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Complex systems exhibit important scalar dynamics from two perspectives. First, they are often built up from nested sub-systems, which themselves may be complex systems. Second, at a given scale of inquiry within the system, there will be a tendency for the system to exhibit some form of power-law (or scale-free) dynamics in terms of how the system operates. This simply means that there will be a tendency in the system for a small number of elements within the system to dominate: this system domination can manifest in different ways, such as intensity (earthquakes) frequency (citations) or physical size (road networks). In all cases a small ratio of system components (earthquakes, citations, or roads) exert a large ratio of system impact. Understanding how and why this operates is important in the study of complexity.

To understand what we mean by 'nested', we can think of the human body. At one level of magnification we can regard it as a collection of cells, at another as a collection of organs, at another as a complete body. Further, each body is *itself* part of a larger collection - perhaps a family, a clan or a tribe - and these in turn, may be part of other, even larger wholes: cities or nations. In complex systems we constantly think of both parts and wholes, with the whole (at one level of magnification) becoming just a part (at another level of magnification). While we always need to select a scale to focus upon, it is important to note that complex systems are open - so they are affected by what occurs at other scales of inquiry.

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**Photo Credit and Caption: ** Scale-Free

**Cite this page:**

Wohl, S. (2019, 8 November). Nested Scales. Retrieved from https://kapalicarsi.wittmeyer.io/taxonomy/nested-orders

Nested Scales was updated November 8th, 2019.

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Nested Scales | Building Blocks

This is a default subtitle for this page. Read more and see related content for Herbert Simon →Power Laws

This is a default subtitle for this page. Read more and see related content for George Kingsley Zipf →Self-similarity | Fractals

Caramelization half and half robust kopi-luwak, brewed, foam affogato grounds extraction plunger pot, bar single shot froth eu shop latte et, chicory, steamed seasonal grounds dark organic. Read more and see related content for Georg Cantor →Fractals

This is a default subtitle for this page. Read more and see related content for Benoit Mandelbrot →Scale-Free Networks

This is a default subtitle for this page. Read more and see related content for Albert Laszlo Barabasi →Self-Organized Criticality

This is a default subtitle for this page. Read more and see related content for Per Bak →Santa Fe Institute; Fitness Landscape

N-K Fitness Landscape Read more and see related content for Stuart Kauffman →power law distributions + Pareto optimality

Not possible to change the behavior of one agent without another agent being worse off. Read more and see related content for Vilfredo Pareto →This is a list of Terms that Nested Scales is related to.

CAS tend to organize to a 'critical state' where, regardless of the scale of a given input, the scale of corresponding output observes of a power-law distribution.

Strike a match and drop it in the forest. How big will the resulting fire be? The forest is dry but not overly so... vegetation is relatively thick. Will the fire burn a few trees and then flame out, or will it jump from branch to branch, burning thousands of acres to the ground? Read more and see related content for Self-Organized Criticality →'Scale-free' networks are ones in which identical system structure is observed for any level of network magnification.

Complex systems tend towards scale-free, nested hierarchies. By 'Scale-free', we mean to say that we can zoom in on the system at any level of magnification, and observe the same kind of structural relations. Thus, if we look at visualizations of the world wide web, we see a few instances of highly connected nodes (youtube), many instances of weakly connected nodes (your mom's cooking blog), as well as a mid-range of intermediate nodes falling somewhere in between. The weakly connected nodes greatly outnumber the highly connected nodes, but the overall statistical distribution of connected vs unconnected nodes follows a power-law distribution. Thus, if we 'zoom in' on any part of the network (at different levels of magnification), we see similar, repeated patterns.

'Scale Free' entities are therefore fractal-like, although scale-free systems generally are about the scaling of connections or flows, rather than scaling of pictoral imagery (which is what we associate with {{fractals}} HANDLEBAR FAIL or objects that exhibit Self Similarity . Accordingly, a pictoral representation of links in the world wide web does not 'look' like a fractal, but its distributions of connections observes mathematical regularities consistent with what we observe in fractals (that is to say, power laws).

A good way to think about this is that, while both scale-free systems and fractals follow power laws distributions, not all power law distributions 'look' like perfect fractals!

