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Diagram: Multiple Equilibria

Multiple Equilibria

The idea that systems can have more than one stable state.

Early versions of systems theory assumed that systems could be 'optimized' to a single condition. CAS analysis assumes that more than one system state can satisfy optimizing criteria, and so the system is able to gravitate to multiple equilibria.

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Wohl, S. (2022, 9 June). Multiple Equilibria. Retrieved from https://kapalicarsi.wittmeyer.io/definition/multiple-equilibria

Multiple Equilibria was updated June 9th, 2022.

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Complex systems do not follow linear, predictable chains of cause and effect. Instead, system trajectories can diverge into wildly different regimes. The moment when a complex system move from one trajectory to another is known as a system bifurcation.

This feature of complex systems means that the behavior of a system cannot be known in advance, but instead needs to be enacted in time. Learn more →
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Cellular Automata & Agent-Based Models offer city simulations whose behaviors we learn from. What are the strengths & weaknesses of this mode of engaging urban complexity?

There is a large body of research that employs computational techniques - in particular agent based modeling (ABM) and cellular automata (CA) to understand complex urban dynamics. This strategy looks at how rule based systems yield emergent structures.

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How can our cities adapt and evolve in the face of change? Can complexity theory help us provide our cities with more adaptive capacity to respond to uncertain circumstances?

Increasingly, we are becoming concerned with how we can make cities capable of responding to change and stress. Resilient urbanism takes guidance from some complexity principles with regards to how the urban fabric can adapt to change.
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New ways of modeling the physical shape of cities allows us to shape-shift at the touch of a keystroke.  Can this ability to generate a multiplicity of possible future urbanities help make better cities?

Parametric approaches to urban design are based on creating responsive models of urban contexts that are programmed to change form according to how inputs are varied. Rather than the architect creating a final product, they instead create a space of possibilities ({{phase-space}}) that is activated according to how various flow variables - economic, environmental, or social, are tweaked. This architectural form-making approachholds similarities to complex systems in terms of how entities are framed: less as objects in and of themselves, and more as responsive, adaptive agents, activated by differential inputs.
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Complex Systems can unfold in multiple trajectories. However, there may be trajectories that are more stable or 'fit'. Such states are considered 'attractor states'.

Complex Adaptive Systems do not obey predictable, linear trajectories. They are "Sensitive to Initial Conditions", such that small changes in these conditions can lead the system to unfold in unexpected ways. That said, in some systems, particular 'potential unfoldings' are more likely to occur than others. We can think of these as 'attractor states' to which a system will tend to gravitate.

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There would be some thought experiments here.

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Related (this page): Urban Modeling (11), Resilient Urbanism (14), Parametric Urbanism (10), Non-Linearity (26), History Matters (116), Degrees of Freedom (78), Attractor States (72), 
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Emergence
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Related (all): Urban Modeling (11, fields), Urban Informalities (16, fields), Tactical Urbanism (17, fields), Parametric Urbanism (10, fields), Landscape Urbanism (15, fields), Incremental Urbanism (13, fields), Evolutionary Geography (12, fields), Feedback (88, concepts), Degrees of Freedom (78, concepts),