Constellations: Preliminary Design

Because I am way too excited to begin work on this, I thought I'd go ahead and be the first to submit my idea for the game jam. For those of you who don't know me, please see my previous introduction for Crossword-Z here!

Title:   Constellations
Catchphrase:   "Graphs in the Sky"
Type:   Puzzle Game!
Inspiration:   Flow (Android/Apple top-selling game)

Idea Behind the Game:
Recently I've become very interested in Graph Theory, precisely because it lends itself to so many different puzzles and interesting questions. I think that there is so much that can be visualized in Graph Theory that it is a shame that there isn't already an app that allows you to learn by seeing, touching, and experimenting with graphs. Thus Constellations was born as a solution to this problem.

Theme:   The idea for the theme is that the player is looking out her window and tracing graphs through the stars. I believe that there is so much beauty in graph theory in that it is a powerful tool for visualizing the relationships of our world. I want the art and style of my game to to capture this beauty, and there is no more beautiful a graph in nature than the constellations. I want the player to become immersed in a starry night sky and feel time pass slowly by as she relaxes and observes the constellations she creates. To make this atmosphere I will use a dark palette with quiet colors and storybook art and bright white stars in the sky (See the screenshot below for an example). I will also include some relaxing, non-vocal music playing in the background to fully immerse the player in the experience. I'm thinking of sampling some tracks by the Japanese band Mono, who have a very quiet, fantasy sound.

The puzzle screen, with an example graph drawn in the sky.

Mechanics:   My idea for this game jam is to create a number of interesting levels based around two different game modes: Create and Traverse.

• In the Create puzzles, the player will be given certain restraints (such as a degree sequence), and then they are told to draw a graph that meets all of the requirements. I want as many of these puzzles as possible to have multiple solutions, or even some solutions that better meet the requirement (such as, "a connected graph that has the fewest possible edges") to allow the player to experiment and improve upon her solutions.
• In the Traverse puzzles, the player will be given a Constellation, and told to analyze it in some way (such as finding the shortest path). Again, for most of these puzzles I want the player to have the option to experiment and improve upon their solutions. The game will only tell the player if their solution does not meet the criteria, but it will not tell her if it is sub-optimal.

Goals:   I want to make this game educational in that playing will serve as an introduction to the topics and ideas of Graph Theory. However, I don't want the game to feel like a textbook. Instead, I want the game to be an interactive experiment, where the player can learn herself by pushing for optimal solutions in each puzzle. To this end, I have a few ideas for how to incorporate an educational component:

1. Make the many theorems of Graph Theory unlockable as "achievements" when a player creates a graph that demonstrates knowledge of the theorem.
2. Include narration that comments on each puzzles after a solution is reached. This would just be enough to get the player curious, but not require a great deal of advanced mathematics to understand.
3. Include a "Storybook" section that gradually fills with information as levels are cleared. I would model this book as a student's journal that she gradually fills up with thoughts about the constellations shes sees. I could even include hints about to how to improve solutions that are less than optimal.

With all of these elements, I want the game itself to be a guide, not a lecturer. I want all insights to come from the player, so that she can learn on her own without being taught. I think that interaction and discovery are the best ways for anybody to learn a subject, and that's what I want this game to be about.