Associative memories include associative memory cells. A respective cell includes a sensor input, a prior association representation, a next association representation and an associative output. The cells are serially interconnected to form a linear array, such that the sensor inputs, the prior association representations and the next association representations of the serially connected cells are arranged in a sequence from distal to proximal cells based on affinities of associations among the series of sensor inputs. A respective cell also includes processing logic. The processing logic is responsive to the associated sensor input being active, to send a measure of the next association representation to an adjacent proximal cell and/or to send a measure of prior association representation to an adjacent distal cell. The processing logic may be further responsive to the associated sensor input being active, and to receipt of the measure of the next association representation from an adjacent distal cell, to accumulate an associative count in the associative output.