At the same time, sometimes the dynamics of scale free networks align with the visuals we consider to be fractal-like. A good example here is the fractal features of a leaf:

Read more and see related content for Scale-Free →

Complex System behaviors often exhibit power-laws: with a small number of system features wielding a large amount of system impact.

Power laws are particular mathematical distribution that appear in contexts where a very small number of system events or entities exist that, while rare, are highly impactful, alongside of a very large number of system events or entities exist that, while plentiful, have very little impact. Power laws arise in both natural and social system, in contexts as diverse earthquake behaviors, city population sizes, and word frequency use.

Complex systems are often characterized by power law distributions. A power law is a kind of mathematical distribution that we see in many different kinds of systems. It has different properties from a well known distribution - a 'bell curve' 'normal' or 'Gaussian' distribution.

Let's look at the two here:

Read more and see related content for Power Laws →

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This is a default subtitle for this page. Read more and see related content for Fractals →This is a list of Urban Fields that Nested Scales is related to.

Cellular Automata & Agent-Based Models can provide 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 research looks at rule based systems that yield emergent structures. Read more and see related content for Urban Modeling →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 that are able to respond to change and stress. Resilient urbanism takes guidance from some complexity principles with regards to how the urban fabric can adapt to change. Read more and see related content for Resilient Urbanism →Many cities around the world self-build without top-down control. What do these processes have in common with complexity?

Cities around the world are growing without the capacity of top-down control. Informal urbanism is an example of bottom-up processes that shape the city. Can these processes be harnessed in ways that make them more effective and productive? Read more and see related content for Informal Urbanism →This is a list of Key Concepts that Nested Scales is related to.

CAS tend to organize to a 'critical state' where, regardless of the scale of a given input, the scale of corresponding output observes of a power-law distribution.

Strike a match and drop it in the forest. How big will the resulting fire be? The forest is dry but not overly so... vegetation is relatively thick. Will the fire burn a few trees and then flame out, or will it jump from branch to branch, burning thousands of acres to the ground? Read more and see related content for Self-Organized Criticality →'Scale-free' networks are ones in which identical system structure is observed for any level of network magnification.

Complex systems tend towards scale-free, nested hierarchies. By 'Scale-free', we mean to say that we can zoom in on the system at any level of magnification, and observe the same kind of structural relations. Thus, if we look at visualizations of the world wide web, we see a few instances of highly connected nodes (youtube), many instances of weakly connected nodes (your mom's cooking blog), as well as a mid-range of intermediate nodes falling somewhere in between. The weakly connected nodes greatly outnumber the highly connected nodes, but the overall statistical distribution of connected vs unconnected nodes follows a power-law distribution. Thus, if we 'zoom in' on any part of the network (at different levels of magnification), we see similar, repeated patterns.

'Scale Free' entities are therefore fractal-like, although scale-free systems generally are about the scaling of connections or flows, rather than scaling of pictoral imagery (which is what we associate with {{fractals}} HANDLEBAR FAIL or objects that exhibit Self Similarity . Accordingly, a pictoral representation of links in the world wide web does not 'look' like a fractal, but its distributions of connections observes mathematical regularities consistent with what we observe in fractals (that is to say, power laws).

A good way to think about this is that, while both scale-free systems and fractals follow power laws distributions, not all power law distributions 'look' like perfect fractals!

At the same time, sometimes the dynamics of scale free networks align with the visuals we consider to be fractal-like. A good example here is the fractal features of a leaf:

Read more and see related content for Scale-Free →

Complex System behaviors often exhibit power-laws: with a small number of system features wielding a large amount of system impact.

Power laws are particular mathematical distribution that appear in contexts where a very small number of system events or entities exist that, while rare, are highly impactful, alongside of a very large number of system events or entities exist that, while plentiful, have very little impact. Power laws arise in both natural and social system, in contexts as diverse earthquake behaviors, city population sizes, and word frequency use.

Complex systems are often characterized by power law distributions. A power law is a kind of mathematical distribution that we see in many different kinds of systems. It has different properties from a well known distribution - a 'bell curve' 'normal' or 'Gaussian' distribution.

Let's look at the two here:

Read more and see related content for Power Laws →

There would be some thought experiments here.

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