One of the first steps in solving any problem is identifying that something is wrong, i.e. that what you observe doesn't fit with a set or acceptable pattern. As humans, we are keenly in tune with some patterns and unaware or oblivious to other patterns. Even as we experience our environment in our non-scientific, day-to-day, life we see patterns that we act on. For example, we see the weather change over the day and we expect rain.
The scientific method builds on our observation skills by formalizing the process to hypothesize an underlying mechanism for the pattern we see. From the pattern (observation) we draw on our experience to make a prediction about what will happen (hypothesis). Some problems that we deal with have simple cause and effect relationships. For example if we see a clump of dead trees by a newly excavated house lot, the simplest cause is probably that a bulldozer drove over the roots and caused damage. This would be easy to check by examining the soil around the trees. Other observations might be based on data that is collected over time or space or a range of concentrations of some pollutant. From these data we might see a relationship that is a simple correlation, the change in one factor is a major predictor of the change in the dependent variable. Again, a simple example could be that the number of dead plants might be correlated to measured levels of a pollutant at each spot. You will encounter many of these correlations in environmental science. Our discipline has well developed protocols for making observations that can be studied using statistics to test the validity of the prediction. We have made progress using these methods but there are limitations.
Some of the processes that we should be observing are not the result of a simple cause and effect, but rather a more complex interaction of parameters. In a complex process, components of the system interact continually and any change in one part is accompanied by changes in other parts of the process. It is important that we learn how to identify these complex patterns. The purpose of this catalog is to introduce you to a variety of patterns.
If you are studying an environmental problem that is built on simple, cause and effect, relationships it is very valuable to create strong hypotheses based on general laws of chemistry, physics and biology. These laws will help you determine what parameters should be measured. While this process is very efficient, it tends to pre-bias the student to observe some parameters and ignore other details. To learn about and study complex systems the student needs to start by considering a wider range of alternatives and pay attention to the details. This process may be much less efficient in terms of the progress made toward a coherent description of the system.
In another paper I describe how to learn about complex systems (Teaching about complexity). I claim that the study of complex systems requires the following five components:
This catalog is intended to help you build a wider repertoire of metaphors for how complex systems work. In an introductory course like this, we expect that students will make progress on steps 1, 2 and 3. Steps 4 and 5 are require much more time than is available here.
This catalog is divided into eleven classes of patterns ranging from simple to complex to multiple-complex systems. The purpose of this categorization is to facilitate learning and teaching. Each category has similarities that can be discussed and leads to the next levels of complex systems. A particular category should share a general metaphor. These general metaphors contain the salient features of the system. For example, "swarm" patterns are all related to a group of bees or any colony. There are simulations and analysis tools that are appropriate for understanding and describing these patterns.
The catalog contains the following patterns that can be related to their dominant metaphor.
Pattern category | short description | general metaphor/ characteristic example |
1. Regular and geometric patterns | can be described by simple algebraic relationships in 2 or 3 dimensions | sphere that results from surface area to volume relationships linear correlation between cause and effect |
2. Dynamic systems | description of a process over time that obeys simple relationships at any instant | exponential, positive feedback systems "logistic" growth model |
3. Fractal shapes | geometric shapes that have constant ratios between the components | tree branching coast line |
4. Fractal frequencies | temporal or distribution patterns that when analyzed for which a change in rank results in the same ratio of change in the frequency | Zipf's law for city size word use frequency |
5. 2D mosaic | any spatial pattern that has patchiness between several to many components | forest fire patches patchiness of housing and farms fragmentation of landscape that leads to biodiversity loss |
6. Pulsing | temporal pattern that switches between resource accumulation and resource exploitation | predator prey interaction "bubble" of the exploitation of a non-renewable mineral resource |
7. Turbulence and self-organized dissipative structures | turbulent flow in a stream of water
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8. Flow and stress | patterns that result from low energy solutions to dynamic processes of flow or stress from placement | hexagonal packing flow of water around a rocks or of tree growth around a branch
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9. Bistable/threshold with hysteresis | processes that have a distinct threshold from changing from one state to another (sigmoidal instead of linear) and with the characteristic that it is more difficult to change the current state away from that threshold (bistable) | lake with marsh and open water islands of hummocks of grass in a xeric environment |
10. Swarm | individual agents each following very simple rules leads complex emergent behavior of the group | insect or bird flock percolation of an innovation or disease in a society |
