble into complex mesophases including the beautiful cubic gyroid phase. The goal of the TeraGyroid experiment was to study defect pathways and dynamics in these gyroids. The UK's supercomputing and USA's TeraGrid facilities were coupled together, through a dedicated high-speed network, into a single computational Grid for research work that peaked around the Supercomputing 2003 conference. The gyroids were modeled using lattice Boltzmann methods with parameter spaces explored using many 1283 and 3grid point simulations, this data being used to inform the world's largest three-dimensional time dependent simulation with 10243-grid points. The experiment generated some 2 TBytes of useful data. In terms of Grid technology the project demonstrated the migration of simulations (using Globus middleware) to and fro across the Atlantic exploiting the availability of resources. Integration of the systems accelerated the time to insight. Distributed visualisation of the output datasets enabled the parameter space of the interactions within the complex fluid to be explored from a number of sites, informed by discourse over the Access Grid. The project was sponsored by EPSRC (UK) and NSF (USA) with trans-Atlantic optical bandwidth provided by British Telecommunications.