The general problem of finding the maximum density of an nxn square [[pseudo]] [[still life]] was solved for all n in 2012.<ref>{{cite web|url=https://people.eng.unimelb.edu.au/pstuckey/papers/still-life.pdf | title=A Complete Solution to the Maximum Density Still Life Problem | publisher=Geoffrey Chu, Peter J. Stuckey, NICTA Victoria Laboratory, Department of Computing and Information Systems, University of Melbourne, Australia | date=November 8, 2013}}</ref> The maximum densities of square still lifes up to 20×20 were known ten years earlier; those results are summarized in the following table:<ref>{{cite web|url=https://web.archive.org/web/20130731001049/http://www.ai.sri.com/~nysmith/life |title=Maximum Density Still Life |publisher=Neil Yorke-Smith|date=August 4, 2003}}</ref>
The general problem of finding the maximum density of an nxn square [[pseudo]] [[still life]] was solved for all n in 2012.<ref>{{cite web|url=https://people.eng.unimelb.edu.au/pstuckey/papers/still-life.pdf | title=A Complete Solution to the Maximum Density Still Life Problem | publisher=Geoffrey Chu, Peter J. Stuckey, NICTA Victoria Laboratory, Department of Computing and Information Systems, University of Melbourne, Australia | date=November 8, 2013}}</ref> The maximum densities of square still lifes up to 20×20 were known ten years earlier.<ref>{{cite web|url=https://web.archive.org/web/20130731001049/http://www.ai.sri.com/~nysmith/life |title=Maximum Density Still Life |publisher=Neil Yorke-Smith|date=August 4, 2003}}</ref>
The following table contains maximum density still life information for various side lengths.
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 various side lengths.
†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]
The density of ash is approximately 0.0287 (1 in 35).[6]
By observation, the density of a space dusty oscillator or spaceship is usually between 0.25 and 0.3.[7]