1. A computer-implemented method comprising: receiving input data including a temporal sequence of spatial patterns at a predictive system, the input data in a distributed representation form; spatially pooling the input data to generate sparse vectors in a sparse distributed representation form by a spatial pooler of the predictive system; temporally processing transitions of the sparse vectors to establish relationships between temporal sequences of spatial patterns in the input data by a sequence processor of the predictive system; detecting a state of the predictive system at a first time responsive to receiving the input data; and generating a prediction for a second time following the first time after a plurality of time steps based on the detected state of the predictive system and stored relationships, the stored relationships mapping states of the predictive system at third times to spatial patterns derived from the input data at fourth times, each of the third times preceding a corresponding one of the fourth times by the plurality of time steps, the fourth times preceding the first time, wherein the states of the predictive system comprise states of the sequence processor.