Programmable emergence through hierarchical self-organisation

Abstract

Predictively steering self-organising systems with hierarchical structure toward intended outcomes across widely separated dynamical scales remains a fundamental challenge. Despite decades of progress, hierarchy remains a descriptive property rather than a mechanism for control. Here, we show how a high-dimensional stochastic system can be steered toward preselected target states by exploiting its internal hierarchy of timescales. Fast variables lock to slower collective variables; iterating this locking across scales progressively reduces the effective dynamics to a small set of externally controllable parameters. This enables directing the system while maintaining dynamical insulation from noise across scales, thereby turning hierarchy from an observation into a mechanism for programmable emergence. We experimentally demonstrate this approach in a fully tractable platform: a mode-locked laser, in which we assemble and stabilise more than 100 pulses into harmonic patterns over timescales spanning 10 orders of magnitude. Phenomena such as nucleation, quantum-noise-induced annihilation, long-range interactions and annealing-like ordering are predicted and exploited to transition the system to preselected states. Our results establish a route to programming emergent behaviour in driven-dissipative systems, with implications ranging from optics to materials.