One-cell-thick pattern

A one cell thick pattern is a pattern that is only one cell thick; that is, it is contained entirely within one dimension of the Life plane. Put another way, it is a pattern with bounding box of the form y×1 for some natural number y. Because of their size restriction, exhaustive computer searches have been carried out to explore unidimensional patterns up to size about 40×1. Despite their inherent limitations, unidimensional patterns can exhibit quite complex behavior, even at reasonably small sizes.

Naively, one would assume that searching all y×1 patterns would require O(2^y) time. However, all such patterns containing one-cell and two-cell islands can be discarded, which reduces the search time to O(phi^y). Callahan employed this optimisation in his search for unidimensional infinite-growth patterns.

comment2, http://freedomandtruth.com Viagra, http://glatthousegallery.org health insurance canada, http://fishfrymadison.com Levitra, http://funpartiesforkids.com cialis levitra viagra vs,

comment3, http://fibcsocialjusticeforum.org cialis online, http://glatthousegallery.org health insurance, http://funpartiesforkids.com Levitra,

comment1, http://goccealvento.com auto insurance quote, http://the-cymbalta.com cymbalta cost, http://freedomandtruth.com Viagra, http://filipinalovesfood.com Viagra, http://gracethroughthedesert.com cigarettes, http://goltermangardens.com home insurance az, http://fishfrymadison.com Levitra,

Spaceships and oscillators

It is unknown whether or not there exists a spaceship that is one cell thick in one of its phases, though it can be shown via symmetry arguments that any such spaceship, if they exist, would have to move in the direction that it "points". The blinker is the only known oscillator that is one cell thick in one or more of its phases, and in April 1992, Allan Wechsler used a search program to show that there are no oscillators of period 3, 5 or 7 that are one cell thick. The situation is unknown for other periods.

A plausible strategy for building such unidimensional oscillators/spaceships is to create a synthesisable unidimensional pattern that is a predecessor to a universal constructor. Creating a unidimensional constructor predecessor is the easy part; synthesising it is much more difficult, as all sparks must disappear before it enters its unidimensional phase.

A weaker problem is to find a unidimensional pattern that is the predecessor of another non-trivial unidimensional pattern. Non-trivial means that it must contain at least one line of length 4; otherwise it would consist of blinkers and disappearing sparks. For example, this rules out the pattern ooooo.ooo, which becomes a single blinker.