Gutter

The gutter is a single straight line of cells along the axis of symmetry of a mirror-symmetric pattern. Most commonly this is an orthogonal line, and the pattern is then odd-symmetric (as opposed to even-symmetric, where the axis of symmetry follows the boundary between two rows or columns of cells).

The birth rule for Conway's Life trivially implies that if there are no live cells in the gutter of a symmetric pattern, new cells can never be born there since they will always have an even number of living neighbours. Examples of patterns containing empty gutters include Achim's p4, brain, centinal, pufferfish, spider, tumbler, and pulsar (the latter of which has gutters along all four lines of symmetry). For more examples see below.

The edge of a bounded plane without wraparound is equivalent to a gutter. Half of a gutter-symmetric pattern can always be supported by the edge of a plane.

A skew gutter is similar to a gutter, except that one side of the gutter is shifted along the gutter. Skew-gutter-symmetric patterns shifted by one cell are known in non-totalistic rules, e.g. in rules similar to Life but missing the birth condition B3n. Skew gutters shifted by two cells are possible already in Life, such as the shift-mirrored bun as a skew-2 gutter equivalent to the regular gutter still life cis-mirrored bun.

Objects with gutters and skew-gutters

Still lifes: Induction coils usually stabilize a pattern across a gutter. Symmetric examples include e.g. table on table, dead spark coil and rotated house, and most of the two-bookend or two-bun still lifes. Most small unsymmetric still lifes with an induction coil, such as block on table as the smallest example, likewise possess a gutter.

Pseudo still lifes usually possess a gutter, though examples are possible that do not, e.g. a block placed within the internal corner of trans-snake-tie.

Oscillators

Pulsar and harbor are composed of four quadrants separated by two gutters at right angles. Their extensions such as quasar contain an increasing number of gutters. Jason's p11 may share this property with proper casing.

Oscillators with two halves separated by a single gutter are more common and include the following:

• Achim's p4
• Scot's p5, extensible to two parallel gutters as swine
• 38P7.2
• Hebdarole in both of its forms
• Tumbler
• Twin bees shuttle in its sparkless stabilizations with e.g. four blocks, four eaters, or eight blocks; as well as the related p54 shuttle and centinal.

Oscillators with two rotor halves separated by a gutter, but whose canonical casing connects the two halves, include Buckingham's p13 and 168P22.1. A larger casing would allow a form containing a gutter.

Spaceships

Barge (spaceship) and the extended versions of Barge 2 are built of individual spaceship components separated by multiple gutters.

Spaceships symmetric across a single gutter are numerous and include the following:

• c/2: X66 and some standard spaceship flotillae, such as MWSS on MWSS 1 and HWSS on HWSS 1. Corresponding skew gutter variants are MWSS on MWSS 2 and HWSS on HWSS 2.
• 2c/5: 44P5H2V0, 60P5H2V0
• c/3: Brain, 72P6H2V0
• c/4: 46P4H1V0, 72P4H1V0
• c/5: Spider, snail
• c/6: 274P6H1V0

See also

• Minor static symmetries#Gutter_symmetry

External links

• Gutter at the Life Lexicon