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Relativity NG

by Matthew Banks (Submitted: 03/20/2011)

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WHAT IS IT?

This simulation is an attempt to simulate special- and general-relativistic effects in NetLogo. In its current form, it is essentially only a demonstration, modeling a relativistic cellular automaton.

HOW IT WORKS

The cells are running the "Brian's Brain" cellular automaton. Each cell can have one of three states: 0, 1, or 2. Cells in state 0 switch to state 1 if they have exactly two neighbors (horizontally and diagonally) in state 1. Cells in state 1 switch to state 2. Cells in state 2 switch to state 0.

At setup, each cell is assigned a "delay" parameter based on the following equation:

Delay = (Distance from Center) / (Speed of Light)

The speed of light can be controlled by the "c" slider. (NOTE: If the value of c is equal to or less than 1, that means that the objects generated by the cellular automaton are capable of moving at or faster than the speed of light, which is not realistic.)

In "Newtonian" mode, the visualization is updated normally (that is, the state of each cell is displayed as it is at that timestep).

In "Special Relativistic" mode, the visualization is updated according to the delay value of the cells. Cells which are too far from the center for their light to have reached the center are drawn as gray. Cells which are visible to the observer are shown as they existed *Delay* timesteps ago. This simulates the effects of the finite speed of light.

In "General Relativistic" mode, cells in state 1 are treated as though they have mass, effectively increasing the delay value for all cells within 2 cells of them. This is a grossly oversimplified approximation of general relativity, but it demonstrates the kinds of effects seen with real astronomical objects such as galaxies and galaxy clusters.

THINGS TO TRY

Start the simulation in Newtonian mode and observe the structures that emerge from the cellular automaton. Then, switch to Special Relativistic mode and observe the differences in the structures' appearances. Note how objects moving towards the observer appear much wider than objects moving away. This may be a relativistic effect. Then switch to General Relativistic mode and observe how the mass distribution of the objects affects their appearance.

CREDITS AND REFERENCES

Coded by Matthew Banks. http://asymptote.wordpress.com

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