We consider the problem of distributed terrain or area coverage of an initially unknown environment using a set of mobile robots. We describe a distributed algorithm that is able to solve the distributed coverage problem without having each robot exchange its complete coverage map with other robots. The central part of our technique is a compression algorithm used by a robot to approximate the regions that have been previously covered and a fitness function that calculates the degree of accuracy of the approximated coverage information. The operation of our coverage algorithm is evaluated through experiments on simulated as well as physical Corobot robots. We have quantified the extent of overhead introduced by our coverage algorithm to prevent robots from performing repeated coverage. Overall, our results show that the robots are able to cover the environment within different environment settings while significantly reducing the amount of coverage information communicated between different robots.