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"source": [
"**Connection to course-wide learning goals:**\n",
"\n",
"* _Gain insight into physical, biological, and social systems through the use of computational algorithms and tools_.\n",
" - Modeling the spread of information/rumors through a population using agent-based modeling.\n",
"* _Identify salient features of a system that be codified into a model_.\n",
" - Different neighborhoods are used to model the same phenomenon, turning rules of interactions into an algorithm.\n",
"* _Manipulate, analyze, and visualize datasets and use this data to evaluate models_.\n",
" - Create visualizations and animations of our system, interpret model behavior from these visualizations and note interesting results.\n",
"* _Have an understanding of basic numerical methods and be able to use them to solve problems_.\n",
" - Using agent-based modeling to model a system.\n",
"* _Be able to take results from a scientific computing problem and present it both verbally and in writing_.\n",
" - Describe and discuss the results of your models, comparing and contrasting models with different input parameters.\n",
"\n",
"**Assignment-specific goals:**\n",
"* More practice with agent-based modeling\n",
"* Work on exploring different kinds of interactions in a model (i.e., using a Von Neumann neighborhood and a Moore neighborhood)\n",
"* Identifying and comparing the \"tipping points\" for different models"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Assignment instructions\n",
"\n",
"Work through the following assignment, making sure to follow all of the directions and answer all of the questions.\n",
"\n",
"**This assignment is due roughly three weeks from now at 11:59pm on Sunday, March 17th.** It should be uploaded into the \"Homework Assignments\" dropbox folder for Homework #4. Submission instructions can be found at the end of the notebook."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Grading\n",
"\n",
"\n",
"* Part 1: Basic model (29 points)\n",
" \n",
"* Part 2: Improving the model (8 points)\n",
" \n",
"* Part 3: Wrap up (3 points)\n",
"\n",
"* Bonus -- Part 4: Challenge Problem (4 bonus points)\n",
"\n",
"Total points possible: **40 (+4 bonus points)**\n",
"___"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src=\"http://foolishwisdom.com/wp-content/uploads/2014/02/Gossip.jpg\" alt=\"shocking rumor!\" width=400px>\n",
"\n",
"**Overview of the Assignment:**\n",
"\n",
"In this homework, you will be continuing to learn about constructing agent-based models (ABM's) in a new and interesting context. So far in class, we have used ABM's to model the spread of a forest fire and social dynamics by constructing the Schelling model. Here, we are going to model the spread of information or a rumor through a population of people, which we will refer to as a city or a board in this assignment (we might use these terms interchangeably, but we are referring to the same thing). This model will introduce a few new concepts of building agent-based models. Namely, we will be working with different kinds of \"neighborhoods.\" We will also be constructing a [_stochastic_](https://en.wikipedia.org/wiki/Stochastic) model if you so choose to work on the challenge problem at the end. Stochastic models are used [often when modeling scientific phenomena](https://en.wikipedia.org/wiki/Stochastic#Natural_science), so we felt that it would be a good idea to introduce this concept in the context of the model we are going to be building in this homework. Basically, this means that our model is going to include a little bit of random numbers and probabilities in it. We haven't worked with random numbers in class yet, but don't worry, the focus of this assignment is going to be on the agent-based modeling. Any code using random numbers will be provided for you and explained so you can focus on further developing your understanding of ABM's."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Background - What are we building?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At this point in your life, you have probably experienced the phenomena of how quickly information can spread from individual to individual. This could include:\n",
"* News travelling fast once a report has been released. People either see it on their news feed and share it on social media, which lead others to read it and perhaps do the same. Or, people talk about it in public settings, which lead others to search the piece of news on Google and read up on it.\n",
"* A rumor or piece of gossip is discussed openly. Someone overhears it and goes and tells other individuals. All of a sudden, everyone knows the hot gossip now!\n",
"* Within a circle of friends, drama between individuals can be discussed by others in the group. Like a game of telephone, the information can get distorted and now all of a sudden, people are mad about things that may have never happened or have been said.\n",
"\n",
"These are just a few examples of what we are going to try and model in this assignment. **How can we describe the spread of information throughout a population of individuals? What can we learn from a model such as this?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"# 1. Basic Model - \"Spreading like Wildfire\" (29 points)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first way we are going to try and model this phenomena is going to be very similar to how we modeled the forest fire in class. Good news, if you understood how we constructed this model and got it working in class, then this part of the assignment should go very quickly for you! If not, more good news: you get another opportunity to practice!\n",
"\n",
"In this model, an individual who is \"on fire\" (knows the information) and spreads that \"fire\" (information) to the individuals surrounding them. Specifically, they spread this information to the neighboring individuals who are in their [_Von Neumann Neighborhood_](https://en.wikipedia.org/wiki/Von_Neumann_neighborhood). This refers to the individuals who are directly above, below, and to the right or left of a given person (as described by agents on a board). A diagram of this is given below.\n",
"\n",
"<img src=\"https://i.imgur.com/TwcKZ0D.png\" alt=\"vonneumann\">\n",
"\n",
"Here's what we need to do to build this model. These steps should look very familiar to what we did in class with the forest fire model.\n",
"\n",
"1. We need to construct our city of individuals. There are **many** ways that we can do this. One possible solution would be to make a 2D NumPy array and fill it full of random numbers which range 0 to 1 (is there a NumPy tool we can use to do this quickly?). Once we have this array, we should change some of the values to 1 to represent people being there (how should we do this? Loops? Masking?). The rest of the values should be set to 0 to represent the lack of an individual. We'll talk more about this in the sections to come.\n",
"2. We're going to need to make a lot of visualizations of our city, so before we get going too far into this, let's also make a function to visualize our agents.\n",
"3. We are going to need some way of determining the neighbors of an individual.\n",
" 1. We first need a way to determine all of the neighboring indices of an individual in our city. These are going to be the possible individuals that they can interact with.\n",
" 2. Once we have all of those indices, we need to check to make sure they're \"on the board\" (in class, when we modeled the forest fire, we had to be careful with the edges of our array so we didn't reference indices that were off of the array).\n",
"4. We need the rumor or information to start somewhere. In the forest fire model, we designated an entire edge of the array as \"on fire\" and let it spread from there. In this model, we are going to start the rumor somewhere in the middle of the board at a single individual and let it spread from there.\n",
"5. Then we need to write some loops to update our board. Specifically, for each individual on the board, if they know the information, they need to spread it to those around them. We then have to repeat this process a number of times to represent some passage of time that we allow the information to spread (e.g., hours, days, weeks).\n",
"\n",
"\n",
"This sounds like a lot of work, but we are going to break this down piece by piece. If you have code from class that you think accomplished these tasks already, then feel free to copy and paste that here.\n",
"\n",
"**Just make sure you make a note that you took the code from another notebook** (e.g., `##Taken from in-class day 11`)."
]
},
{
"cell_type": "code

Artificial Intelligence Searching like a homo sapien (a.k.a., a...