Inflation: Difference between revisions
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{{Glossary}} | |||
'''Inflation''' is the process of replacing each cell in a pattern, live or dead, with a larger ''m'' | '''Inflation''' is the process of replacing each cell in a [[pattern]], live or dead, with a larger {{times|''m''|''n''}} rectangle of cells in the same state. | ||
{| style="margin-left: auto; margin-right: auto;" | {| style="margin-left: auto; margin-right: auto;" | ||
|- | |- | ||
| [[File:Inflation.png|frame|center|Inflation of a 4 | | [[File:Inflation.png|frame|center|Inflation of a {{times|4|4}} [[soup]] to {{times|8|8}}.]] | ||
|} | |} | ||
Inflation can be thought of as taking the Kronecker product of, in order, a given pattern and an {{times|''m''|''n''}} matrix of ones. | |||
==Uses== | ==Uses== | ||
[[apgsearch]] 4.x (apgluxe) | [[apgsearch]] 4.x and above (apgluxe) support inflation of [[soup]]s of arbitrary (pseudo-)symmetry by a factor of {{times|2<sup>''n''</sup>|2<sup>''n''</sup>}} by prefixing the <tt>i</tt> operator to the desired symmetry string ''n'' times. | ||
==Interesting finds== | |||
The [[hook]] inflated once (i.e. {{times|2|2}} cells) becomes a regular-sized hook in the same orientation after 34 generations. | |||
==See also== | |||
* [[2×2 block rule]]s, where {{times|2|2}} blocks remain {{times|2|2}} blocks | |||
==External links== | |||
* {{LinkWikipedia|Kronecker_product|pagename=Kronecker product}} | |||
* {{LinkMathworld|filename=KroneckerProduct.html|pagename=Kronecker Product}} | |||
* {{LinkForumThread|t=3629|title=Unofficial symmetries|date=20 Dec 2018}} | |||
[[Category:Mathematical miscellany]] | |||
Latest revision as of 03:18, 3 August 2024
Inflation is the process of replacing each cell in a pattern, live or dead, with a larger m × n rectangle of cells in the same state.
 |
Inflation can be thought of as taking the Kronecker product of, in order, a given pattern and an m × n matrix of ones.
Uses
apgsearch 4.x and above (apgluxe) support inflation of soups of arbitrary (pseudo-)symmetry by a factor of 2n × 2n by prefixing the i operator to the desired symmetry string n times.
Interesting finds
The hook inflated once (i.e. 2 × 2 cells) becomes a regular-sized hook in the same orientation after 34 generations.
See also
- 2×2 block rules, where 2 × 2 blocks remain 2 × 2 blocks
External links
- Kronecker product at Wikipedia
- Kronecker Product at Wolfram Mathworld
- Unofficial symmetries (discussion thread) at the ConwayLife.com forums