We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 26 October 2009
Why cellular automata are useful in physics
The purpose of this section is to show different reasons why cellular automata may be useful in physics. In a first paragraph, we shall consider cellular automata as simple dynamical systems. We shall see that although defined by very simple rules, cellular automata can exhibit, at a larger scale, complex dynamical behaviors. This will lead us to consider different levels of reality to describe the properties of physical systems. Cellular automata provide a fictitious microscopic world reproducing the correct physics at a coarse-grained scale. Finally, in a third section, a sampler of rules modeling simple physical systems is given.
Cellular automata as simple dynamical systems
In physics, the time evolution of physical quantities is often governed by nonlinear partial differential equations. Due to the nonlinearities, solution of these dynamical systems can be very complex. In particular, the solution of these equation can be strongly sensitive to the initial conditions, leading to what is called a chaotic behavior. Similar complications can occur in discrete dynamical systems. Models based on cellular automata provide an alternative approach to study the behavior of dynamical systems. By virtue of their simplicity, they are potentially amenable to easier analysis than continuous dynamical systems. The numerical studies are free of rounding approximations and thus lead to exact results.
Crudely speaking, two classes of problem can be posed. First, given a cellular automaton rule, predicts its properties.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
