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## 1. Introduction to ABM
						
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						## 1.1 A teaser: Schelling's segregation model

<a href="https://ncase.me/polygons" target="_blank">
							<img src="assets/images/ncase-shelling.PNG" alt="ncase-shelling" style="width: 450px; border: none; box-shadow: none; vertical-align:super">
						</a>
						<a href="http://ccl.northwestern.edu/netlogo/models/Segregation" target="_blank">
							<img src="assets/images/Segregation Simple interface.png" alt="shelling-netlogo" style="width: 350px; border: none; box-shadow: none">
						</a>
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						## 1.2 ABM as a tool for complexity
						
						<a title="Acadac, Public domain, via Wikimedia Commons" href="https://commons.wikimedia.org/wiki/File:Complex-adaptive-system.jpg"><img width="512" alt="Complex-adaptive-system" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/00/Complex-adaptive-system.jpg/512px-Complex-adaptive-system.jpg?20050529073219"></a>
						
						[Complex systems](https://en.wikipedia.org/wiki/Complex_system) | [Complex adaptive systems](https://en.wikipedia.org/wiki/Complex_adaptive_system)

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						## 1.2 ABM as a tool for complexity
						### How does ABM help us to study complex systems?

*   **Formalizing definitions** of elements within the system.
						*   Defining **rules as algorithms** to govern interactions between elements.
						*   Simulating a **population as distributed processes**.
						*   Creating a **bottom-up approach to modelling** to study emergent properties.
						*   Incorporating **stochasticity** to generate probabilistic results.

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						## 1.2 ABM as a tool for complexity
						<a href="https://link.medium.com/1uqbZW0M2T" target="_blank"><img src="https://cdn-images-1.medium.com/max/1600/1*yrVzKSeqaA1O3G3HF-AHlw.gif">
 Flocking behaviour in 'Behavioral systems' by Danil Nagy in 'Generative Design', medium.com</a>

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						## 1.2 ABM as a tool for complexity
						### What can we study with ABM?

*   Tool for social science
							- interactions/behaviours and emergence/structure
							- mentality and agency
							- cultural evolution
							- social norms and institutions
						
						*   Tool for socio-ecological systems
							- Spacially explicit environment and resources
							- Human and non-human agency
							- Handling coupled human-environment systems feedbacks
						
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						## 1.3 ABM as mathematical models

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						## 1.3 ABM as mathematical models
						### A simple example: a linear regression model

>y = a + b·x
						
						![Geometric representation of a linear regression model](assets/images/LinearModel.png)
						<a title="Krishnavedala, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons" href="https://commons.wikimedia.org/wiki/File:Linear_least_squares_example2.svg"><img width="256" alt="Linear least squares example2" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Linear_least_squares_example2.svg/256px-Linear_least_squares_example2.svg.png?20110610033522"></a>
						
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						## 1.3 ABM as mathematical models
						### Francis Anscombe's quartet
						
						<a title="Anscombe.svg: Schutz
(label using subscripts): Avenue, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons" href="https://commons.wikimedia.org/wiki/File:Anscombe%27s_quartet_3.svg"><img width="512" alt="Anscombe's quartet 3" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Anscombe%27s_quartet_3.svg/512px-Anscombe%27s_quartet_3.svg.png?20100326171813"></a>

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						## 1.3 ABM as mathematical models
						### Spurious correlations

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						## 1.3 ABM as mathematical models
						### Example: modelling a watering can

<a title="Santeri Viinamäki, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons" href="https://commons.wikimedia.org/wiki/File:Green_watering_can.jpg">
						<img width="256" alt="Green watering can" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Green_watering_can.jpg/512px-Green_watering_can.jpg"	style="border: none; box-shadow: none;"></a>
						          <img width="256" alt="Picture maze solving -observations" src="assets/images/Picture_maze_solving_observations.png" style="border: none; box-shadow: none; margin-bottom: -2%;">

Target reality      |      Observations

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						## 1.3 ABM as mathematical models
						### Example: modelling a watering can

A model that returns...

