Difference between revisions of "Inflation"
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'''Inflation''' is the process of replacing each cell in a [[pattern]], live or dead, with a larger {{times|''m''|''n''}} rectangle of cells | '''Inflation''' is the process of replacing each cell in a [[pattern]], live or dead, with a larger {{times|''m''|''n''}} rectangle of cells of the same state. | ||
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Revision as of 03:17, 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 of the same state.
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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