A neural network, like a sheet of graph paper, receives homogeneous signals at its input, and draws its own coordinate grid. Initially, connections between inputs and network cells form a gentle hill: the response is strongest at the center and fades toward the edges. This gives rise to a stable activity bump — a collective pattern that holds on its own.
Then something unexpected happens: without any feedback, this bump begins to shift forward. The network, without 'planning' it, predicts where the signal will be at the next moment. In layered structures resembling the brain's cortex, this shift accumulates, as in the entorhinal cortex, where neurons activate slightly before the real stimulus arrives.
If the network is allowed to close connections onto itself, it learns to sustain a traveling wave without external cues. And if a current that changes over time and encodes velocity is added, the network becomes a path integrator: its internal speed adjusts, and the bump moves strictly in one direction, counting the distance traveled. Thus, from simple rules of learning and inhibition, a system that both builds a map and navigates by it assembles itself.
The activity bump in such networks resembles a 'bubble' of excitation: its position encodes a coordinate, while its shape remains nearly unchanged during motion, like a rogue wave, but stable.