Math for Programmers

11 Simulating force fields

This chapter covers

• Modeling forces like gravity using scalar and vector fields
• Calculating force vectors using the gradient
• Taking the gradient of a function in Python
• Adding gravitational force to the asteroid game
• Calculating gradients and working with vector fields in higher dimensions

There has just been a catastrophic event in the universe of our asteroid game: a black hole has appeared in the center of the screen! As a result of this new object in our game, shown in figure 11.1, the spaceship and all of the asteroids will feel a “gravitational pull” toward the middle of the screen. This makes the game even more challenging, and it gives us a new mathematical challenge as well−understanding force fields.