The Sub-Critical City

A system held below its critical slope: grains settle quietly, avalanches rare. Eugene’s growth boundary has shaped a city that resists sudden cascades.

Cities often drift toward what complexity science calls the critical slope, where countless small choices accumulate into patterns of sudden avalanches—some minor, some transformative. Eugene has resisted that drift, making it a useful case for thinking about self‑organized criticality in urban form. 

I first encountered the idea of self‑organized criticality in 2008, in discussions of emergent urbanism and systems thinking under the tutelage of Alder Fuller. A recent Veritasium video on power laws reignited my interest and prompted me to consider how these ideas apply to Eugene’s development. 

Self‑organized criticality describes the way certain systems—sandpiles, forests, stock markets, earthquakes—drift toward a balance point where tiny disturbances can produce anything from nothing to catastrophe. At that balance point, the size of events follows a power‑law distribution: countless small events, far fewer medium ones, and a rare but inevitable handful of giants. These “heavy tails” mark a critical system. The same mathematical signatures appear across wildly different domains, a phenomenon physicists call universality. Cities belong to that list, and Eugene’s exception makes the concept especially revealing. 

No large city grows in a vacuum. All face shaping by topography, zoning, land prices, infrastructure budgets, and political decisions. Yet worldwide, power‑law patterns appear with remarkable consistency: in street lengths, traffic congestion, building heights, rates of innovation, even the spacing of coffee shops. The driver lies not in the absence of rules, but in the presence of millions of small, local, decentralized choices: where to build a house, extend a road, or open a business. Those choices act like grains of sand dropped onto a pile. Over time, cities tune themselves toward a threshold slope, even if aspects of that slope are far from perfectly free. 

Eugene’s growth has been pressed by constraints tighter than those shaping many other cities. The Willamette and McKenzie rivers, the Coburg Hills, and Spencer Butte already form a natural bowl. Oregon’s statewide land‑use program, enacted in 1973, was the first of its kind in the nation. It required every city to draw an urban growth boundary, a bold experiment in curbing sprawl and preserving farmland. Typically, a city’s boundary expands in response to population growth; in Eugene, such expansions have been small and infrequent. From the air, the city still shows a discernible edge: roofs and streetlights give way to fields and oak savanna more abruptly than in most American cities of comparable size and wealth, though ragged in places. 

A walk from the downtown grid toward the South Hills reveals streets that begin to branch and loop like tributaries. Cul‑de‑sacs and winding lanes mark a departure into branching patterns that resemble fractals. One accident on the Beltline at rush hour can paralyze half the city. Housing prices jump in ways that feel disproportionate to the trigger. Even in sub‑critical systems, small avalanches still occur. 

Explosive rings of subdivisions and sudden satellite towns have been kept at bay, leaving Eugene’s sandpile noticeably flatter than most cities of comparable size and wealth. In the language of complexity science, the city qualifies as sub‑critical: orderly, green, bikeable, and still livable. Most other cities, even with their own zoning codes, greenbelts, and natural barriers, live closer to the slope that complexity science describes. 

Eugene's urban growth boundary.

Whether such restraint proves beneficial remains uncertain. The gains are clear: farmland and wetlands preserved, infrastructure costs contained, weekend rides across town that still feel relaxed. Most residents value these outcomes and would not trade them for the unchecked suburban expansion visible in other regions. 

The concerns are less visible. Critical systems acquire remarkable properties—rapid adaptation, outsized creativity—precisely because they tolerate extremes. When a city holds back more forcefully than most, it intervenes in a process that has proved robust at finding its own balance. In Eugene, the muted tails stand out in housing: supply has lagged demand, and affordability has eroded more sharply than in cities that allowed broader expansion. 

Complexity science offers no prescription; it only reminds us that every path carries its own heavy‑tailed consequence. One set of consequences is visible now: open fields west of Bertelsen Road, a skyline that ends where the hills begin. Another set may lie ahead: reduced adaptability, economic stagnation, or exclusion dressed up as preservation. 

The urban growth boundary undergoes periodic review, and the same public process that set it can still adjust it. Eugene has not become locked into permanent sub‑criticality, only into a prolonged and unusually deliberate constraint as the region decides what it values more: the known benefits of containment or the unknown potentials that most cities, despite their own rules, still manage to reach. 

Eugene’s growth boundary has kept the city flatter than the slope that complexity science describes. Whether this restraint preserves resilience or erodes adaptability remains uncertain. Self‑organized criticality only reminds us that even deliberate interventions cannot escape heavy‑tailed consequences.