<img width="256" alt="Picture maze solving - descriptive model" 
						src="assets/images/Picture_maze_solving_descrip-model.png"
						style="border: none; box-shadow: none; margin-bottom: -2%;">                 <a title="Original: User:Icey, Animation: User:MichaelFrey, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons" href="https://commons.wikimedia.org/wiki/File:Picture_maze_solving.gif">
						<img width="256" alt="Picture maze solving - explanatory model" src="https://upload.wikimedia.org/wikipedia/commons/b/b2/Picture_maze_solving.gif" style="border: none; box-shadow: none; margin-bottom: -2%;"></a>

the output given the input        |    ... **and the definition of a mechanism**
						
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						## 1.3 ABM as mathematical models
						
						<img src="https://github.com/Andros-Spica/modelling-simulation-graphs/blob/main/from-model-to-simulation-models/from-model-to-simulation-models_p2.png?raw=true" alt="models to math models"
					style="width: 550px; border: none; box-shadow: none; margin-bottom: 0%; background-color: azure;"/>

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						## 1.4 ABM as simulation models

>"A simulation is an **imitative representation of a process or system** that could exist in the real world. In this broad sense, simulation can often be used interchangeably with model. Sometimes a clear distinction between the two terms is made, in which simulations require the use of models; the model represents the **key characteristics or behaviors** of the selected system or process, whereas the simulation represents the **evolution of the model over time**. Another way to distinguish between the terms is to define simulation as experimentation with the help of a model." *Simulation*, [Wikipedia](https://en.wikipedia.org/wiki/Simulation)

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						## 1.4 ABM as simulation models
						### 1.4.1 Algorithmic process

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						## 1.4 ABM as simulation models
						### 1.4.1 Algorithmic process

![Pseudo-code for the Gale–Shapley algorithm to solve the [Stable Marriage Problem](https://en.wikipedia.org/wiki/Stable_marriage_problem)](assets/images/Gale-Shapley-algorithm.png)
						
						Pseudo-code for the Gale–Shapley algorithm to solve the [Stable Marriage Problem](https://en.wikipedia.org/wiki/Stable_marriage_problem)

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						## 1.4 ABM as simulation models
						### 1.4.2 Distributed processes

<a href="http://jasss.soc.surrey.ac.uk/12/1/1.html" target="_blank"><img src="http://jasss.soc.surrey.ac.uk/12/1/1/fig1.jpg" alt="Galan et al. 2009" style="width: 450px; border: none; box-shadow: none"> Galan et al. 2009</a>

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						## 1.4 ABM as simulation models
						### 1.4.2 Distributed processes

<a href="https://www.gisagents.org/2016/10/agent-based-modeling-in-geographical.html" target="_blank">Heppenstall and Crooks 2016</a> | <a href="http://jasss.soc.surrey.ac.uk/14/3/7.html" target="_blank">Rebaudo et al. 2011</a>

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						## 1.4 ABM as simulation models
						### 1.4.3 Stochasticity

<a href="https://www.google.com/url?sa=i&url=https%3A%2F%2Fstatisticsbyjim.com%2Fbasics%2Fnormal-distribution%2F&psig=AOvVaw38IuTrWyj0a4a-cCG0O_ms&ust=1760550183519000&source=images&cd=vfe&opi=89978449&ved=0CBgQjhxqFwoTCLDV49mepJADFQAAAAAdAAAAABAE" target="_blank"><img src="https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2018/04/pizza_delivery.png" alt="Normal distribution - example of pizza delivery" style="width: 550px; border: none; box-shadow: none; margin-bottom: 0%; background-color: azure;"/></a>
						
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						## 1.4 ABM as simulation models
						### Random number generators

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						## 1.4 ABM as simulation models
						### 1.4.4 A point of comparison
						
