* The maximum density of a still life agar was proven to be 1/2 by [[Noam Elkies]]<ref>{{cite web|url=https://arxiv.org/abs/math/9905194 |title=The still-Life density problem and its generalizations|author=Noam D. Elkies| accessdate=May 26, 2022| date=May 31, 1999}}</ref> (this is known as the '''still life conjecture''').
* The maximum density of a still life agar was proven to be 1/2 by [[Noam Elkies]]<ref>{{cite web|url=https://arxiv.org/abs/math/9905194 |title=The still-Life density problem and its generalizations|author=Noam D. Elkies| accessdate=May 26, 2022| date=May 31, 1999}}</ref> (this is known as the '''still life conjecture''').
* The maximum average density of an oscillating agar is conjectured but not proven to be 1/2. The current upper bound is 8/13, proven by [[Hartmut Holzwart]] in {{year|1992}}.<ref name="post147457" />
* The maximum average density of an oscillating agar is conjectured but not proven to be 1/2. The current upper bound is 8/13, proven by [[Hartmut Holzwart]] in {{year|1992}}.<ref name="post147457" />
* The density of [[ash]] is approximately 0.0287 (1 in 35).<ref name="post55185" />
* The density of [[ash]] is [[Achim Flammenkamp's census|approximately 0.0287]] (1 in 35).
* By observation, the density of a [[space dust]]y oscillator or spaceship is usually between 0.25 and 0.3.<ref name="post146282" />
* By observation, the density of a [[space dust]]y oscillator or spaceship is usually between 0.25 and 0.3.<ref name="post146282" />
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|author = Hartmut Holzwart
|author = Hartmut Holzwart
|date = June 22, 2022
|date = June 22, 2022
}}</ref>
<ref name="post55185">{{LinkForumThread
|format = ref
|title = Re: Life Thermodynamics
|p = 55185
|author = Oscar Cunningham
|date = January 17, 2018
}}</ref>
}}</ref>
<ref name="post146282">{{LinkForumThread
<ref name="post146282">{{LinkForumThread
Revision as of 08:23, 2 July 2022
The density of a pattern is the proportion of live cells within its bounding box.
The general problem of finding the maximum density of an nxn square pseudostill life was solved for all n in 2012.[1] The maximum densities of square still lifes up to 20×20 were known ten years earlier.[2]
The following table contains maximum density still life information for side lengths through 25.
†After the first few terms, the numbers in this sequence closely approximate the triangular number sequence.[3]
For any side length of the form 3n-1, a segment of block agar can be used to reach a population of 4n²; to n=4 this is the optimal solution, as can be seen in the above table.
Densities of other objects
The maximum density of a still life agar was proven to be 1/2 by Noam Elkies[4] (this is known as the still life conjecture).
The maximum average density of an oscillating agar is conjectured but not proven to be 1/2. The current upper bound is 8/13, proven by Hartmut Holzwart in 1992.[5]