A coupled map lattice is a mapping of continuous dynamic state values to nodes on a lattice that interact (are ‘coupled’) with a set of other nodes in the lattice according to specified rules. Coupled map lattices were developed by Kunihiko Kaneko for the purpose of studying spatio-temporal dynamics and chaos. Since their introduction, CML techniques have been used extensively in the fields of physics and mathematics for the simulation of a variety of phenomena, including boiling, convection, cloud formation, chemical reaction-diffusion, and the formation of sand ripples and dunes.

In our implementation we store the lattice values in textures, and use pixel-level programming to implement simple next-state computations on lattice nodes and their neighbors. We apply these computations successively to produce interactive visual simulations of convection, reaction-diffusion, and boiling. The simulations run on NVIDIA GeForce 3 and 4 GPUs. For details of implementation and performance, see the publications section.

We have designed and built an interactive framework, “CMLlab”, for constructing and experimenting with CML simulations. The user constructs a simulation from a set of operations, such as diffusion and advection. Each operation processes a set of input textures and produces a single output texture. The user connects the outputs and inputs of the selected operations into a directed acyclic graph. An iteration of the simulation consists of traversing the graph in depth-first fashion so that each operation is performed in order. The state textures resulting from an iteration are used as input state for the next iteration, and for displaying the simulated system. The results of intermediate passes in a simulation iteration can be displayed to the user in place of the result textures. This is useful for visually debugging the operation of a new simulation.