						[Lotka-Volterra predator-prey model](https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations)

![Lotka-Volterra predator-prey model](assets/images/LV-predator-prey-equations.png)
						<a title="AspidistraK, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons" href="https://commons.wikimedia.org/wiki/File:Lotka_Volterra_dynamics.svg"><img width="400" style="background-color: white" alt="Lotka Volterra dynamics" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/Lotka_Volterra_dynamics.svg/512px-Lotka_Volterra_dynamics.svg.png"></a>

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						## 1.4 ABM as simulation models
						### 1.4.4 A point of comparison
						
						[NetLogo's Wolf-Sheep Predation model](http://ccl.northwestern.edu/netlogo/models/WolfSheepPredation(DockedHybrid))
						
						<a title="SethTisue, GPL <http://www.gnu.org/licenses/gpl.html>, via Wikimedia Commons" href="https://commons.wikimedia.org/wiki/File:Netlogo-ui.png"><img width="512" alt="Netlogo-ui" style="width: 450px; height: 350px; object-fit: cover; object-position: 0% 0%;" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Netlogo-ui.png/512px-Netlogo-ui.png"></a>

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						## 1.5 ABM? It's probably multiparadigm modelling

Bissett et al. 2021. ‘Agent-Based Computational Epidemiological Modeling’. Journal of the Indian Institute of Science 101 (3): 303–27. [https://doi.org/10.1007/s41745-021-00260-2](https://doi.org/10.1007/s41745-021-00260-2).

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						## 2. ABM in archaeology
						### 2.1 A transdisciplinary field
						
						* Adapts well to research spanning multiple disciplines and scales. 
						* Can handle multiple layers of entities, relationships or even submodels.
						* Also used in Ecology, Economics, Sociology, Environmental Science, Geography, etc.

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						## 2. ABM in archaeology
						### Socio-ecological systems (SES)

* SES: the complex interplay between human societies and their environments
						* Archaeological questions from prism of complex adaptive systems (CAS)
						* ABM of SES has been prolific in archaeology since the 2000s
						* But this has also limited the field's theoretical diversity and scope

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						## 2. ABM in archaeology
						### 2.2 Domains of application and examples
						**Physico-chemical dynamics**
						* Artefact production
						* Site formation

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						## 2. ABM in archaeology
						### 2.2 Domains of application and examples
						**Ecological dynamics**
						* Climate patterns
						* Soils
						* Hydrological dynamics
						* Vegetation
						* Non-human animal behaviour
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						## 2. ABM in archaeology
						### 2.2 Domains of application and examples
						**Anthropological dynamics**
						* Individuals
						* Groups
						* Settlements
						* Regional to global

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						## 2. ABM in archaeology
						### 2.3 Examples
						<img src="assets/images/ArtificialAnasazi.PNG" alt="Artificial Anasazi" style="width: 400px; border: none; box-shadow: none; vertical-align:super">
						   <img src="https://jasss.soc.surrey.ac.uk/12/4/13/figure4.jpg" alt="Artificial Anasazi" style="width: 500px; border: none; box-shadow: none; vertical-align:super">
						 "Artificial Anasazi" (Axtell et al. 2002; Janssen 2009)
						
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						## 2. ABM in archaeology
						### 2.3 Examples
						<img src="assets/images/griffin-et-al-2010-fig1.PNG" alt="Griffin et al. 2010, Fig. 1" style="width: 450px; border: none; box-shadow: none; vertical-align:super">
						   
						<img src="assets/images/griffin-et-al-2010-fig6b.PNG" alt="Griffin et al. 2010, Fig. 6b" style="width: 450px; border: none; box-shadow: none; vertical-align:super">
						 "HOMINIDS" (Griffith, Long, and Sept 2010)
						
