Abstract We develop a method for calculating energy migration in random heterogeneous aggregates, with potential application to the primary process in photosynthetic units. A Monte Carlo technique is employed to study several types of random walk motion in a random binary lattice. Our computations include 2 and 3 dimensional lattices of different topology and employ correlated steps with a Gaussian distribution of directional memory. The effects of the characteristics of the motion and its parameters are displayed and discussed. The lower threshold for efficient visitation by the walker is given by the critical percolation concentration. However, a higher threshold is found in the case of coherent motion. This new “turning point” appears to play an important role in the process of exciton transport. The exciton percolation formalism is utilized, giving results for ternary random lattices where the third component is very dilute and acts as a sensor. The results are applied to a system representing the 11B 2u , naphthalene exciton dynamics in an isotopic and chemically mixed crystal, which by itself is supposed to mimic the exciton transport in the photosynthetic units of green plants. Physically reasonable parameters, trends and limits are discussed. Also, an analytical solution is derived and tested for a physically reasonable limit of semicoherent motion in a perfect lattice. The ramification of this work on bioexciton transfer is discussed, especially concerning the light harvesting units in green plants. It leads to a simple minded model that rationalized the ratio of antenna to active-center molecules. Our most important result is that incoherent exciton transfer, i.e. simple random walk, is the most efficient process for significantly heterogeneous aggregates.