The filtering action of some type of cellular automata has been known about since the mid I960’s. These cellular filters, based on a combination of reducing and augmenting kernels operating on a series of thresholded images, are derived empirically and have fixed characteristics. This thesis presents a method for synthesising 2 dimensional grey level image filters using cellular automata. This method takes as its starting point the characteristic equation of a filter expressed in the Laplace domain, and derives from this equation the kernel of the cellular filter which has the same characteristics as the filter defined by the Laplacian equation. The advantage of using' cellular automata for image filtering is that they are highly parallel in nature, and as such, are a natural algorithm for image filtering on a parallel computational engine.