Cosmology: Difference between revisions
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In the context of [[cellular automata]], [[cosmology]] is the study of the ultimate fate of patterns over time. | In the context of [[cellular automata]], [[cosmology]] is the study of the ultimate fate of patterns over time. | ||
An early classification | An early cosmological classification was introduced in [[Lifeline Volume 2]], aiming to cover all Life patterns according to the [[ash]] they produce: | ||
# Patterns that eventually die out entirely. | # Patterns that eventually die out entirely. These are known as '''[[sparks]]''' or '''[[diehard]]s'''. | ||
# Patterns that eventually stabilize in a constellation of periodic, unmoving objects ([[still life]]s and [[oscillator]]s). | # Patterns that eventually stabilize in a constellation of periodic, unmoving objects ([[still life]]s and [[oscillator]]s). | ||
# Patterns that eventually create a set of periodic, moving objects ([[spaceship]]s) that escape to infinity. Known as '''[[pure glider generator]]s'''. | # Patterns that eventually create a set of periodic, moving objects ([[spaceship]]s) that escape to infinity. Known as '''[[pure glider generator]]s'''. | ||
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This leaves out as interesting edge cases patterns that do not stabilize into ash and instead show more complex long-term behavior. Examples of such behavior include all [[infinite growth]] patterns, such as [[gun]]s, [[sawtooth]]s, and [[spacefiller]]s; but also some patterns with bounded population. | This leaves out as interesting edge cases patterns that do not stabilize into ash and instead show more complex long-term behavior. Examples of such behavior include all [[infinite growth]] patterns, such as [[gun]]s, [[sawtooth]]s, and [[spacefiller]]s; but also some patterns with bounded population. | ||
[[Class three]] automata additionally show a large (and possibly dominating) residue of [[chaotic growth]] patterns | The scheme generalizes readily for all [[class two]] and [[class four]] cellular automata. [[Class three]] automata additionally show a large (and possibly dominating) residue of [[chaotic growth]] patterns; typically appearing to grow infinitely, but whose ultimate fate is not predictable. The existence of such patterns is predicted, though in most cases not proven, for class four automata as well. | ||
Revision as of 13:26, 30 November 2014
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In the context of cellular automata, cosmology is the study of the ultimate fate of patterns over time.
An early cosmological classification was introduced in Lifeline Volume 2, aiming to cover all Life patterns according to the ash they produce:
- Patterns that eventually die out entirely. These are known as sparks or diehards.
- Patterns that eventually stabilize in a constellation of periodic, unmoving objects (still lifes and oscillators).
- Patterns that eventually create a set of periodic, moving objects (spaceships) that escape to infinity. Known as pure glider generators.
- Patterns that eventually create both moving and unmoving ash.
This leaves out as interesting edge cases patterns that do not stabilize into ash and instead show more complex long-term behavior. Examples of such behavior include all infinite growth patterns, such as guns, sawtooths, and spacefillers; but also some patterns with bounded population.
The scheme generalizes readily for all class two and class four cellular automata. Class three automata additionally show a large (and possibly dominating) residue of chaotic growth patterns; typically appearing to grow infinitely, but whose ultimate fate is not predictable. The existence of such patterns is predicted, though in most cases not proven, for class four automata as well.