Density: Difference between revisions
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For any side length of the form 3n-1, a segment of [[block agar]] can be used to reach a population of 4n². Up to n = 4 this is the optimal solution. | For any side length of the form 3n-1, a segment of [[block agar]] can be used to reach a population of 4n². Up to n = 4 this is the optimal solution. | ||
== Densities of other objects == | |||
* The maximum density of a still life agar is proven to be 1/2. | |||
* The maximum average density of an oscillating agar is conjectured but not proven to be 1/2. | |||
* The density of [[ash]] is 0.0287 (1 in 35). | |||
* The density of a [[space dust]]y oscillator or spaceship is usually between 0.25 and 0.3. | |||
==References== | ==References== | ||
{{LinkLexicon|lex_d.htm#density}} | {{LinkLexicon|lex_d.htm#density}} | ||
* http://www.ai.sri.com/~nysmith/life/ | * http://www.ai.sri.com/~nysmith/life/ | ||
Revision as of 13:13, 12 October 2021
The density of a pattern is the proportion of live cells within its bounding box.
The maximal densities of square (pseudo) still lifes up to 20×20 are:
| Side length | Max. density | Max. population | Pattern |
|---|---|---|---|
| 1 | 0 | 0 | |
| 2 | 1 | 4 (block) | |
| 3 | 0.6̄ | 6 (ship) | |
| 4 | 0.5 | 8 (pond, long ship) | |
| 5 | 0.64 | 16 (four blocks) | (click above to open LifeViewer) |
| 6 | 0.5 | 18 (eg. two long shillelaghs) | (click above to open LifeViewer) |
| 7 | 0.5714 | 28 | (click above to open LifeViewer) |
| 8 | 0.5625 | 36 (eg. nine blocks) | (click above to open LifeViewer) |
| 9 | 0.5309 | 43 | (click above to open LifeViewer) |
| 10 | 0.5400 | 54 | |
| 11 | 0.5289 | 64 | |
| 12 | 0.5278 | 76 | |
| 13 | 0.5325 | 90 | |
| 14 | 0.5306 | 104 | |
| 15 | 0.5289 | 119 | |
| 16 | 0.531 | 136 | |
| 17 | 0.526 | 152 | |
| 18 | 0.528 | 171 | |
| 19 | 0.526 | 190 | |
| 20 | 0.525 | 210 |
For any side length of the form 3n-1, a segment of block agar can be used to reach a population of 4n². Up to n = 4 this is the optimal solution.
Densities of other objects
- The maximum density of a still life agar is proven to be 1/2.
- The maximum average density of an oscillating agar is conjectured but not proven to be 1/2.
- The density of ash is 0.0287 (1 in 35).
- The density of a space dusty oscillator or spaceship is usually between 0.25 and 0.3.