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Programming Mathematical
Models…with NetLogo
Juan Carlos García Vázquez / Fernando Sancho Caparrini
5ª Escuela Internacional de Verano de Matemáticas (5ª EIVM)5th International Summer School of Mathematics (5th ISSM)
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
What we will see today…
Modeling + Experimentation in MathematicsProblem + Tool
Complex System + Computational ModelCellular Automata + Multiagent System
(NetLogo)
On Problem Modeling
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Discovering the World
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Discovering the World
ScientificMethod
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Discovering the World
ScientificMethod
• Observation• Hypotheses Formulation• Experimentation• Theses (or refutation)
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Modeling the World
Real World
Models
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
What is a Model
A model is an abstract representation of some concrete aspects of “reality”. It consists of:• The elements that characterize the aspects of the modeled reality, and• The relations between these elements
• Mathematical Theories
• Numerical Models
• Computational Models
Mathematical Modeling
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Modeling ProcessPhenome
non
FormalizationModel
Interpretation
Implementation
Evaluation
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Modeling Process: NetLogoPhenome
non
FormalizationModel
Implementation
Evaluation
NetLogo
Interpretation
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Modeling Process: NetLogoPhenome
non
FormalizationModel
Implementation
Evaluation
NetLogo
Interpretation
This is what
we do in Mathemati
cs!!!
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Selecting a Problem…• One hard… really hard• In the limit of standard Mathematics• One we can find everywhere• Pure and Applied… at a time• Where we can make experiments and provide
hypotheses
Complex Systems
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
What is a Complex System?
Science of Complex Systems tries to describe different systems (biological, mathematical, social, physical,…) emphisizing their decomposition in simple elements and the interactions between them, and in the emergence of behaviours that are not a priori predictable by using the current tolos (mathematical, theoretical, etc.).
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
What is a Complex System?
They are everywhere…
… think and say…
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Cellular Automata: A “Simple” Complex System
1D All the cells work on a parallel and
synchronized way
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Cellular Automata: A “Simple” Complex System
1D All the cells work on a parallel and
synchronized way Some Questions:• Can you enumerate 1D
CA?• How many 1D CA can
you build?• Can you think in
methods to create variants of 1D CA?
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Cellular Automata: A “Simple” Complex System
2D
All the cells work on a parallel and
synchronized way
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Cellular Automata: A “Simple” Complex System
2DSome Questions:• Can you enumerate 2D
CA?• How many 2D CA can
you build?• Can you think in
methods to create variants of 2D CA?
NetLogo: A Modeling Tool
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
3 Types of AgentsAgent
• Artificial and autonomous Individual.• Endowed with rules governing their behavior and their ability to make decisions.• Interact between them and with the environment.
Environment
Agent
Links
Interactions
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
3 Types of Agents
Patches
Turtles
Links
Interactions
Agent
• Artificial and autonomous Individual.• Endowed with rules governing their behavior and their ability to make decisions.• Interact between them and with the environment.
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Patches World• Rectangular 2D World tessellated by patches• Associated coordinate system• Several topologies
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Patches World• Rectangular 2D World tessellated by patches• Associated coordinating system• Several topologies
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Patches WorldWorld Settings View Settings
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Patches World
Properties:• (pxcor, pycor)• pcolor• plabel, plabel-color
InspectPatch
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Let’s Go!!
We will use patches to model a specific (and very interesting) type of 2D Cellular Automata:• The behavior of every cell depends on:• The cell is alive or not, and• How many neighbors are alive
•… and then we will play with a concrete case called Game of Life
J. Conway
5ª Escuela Internacional de Verano de Matemáticas / 5th International Summer School of Mathematics (5th EIVM)
Conways’ Game of Life
• A live cell stays alive if it has 2 or 3 live neighbors, otherwise it died
• A dead cell comes to life if it has exactly 3 live neighbors, otherwise it stays dead