John Conway’s Game of Life is an algorithmic model for cellular automata and provides a leading example of emergent behavior. In two-dimensions, each cell in a given matrix is considered either alive or dead. Wikipedia succinctly states the rules that dictate the activity of this population of living cells.
- Any live cell with two or three live neighbors survives.
- Any dead cell with three live neighbors becomes a live cell.
- All other live cells die in the next generation. Similarly, all other dead cells stay dead.
As these rules are cyclically applied, populations of cells grow, traverse their 2-dimensional world, and die in complex patterns that bely the simplicity of the rules. The apparent “organic” lifecycle of these cellular automaton can be explained in the terms of emergence. The concept of emergence has been invoked in all sorts of disciplines, from meteorology, to statistics, biology, physics and of course, computer science. We’ll take a look at a couple more examples to try and understand this nebulous concept.
The Boids algorithm, developed by Craig Reynolds, is another example of a computational model that displays emergent behavior. Reynold’s algorithm simulates murmuration, the flight behavior of large flocks of birds by simulating a set of simple rules for how each individual boid relates to its neighbors.
- Separation: Each boid avoids getting too close to its neighbors.
- Alignment: Each boid moves toward the average heading of its neighbors.
- Cohesion: Each boid moves toward the average position of its neighbors.
Once again, complex and mesmerizing patterns emerge from a set of simple reactionary rules.
Further examples are the formation of rolling sand dunes caused by shifting winds, complex and branching geomorphic drainages formed by the ebb and flow of water, the formation of increasingly complex biomolecules from simple buildings blocks, and from those biomolecules, perhaps even the biogenesis of life, as investigated in the class Miller-Urey experiment. The complex behavior of ants
Other complex phenomenon, such as the formation of intricate ice crystals of snowflakes, are considered emergent behavior. The initial starting shape of the crystal seed, subtle changes in temperature and humidity, and even friction from surrounding materials have an effect on the ice crystal shape. But we can also understand the crystalline structure of these patterns on an atomic level using techniques such as x-ray powder diffraction (XRD). We understand the phenomenon that will cause a water molecule to bond to its neighbors under different conditions, and ultimately would be able to predict the shape of snowflakes with knowledge of their starting state, the set of rules that dictate the interaction of the molecules, and the inputs of each cycle. At this point, the behavior of the system becomes predictable, and if it’s predictable, can it really be considered emergent?
Perhaps it’s a question of scale. Each of the minutia can be understood as discrete pressures, but from the macroscopic view, it appears the crystalline fractal patterns of arise from some unfathomably complex set of interactions. In this view, to claim a system has emergent behavior is really a statement on a current lack of understanding.
But is it really feasible to understand all the complexity that goes into forming a single snowflake? Maybe it’s not just that we don’t understand emergent behaviors. Maybe it’s not possible for them to be understood. Whether it’s because we have no way of accurately measuring countless inputs, or the rational mind is simply incapable of understanding the innumerable factors that can affect an open system, or the systems are so complex that it’s physically impossible to resolve these solutions on a universal time scale, we might never be able to accurately predict emergent behavior.
Maybe emergent behaviors are the NP-Hard systems of the human universe, existing in a realm beyond the reaches of the rational mind.
On the other hand, maybe emergence has nothing to do with whether a system can be understood. After all, emergent patterns, presumably, exist outside of perception. Perhaps emergence is best understood not in terms of computational complexity, but in relation to entropy, as an intrinsic feature of the universe.
Ultimately, we can think of emergence as the behavior of a system that is more complex than its individual parts. Even simple emergent behaviors may become part of a larger pattern, feeding into a cascade of ever increasing complexity with no comprehensible end.
See Also: Smithsonian Magazine – The Origins of Life