Games and Models

One course we offer is on game creation to teach modeling, computer codingart and game design more generally.

We will use Little Tip, Tolerance, Meadowkin as examples, but will start with simpler games, such as Tic Tac Toe. We make available first a simple Tic Tac Toe that we wrote in Scratch (a drag and drop type programming for young kids). More fun yet is our Bug in a Row (Tic Tac Toe Bugs) in Scratch.

We compare our NetLogo model of Tic Tac Toe for 2-humans, and a NettLogo human against the computer.


We also compare this to our Tic Tac Toe written in Python. The first python program is easy to follow but unnecessarily long code, with separate lines of code written for every possible win. To show how thinking about abstract and general mathematical patterns can make more concise and efficient code, we then show our very concise Tic Tac Toe program in Python. Our Tic Tac Toe computer simulations will then substitute spiders for X and a round bug for O, showing principles of abstraction and pattern. This is a simple art lesson. Students also learn simple game design.


We examine “game models,” first very simple zero player games such as Conway’s Game of Life and a model of segregation. Students proceed to learn more elaborate games, including writing rules, designing images and, if they wish, creating computer simulations. We make available an option to print student’s games on card board.

Our own board games come in a cardboard version, with beautiful art and fun stories, and in a computer simulation version. To see some samples, click on other tabs for all our games, including Tolerance, Meadowkin, Hunters and Grazers and Little Tip. For example, here’s our Little Tip simulation in NetLogo. Here’s our very simplified Little Tip in Scratch. In general, we present all our games in cardboard form along with simulations in Scratch, NetLogo and Python. You can choose the simple Scratch versions to get a feel for coding, a visually intuitive drag-and-drop block version. Or choose our NetLogo versions to get a bird’s-eye view of the global patterns resulting from our game models. Then you might use our Python versions to see how to code a game model in an advanced programming language. The choice is yours. Yet designing models can be done with cardboard game board models and so does not require computers. Students design their games, or alter our games, writing the rules as clearly and simply as they can. The experience with playing board games or designing their own sets down a foundation for moving on to computer coding the game models.

This course teaches application of technology, art, math and science to game models.

A cross-cutting theme, applied to the art and science of modeling, is simplicity, abstraction. Students will apply abstraction to art, to create almost iconic figures, such as spiders and bugs, and to modeling, creating the simplest possible coding. For example in tic tac toe, there are ways to create general algorithms which handle every possible combination. Students learn to simplify game rules, for human players, creating simple rules.

The other cross-cutting theme is pattern. All games that we explore in the course produce spatial patterns, and patterns over time. Math is the study of pattern. Science explains generation of patterns. We use Art to celebrate pattern, and illustrate principles of abstraction. The technology of computer simulations generates patterns. Patterns emerge from our game play. The patterns emerging from our game rules are “emergent” and complex (for all but the first game we use). Thus the games themselves are complex system models.

Most game models we examine (excluding tic tac toe) simulate dynamics found in nature, especially ecological and behavioral dynamics. Such models are a very important tool in science. Without such models, we don’t know what data to collect.

We created toy models for all levels of education. These toy models are low threshold and high ceiling, so there’s no age limit, this is trans-generational. There’s also hardly a limit to what you can do with toy models. Modeling is a central part of the New Generation Science Standards (NGSS), which builds upon the STEM approach of preparing for careers in Science, Technology, Engineering and Math. Our approach also builds upon aspects the IQWST (Investigating and Questioning our World through Science and Technology), which is highly modeling centered, but begins with students making claims (hypotheses) and incorporates a process of gathering evidence, in exploring real world phenomena.

Because the games and computer simulations are system models, our course also addresses engineering objectives. Thus, completing even one game project, naturally integrates S.T.E.A.M. (Science Engineering Technology Art Math).


How do life patterns emerge?

This big question is central in philosophy, science, and even religion.

Answering the big question involves taking two views, a bug’s-eye view, a closeup of parts and how they interact, and a bird’s-eye view of the whole patterns that emerge. The models we explore all take both these views, using game pieces and model components as the parts, and viewing the whole patterns emerging on the game board and computer screen.

Answering the big questions with games and models naturally streams together science, technology, reading, engineering, art and math (STREAM).

A course we offer focuses on models of patterns in nature, such as golden ratio spirals and Fibonacci numbers in flowers, and spots and stripes in animal fur, feathers, and so on. We first pose the question of how life patterns emerge. These are puzzles challenging students to figure out how to generate these patterns. Students take a shot an answer, make a “claim” about how they think these patterns emerge, then create drawings and a model. Drawings and paintings engage us in the patterns, provoking a sense of wonder and attention to detail. Then, we examine in detail well known models for generating these patterns. For example, we use a model of golden angle spiraling in sunflowers, pine cones and pineapples, in NetLogo and a similar golden angle spiraling model written in Python (Python is an advanced language used in all industries) and the same golden-angle spirals model in Scratch (Scratch is the simplest software, using drag and drop commands).

Likewise we examine a model for generating spots and stripes. This approach of asking questions, making claims and models addresses many New Generation Science Standards and takes an approach similar to Investigating and Questioning our World through Science and Technology. We use NetLogo first and then Python, with the idea that modeling in two different languages strengthens understanding.

For all ages and abilities

Scratch shows code visually with blocks that you can drag and drop to code games, stories, and robots (see our neighbots), a great introduction to NetLogo and Python.

Example: model of emerging spirals in: Scratch (click here) as well as NetLogo (click here) and Python (click here). Our other pages include many other examples. 


Our games have Scratch versions, drag and drop ease for young kids.  Many of our stories have Scratch versions. 


All our games have NetLogo versions, for large-scale global patterns.


We coded several of our models and games in Python, an elegant, advanced, widely used language.


Our cardboard games have extra pieces showing basics of coding the games.
Collective Action for Healthy Communities
Collective action is fascinating to study, but can produce complex patterns. Collective action can be difficult to model. Actions affect common conditions which, in turn, affect the next generation of actions. These interactions often produce complex patterns. For example, modeling social action for climate change is challenging because it involves collective action affecting collectively shared conditions. This challenges a variety of social or ecological issues and community health problems (in the background is collective action in Minneapolis City Hall for “black lives matter”). Below are models and overviews of chapters from my textbook on modeling collective action for healthy communities. This book and accompanying models are part of a course we offer on collective action for community health.