Theory of Complexity in Natural Systems

*Theory of Complexity - Definitions, Models, and Applications*

goal orientation in learning and achievement. Journal of Educational Psychology, *92*(3), 544-555. https://doi. org/10.1037/0022-0663.92.3.544

1750-8606.2011.00211.x

[149] Witherington, D. C., & Margett, T. E. (2011). How conceptually unified is the dynamic systems approach to the study of psychological development? Child Development Perspectives*, 5*(4), 286-290. https://doi.org/10.1111/j.

children learn about balancing. British Journal of Developmental Psychology,

[141] Krist, H., Horz, H., & Schönfeld, T. (2005). Children's block balancing

representational redescription. Swiss Journal of Psychology*, 64*(3), 183-193. https://doi.org/10.1024/1421-0185.

[142] Guzzetti, B. J., & Hynd, C. R. (Eds.). (2013). *Perspectives on conceptual change: Multiple ways to understand knowing and learning in a complex world*.

[143] Hewson, P. W., & Hewson, M. G. B. (1984). The role of conceptual conflict in conceptual change and the

[144] Ohlsson, S. (2011). *Deep learning: How the mind overrides experience*. Cambridge University Press.

Resubsumption: A possible mechanism for conceptual change and belief revision. Educational Psychologist,

design of science instruction. Instructional Science, *13*(1), 1-13.

[145] Ohlsson, S. (2009).

*44*(1), 20-40. https://doi.

https://doi.org/10.1016/ B978-012498360-1/50006-4

classroom study. Learning &

org/10.1080/00461520802616267

[146] Gunstone, R. F., & Mitchell, I. J. (2005). Metacognition and conceptual change. In J. J. Mintzes, J. H. Wandersee, & J. D. Novak (Eds.), *Teaching science for understanding: A human constructivist view* (pp. 133-163). Academic Press.

[147] Mason, L. (2001). Introducing talk and writing for conceptual change: A

Instruction, *11*(5), 305-329. https://doi. org/10.1016/S0959-4752(00)00035-9

[148] Pintrich, P. R. (2000). Multiple goals, multiple pathways: The role of

*21*(2), 285-301. https://doi. org/10.1348/026151003765264093

revisited: No evidence for

64.3.183

Routledge.

**66**

**Chapter 4**

**Abstract**

Complexities

anthropic impacts related to land uses.

**1. Introduction**

**69**

**Keywords:** complexity, Information entropy, landscape metrics

From the perspective of the Complexity Paradigm [1], the landscape can be interpreted as a complex environmental system that is established from the interdependence relationships of the physical-natural system (that is, by the elements and processes present in nature) and the socioeconomic system (that is, the

Metrics Based on Information

*Sérgio Henrique Vannucchi Leme de Mattos,*

*Luiz Eduardo Vicente, Andrea Koga Vicente,*

*Cláudio Bielenki Junior, Maristella Cruz de Moraes,*

*Gabriele Luiza Cordeiro and José Roberto Castilho Piqueira*

Information entropy concept is the base for many measures used to evaluate the complexity of complex environmental systems. Its application has great potential to evaluate landscape organization and dynamics, especially if we consider that there is a direct relation between their patterns and processes: the spatial arrangement (structure) of units within a mosaic reflects on system functions. Consequently, changes on structure reflects on functions and *vice versa*. Here, we exemplify how three measures based on information entropy – LMC and SDL complexity measures and He/Hmax variability measure – could be applied to evaluating the degree of complexity of a landscape and its components by associating their heterogeneity with the diversity of information acquired from the remote sensors' images. For this, we developed two scripts for a Geographical Information System (QGIS): (1) *CompPlex HeROI*, that compares the complexity of a landscape patch with others and also with their transition areas; and (2) *CompPlex Janus*, which analyzes how complexity varies in the landscape over space and time, generating landscape complexity maps. We also use LMC and SDL complexity measures and He/Hmax variability measure to evaluate complexity time series of environmental variables, as rain and temperature, which allow to evaluate how their variations along time and space affects landscape dynamics. Therefore, application of such metrics in multitemporal studies of landscape dynamics provides indicators of landscape resilience and the degree of conservation or degradation of its different fragments due to

Entropy to Evaluate Landscape