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						## 2. ABM in archaeology
						### 2.3 Examples
						<img src="assets/images/Barton-et-al-2012-fig2.PNG" alt="Barton et al. 2012, Fig. 2" style="width: 450px; border: none; box-shadow: none; vertical-align:super">
						   
						<img src="assets/images/Barton-et-al-2012-fig12bc.PNG" alt="Barton et al. 2012, Fig. 12" style="width: 450px; border: none; box-shadow: none; vertical-align:super">
						 "MedLanD" (Barton et al. 2012)
						
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						## 2. ABM in archaeology
						### 2.3 Examples
						<img src="assets/images/Rogers-et-al-2012-fig1.PNG" alt="Rogers et al. 2012, Fig. 1" style="width: 450px; border: none; box-shadow: none; vertical-align:super">
						   
						<img src="assets/images/Rogers-et-al-2012-fig5.PNG" alt="Rogers et al. 2012, Fig. 5" style="width: 450px; border: none; box-shadow: none; vertical-align:super">
						 "HouseholdsWorld" (Rogers et al. 2012)
						
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						## 2. ABM in archaeology
						### 2.3 Examples
						<img src="https://jasss.soc.surrey.ac.uk/16/4/11/Figure1.png" style="width: 400px;">
						   
						<img src="https://jasss.soc.surrey.ac.uk/16/4/11/Figure3.png" style="width: 400px;">
						 "MayaSim" (Heckbert 2013)

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						## 2. ABM in archaeology
						### 2.3 Examples
						<img src="https://pub.mdpi-res.com/quaternary/quaternary-05-00025/article_deploy/html/images/quaternary-05-00025-ag.png?1651888892" style="width: 400px; border: none; box-shadow: none; margin-bottom: 0%;" alt="Angourakis et al. 2022, graphical abstract"/>
						   
						<img src="https://github.com/Andros-Spica/indus-village-model/blob/master/diagrams/RoadMapSoFar_2022-06.png?raw=true" style="width: 400px; border: none; box-shadow: none; margin-bottom: 0%;" alt="Andros-Spica/diagrams/RoadMapSoFar_2022-06.png"/>
						 "Indus Village" (Angourakis 2021; Angourakis et al. 2020; Angourakis, Bates, et al. 2022; Angourakis et al. 2025)

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						## 2. ABM in archaeology
						### 2.4 Unfinished business: representation and validation

* Unsolved debate: How descriptive and explanatory should a model be?
						* Representation: How to represent the (**past**) real world in a model?
						* Validation: How to know if a model is good?

**Modelling** is about *structuring your thoughts about the world*
						
						**mathematical modelling** is doing that with *extra discipline*
						
						**Simulation modelling** is doing that specifically for *reconstructing processes*, 
						stories, or, in other words, the mechanisms presumably behind the semi-static reality we observe 
						(e.g., archaeological materials).
						
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						## 2. ABM in archaeology
						### Non-simulation computational modelling in archaeological research
						<img src="https://github.com/Andros-Spica/modelling-simulation-graphs/blob/main/representation-and-validation/representation-and-validation_notSimulation.png?raw=true" alt="types of math models" style="width: 650px; border: none; box-shadow: none; margin-bottom: 0%; background-color: azure;"/>
						
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						## 2. ABM in archaeology
						### Simulation modelling in archaeological research
						<img src="https://github.com/Andros-Spica/modelling-simulation-graphs/blob/main/representation-and-validation/representation-and-validation.png?raw=true" alt="types of math models" style="width: 650px; border: none; box-shadow: none; margin-bottom: 0%; background-color: azure;"/>

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						## 3. Readings
						Pick a paper and read it! 
						<img src="https://i0.wp.com/nariyoo.com/wp-content/uploads/2024/04/image-28.png?w=700&ssl=1" alt="cartoon about reading procastination" style="width: 350px; border: none; box-shadow: none; margin-bottom: 0%; background-color: azure;"/>
						 We will discuss the paper you read. 
						
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						## 5. Questions?