# Cities, from Information to Interaction

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## Abstract

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## 1. Complex Systems in Relation: Minds, Cities and Societies

## 2. Introducing the Information-Interaction System

- The physical problem: how do we encode and decode information from the environment?
- The semantic problem: how do we make environmental information meaningful?
- The pragmatic problem: how does environmental information affect our actions?

## 3. Environmental Information 1 (Physical Space)

#### Measuring Environmental Information 1

## 4. Environmental Information 2 (Semantic Space)

#### Measuring Environmental Information 2

## 5. Information 3 (Enacted)

## 6. From Information to Interaction: Concluding Remarks

- We measured environmental information 1 in cellular arrangements and assessed order, assumed to guide navigation, through Shannon entropy.
- We measured environmental information 2 as a function of semantic diversity in local relations between urban activities or land uses. Information 2 is highly differentiated, serving as a resource of great combinatorial power in the process of selection of places and actions to be performed.
- We modeled the influence of the environment in enacted information 3, simulated as action types in an ABM. Proximity in physical configurations in information 1 and semantic contents in information 2 were seen to increase the convergence of action types. Contrary to isolated systems where order inexorably dissipates in time, the entropy of interaction decreases as the system of agents is open to and co-evolves with its physical and semantic environment. Aspects of information 1 and 2 find key roles in solving the combinatorial problem of action coordination.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Environmental information (

**1**) physical space and (

**2**) semantic space, and enacted information (

**3**): substantive components and measurable properties. Colours mean different land uses and types of action, i.e., chronically reproduced modalities of work, commerce, leisure and on, usually materialized as activities occurring in buildings and places (see Figure 8).

**Figure 3.**Information in physical space: emblematic arrangements with different levels of order. Case 1 is an extreme example of order, rare in the set of possible arrangements. In cases 2 and 4, cell distributions contain low internal correlations. In case 3, positions follow a patterned distribution, and in case 5 order is visible as a spiraled pattern. The sixth case shows deformed rings, highly unlikely events which bring to mind unplanned urban structures.

**Figure 4.**Spatial distributions in real cities ($9,000,000$ m${}^{2}$ windows, $1000\times 1000$ cells), extracted from Google My Maps. These sections of such emblematic cities will be used to compute Shannon entropy and estimate the degree of disorder in cellular arrangements.

**Figure 5.**Entropy in configurations of different urban areas: Examples of blocks with nine cells are shown in red for selected areas in Rio and Manhattan, NY (left), and are amplified on the right. Rio shows a great deal of variation of configurations like (

**a**). In turn, configurations like (

**b**) are frequently found in Manhattan. Essentially, ${p}_{n}\left(k\right)$ in Equation (1) accounts for the number of times every possible configuration k appears in the map for a block of size n. A high frequency of certain configurations, like in Manhattan, brings the entropy measure closer to 0, i.e., to higher levels of physical order. This procedure for estimating entropy was applied for blocks with different sizes (i.e., number of cells, below on the right). Here, we show the first nine blocks; other block sizes were generated through this approach. Note that there is no unique natural way to scan a 2D matrix [45]. Different forms of interpolating cells do not seem to influence the estimation of ${H}_{n}$.

**Figure 6.**Measuring environmental information 1: estimated values of ${H}_{n}/n$ for areas in five selected cities. Continuous lines represent the best fitting of our data using the function: $a+b/{n}^{c}$. The fitted values of a give a reasonable extrapolation of the Shannon Entropy h of the dataset. Values are reported in the legend. The selected area in Rio de Janeiro shows the highest level of disorder (lower level of physical information) among areas in five selected cities.

**Figure 7.**Colours find their own palette of tones, becoming more diverse and contrasting in the passage from grey to colour scales, leading to an enormous increase in combinatorial possibilities. Photo: Vincent Laforet.

**Figure 8.**Semantic maps: real distribution (

**top**) and fictitious distribution (

**bottom**) of land uses in Porto Alegre’s central business district (CBD), Brazil. Corresponding ${H}_{j}^{m}$ values are shown on the right. Values shown on the right (from blue to red) are calculated with Equation 3. Values are calculated for $m=10$, with the cell j corresponding to a pixel of the maps on the left. The calculation is run over a gray-scale copy of the maps. Source: Authors based on [75].

**Figure 9.**Diagram of agents converging in a fictitious, nearly random distribution (

**left**), and in a real, patterned one (

**right**).

**Figure 10.**Entropy in interactions: histograms of probability distribution of action types show high levels of entropy at the start of simulations (

**left**) in two kinds of scenarios: where distance between activity places is not considered (blue line), and where distance is considered (red line). At the end of simulations (

**right**), scenarios where space is materially active show convergence around certain types of action, indicating a reduction of entropy in action coordination.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Netto, V.M.; Brigatti, E.; Meirelles, J.; Ribeiro, F.L.; Pace, B.; Cacholas, C.; Sanches, P.
Cities, from Information to Interaction. *Entropy* **2018**, *20*, 834.
https://doi.org/10.3390/e20110834

**AMA Style**

Netto VM, Brigatti E, Meirelles J, Ribeiro FL, Pace B, Cacholas C, Sanches P.
Cities, from Information to Interaction. *Entropy*. 2018; 20(11):834.
https://doi.org/10.3390/e20110834

**Chicago/Turabian Style**

Netto, Vinicius M., Edgardo Brigatti, João Meirelles, Fabiano L. Ribeiro, Bruno Pace, Caio Cacholas, and Patricia Sanches.
2018. "Cities, from Information to Interaction" *Entropy* 20, no. 11: 834.
https://doi.org/10.3390/e20110834