# Game Workshop

• Human beings are never more ingenious than in the invention of games.
• I strongly approve the study of games of reason, not for their own sake, but because they help to perfect the art of thinking.
• Even in the games of children there are things to interest the greatest mathematician. (Leibniz)

#### Role of Games

Games represent interaction of one or more players with a symbolic or real model, such as a game of cards or a ball game.  Games serve a basic role in DigiMat to express interaction between human mind and mathematical model in computational form, where mind reacts to output from computation to give input to new computation in a feed back loop. In Angry Birds the player chooses initial data for sling shot aiming to hit a chosen target and the corresponding trajectory is computed by time stepping Newton’s laws of motion which gives feed back to the player to change initial data until hit.

Interaction with a mathematical model in symbolic form typically is difficult, while interaction with a mathematical model in computational form typically is direct  and informative.

#### Role of Simulators

Simulators are interactive computer games used for training to meet challenges in real life, including flight simulators and surgery simulators.

Real Flight Simulator is DigiMat software which captures the true action of an airplane by computational solution of Euler’s equations expressing first principle physics, as the first simulator with this capability.

#### Physics Engines

Game programming often takes the help of physics engines (such as matter.js or Algodoo) as software handling the interaction/collision of mechanical bodies. Here we refrain from using these tools and instead construct (simple) physics engines from scratch to exhibit the core.  At a later stage physics engines can then be used with insight and not only as black box.

#### List of Games

Play game to discover the math behind the game. You may need to initialise game by clicking game name and pressing start arrow.

To do:

• 1d Pong Game for Two Players.
• PinBall (use e g Colliding Balls with one ball free, the other fixed)
• Bungy Jump (start e g from Elastic String of Beads)
• Develop the above games further.
• Invent your own games based on mathematics, with inspiration from  Model Workshop or the world or web.

Everything that is possible demands to exist. (Leibniz)