Screenshot CUDA / OpenGL Demo of Gravitation Map Simulator |

This is just another fun demo for CUDA and OpenGL. It is a slightly modified version of the so called "random oscillating magnetic pendulum" (ROMP). A pixel represents a start position of one particle. This object becomes attracted by all the planets around due to their gravity. After a while the object is going to hit a planet. Now that corresponding pixel gets the color of that planet. You see an evolving map of "gravity" structures in realtime (more or less *cough*).

**Download:**(tested on Linux and Windows (VS2010), needs CUDA, OpenGL, GLUT, GLEW)

Download Source Code v1.1

Download Source Code v1.0

Positions and masses of the planets can be changed by the user as well as the scale of the map.

The simulation uses Euler or Runge-Kutta integration method for solving the
differential equation. It is also possible to use doubles instead of
floats for better precision.

The idea for this demo comes from a friend, he also implemented the algorithm in processing. I ported this to CUDA, so the stuff is entirely computed and rendered on the GPU. You need a Nvidia CUDA capable GPU for that.

The idea for this demo comes from a friend, he also implemented the algorithm in processing. I ported this to CUDA, so the stuff is entirely computed and rendered on the GPU. You need a Nvidia CUDA capable GPU for that.

Screenshot 2.1, different coloring |

Screenshot 2.2 |

### Computation

Given a particle at position at a time t. This particle has a (positive) mass m. In our space there are n planets with their fixed positions and (positive) masses .The following equation represents the gravitational force of planet i acting on our particle. This force comes from Newton's law of universal gravitation:

This integration can be solved numerically, e.g. by Euler's method:

with and as the initial values. h is the size of every step and v represents the velocity of the particle.

Here you see some videos, which are showing the simulation more or less in realtime.

More:

Article by Ingo Berg, 2006, on magnetic pendulum with implementation (using Beeman's algorithm):

http://www.codeproject.com/Articles/16166/The-magnetic-pendulum-fractal

Mathematica implementation:

http://nylander.wordpress.com/2007/10/27/magnetic-pendulum-strange-attractor/

Some more stuff, videos:

http://magnetmfa.wikispaces.com/pendula?responseToken=05ae0f7708a5c4c989455051dc970f570

http://www.youtube.com/watch?v=duy8s8C7-Uc

http://www.youtube.com/watch?v=QXf95_EKS6E

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