Multiple patterns together | patterns that have components of any of the above 10 patterns | patchiness in lake algae that results from predator-prey pulsing and diffusion rates that allow that mosaic to persist
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category | class metaphor | pattern_name | visual images (mine) |
borrowed images no rights |
simulation approach |
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1.1 | regular and geometric | straight line | tall tree | ||
1.2 | regular and geometric | smooth constant angle curve | berry arches | ||
1.3 | regular and geometric | circle | ice puddle a, b, c | ||
1.4 | regular and geometric | polygons | |||
1.5 | regular and geometric | edges | |||
1.6 | regular and geometric | sphere | |||
1.7 | regular and geometric | surface to volume | |||
1.8 | regular and geometric | symmetrical centers | |||
1.9 | regular and geometric | normal distribution Gaussian | |||
1.9 | regular and geometric | spider webs | |||
2.1 | system | source or sink | |||
2.2 | system | postitive feedback | |||
2.21 | systems | increasing slope exponential | |||
2.22 | systems | exponential decay | |||
2.3 | system | negative feedback | |||
2.31 | system | negative feedback with dampening | |||
2.32 | system | negative feedback with oscillation | |||
2.4 | systems | gradient without turbulence | 2.4a, 2.4b, 2.4c, 2.4d, 2.4e | ||
3.1 | fractal shape | tree branching | 31-ant-search-patterns.jpg (Sole & Goodwin 2002) | probability of sideways exploration
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3.2 | fractal shape | leaf patterns | 3.2a, 3.2b, 3.2c, 3.2d | ||
3.3 | fractal shape | 137.5 degree offset | |||
3.31 | fractal shape | 0.618 | 331-golden-rectangle.jpg (Thompson 1942) | ||
3.4 | fractal shape | fractal pattern in river basins | 3.4a, 3.4b |
34-jul17 - erosion of volcanic ash | |
3.4 | fractal shape | erosion of watersheds | |||
3.5 | fractal shape | delta morphology | |||
3.9 | fractal shape | shoreline length | 39-feb19 shoreline 39-may12 shoreline 39-sep06 shoreline |
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3.6 | fractal shape | biological fractal | sand dollar | ||
4.1 | fractal frequency | land slides | 41-avalanche-dist.jpg (Sole & Goodwin 2002) |
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4.2 | fractal frequency | earth quake distribution | |||
4.2 | fractal frequency | Richter law | |||
4.3 | fractal frequency | Zipfs dist of city size | 43-zipfs-city-map.jpg 43-zipfs-data.jpg (Sole & Goodwin 202) |
preferential attachment | |
4.4 | fractal frequency | word use frequency | 4.4a | ||
4.9 | fractal frequency | fashion trends clothing | |||
5.1 | mosaic | spatial patches | 5.1a, 5.1b, 5.1c, 5.1d, 5.1e, 5.1f , 5.1g, 5.1h, 5.1i, 5.1j |
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5.11 | mosaic | mosaic pattern 1 large patch | 511-patch-mosaics.jpg |
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5.12 | mosaiic | mosaic pattern 2 small patch | |||
5.13 | mosaic | mosaic pattern 3 dendritic | |||
5.14 | mosaic | mosaic pattern 4 rectilinear | 5.14 - Seaweed production | ||
5.15 | mosaic | mosaic pattern 5 checkerboard | |||
5.16 | mosaic | mosaic pattern 6 interdigitated | |||
5.2 | mosaic | mosaic of trees in forest | 5.2a, 5.2b, 5.2c-folder | ||
5.21 | mosaic | forest fire burn size distribution | |||
5.3 | mosaic | percolation of water through semiporous soil | |||
5.32 | mosaic | distribution of tree height in canopy | |||
5.32 | mosaic | percolation patttern transition | |||
5.34 | mosaic | damage from habitat fragmentation | 534-habitat-fragmentation.jpg (Sole & Goodwin 2002) |
netlogo | |
5.4 | mosaic | texture | |||
5.42 | mosaic | lumpiness | holling1992-fig4.png | ||
5.9 | mosaic | mosaic pattern indices | |||
6.1 | pulsing | pulsing | |||
6.2 | pulsing | sand dune | 6.2a | ||
6.3 | pulsing | oscillation in predator prey | |||
6.4 | pulsing | Hubbert type resource bubble | |||
6.5 | pulsing | geisers | 6.5a, 6.5b | ||
6.9 | pulsing | boxcaring | |||
7.1 | dissipative structures | laminar to turbulent flow of water | 7.1a | ||
7.11 | dissipative structures | gradient with turbulence | |||
7.2 | dissipative structures | Bernard cells in heated water | |||
7.3 | dissipative structures | river meanders | 7.3c, 7.3d, 7.3e, 7.3f |
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7.32 | dissipative structures | rock size in streams | 7.3a, 7.3b, | ||
7.34 | dissipative structures | Hjulstron curves for transport of material | |||
8.1 | flow stress | hexagonal packing | |||
8.2 | flow stress | spiral phyoltaxis | see section 3.3? | ||
8.3 | flow stress | flow lines in trees | |||
8.4 | flow stress | stress cracking | 8.4a, 8.4b, 8.4c |
84-feb03 glacier 84-jul13 mud in the Carmargue |
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9.1 | threshold and bistable | sigmoidal dose response | |||
9.12 | threshold and bistable | sharp threshold - stress | 9.12a | ||
9.2 | threshold and bistable | levels of network connectivitiy | |||
9.25 | threshold and bistable | habitat fragmentaion phase transition | |||
9.3 | threshold and bistable | bistable states with hysteresis | |||
9.32 | threshold and bistable | bistable states in lakes | |||
9.4 | threshold and bistable | island labrynth pool | 9.4a, 9.4b, 9.4c, 9.4d, 9.4e and more |
94-oct31potash plant on Dead Sea | |
10.1 | swarm | flocking | |||
10.2 | swarm | stigmergy | |||
10.22 | swarm | termite mound columns | |||
10.9 | swarm | terracing | 10.9a, 10.9b, 10.9c and more |
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11 | multiple | algal patchiness streams with natural debris |
Arthus-Bertand, Y. Earth from above: 365 days, Harry N. Abrams, Inc. Flake, G. W. (2001). The computational beauty of nature: Computer explorations of fractals, chaos, complex systems and adaptation. Cambridge, MA, The MIT Press. Forman, R. T. T. (1995). Land Mosaics: The ecoogy of landscapes and regions. Cambridge, Cambridge University Press. Sole, R., and Brian Goodwin (2000). Signs of Life: How complexity pervades biology. New York, Basic Books/Perseus Books Group. Thompson, D. A. W. (1942). On Growth and Form. New York, Dover Publications. Wolfram, S. (2002). A New Kind of Science. Champaign, IL, Wolfram Media. |