The second order Taylor expansion of h around x is and, around the fixed points, we have and . In this second analysis, all cells but one are initially set to 0. Evolution from a in a zero background. Definition 2 Definition 3 Definition 4 Proposition 1 Let , where . Grey levels indicate different value ranges.
Time evolves from top to bottom.
We first establish useful lemmas, then we prove the main result. The next example gives a convergence rate for purely temporal sequences of the diagram, i.e. columns, if one every other row is ignored, as g does not depend on its central argument. The proof easily follows from the previous lemma. If connected paths are considered in the spatio-temporal diagram, the convergence rate is k . We know that Fuzzy Rule 90 attracts everything to .