T-nose
An oscillator is said to be T-nosed if, at one (and only one) point in its evolution stage, a T-pentomino forms at an edge of the pattern, specifically in a way that allows it to interact as a finger.
Currently, T-nose oscillators are known for periods 4 (T-nosed p4), 5 (T-nosed p5), 6 (T-nosed p6), 7 (T-nosed p7), 8 (Catagolue: here), 15 (Karel's p15), 16 (Rich's p16), 20 (Catagolue: here), 28 (Catagolue: here), 32 (Period-32 pi-heptomino hasslers), and 73 (Honey farm hasslers#p73), with the p20 coming from the evolution of a phi spark and the p28 coming from the evolution of a pi-heptomino.
Oscillators which are not T-nosed
The pentadecathlon is generally not considered a T-nose as, despite the fact that it does produce an isolated T-tetromino in one of its phases that lends itself to catalysis, the cell at the point of that T is also alive four and five generations afterwards, where a true "T-nosed p15" would have these cells dead for all 14 other generations of the oscillator.[1] Instead, the pentadecathlon is a phi-sparker. The same applies to Tanner's p46.
For the same reason, the second oscillator below[2][3] cannot be called a "T-nosed p8" as a blinker created by it turns the cell at the tip of the T on two extra times.
See generations 4 and 5 (click above to open LifeViewer) RLE: here Plaintext: here |
See generations 4 and 6 (click above to open LifeViewer) RLE: here Plaintext: here |
Oscillators like the pulsar and pulsar quadrant are also not T-nosed as the fingers they produce come from an L-tetromino, rather than a T-pentomino, even though they can interact in much the same way (see boring p24 and uninteresting p24).
Known T-nose reactions
There are at least four known p4 t-nose reactions, with the T part remaining the same but the immediate hassling region differing. An Octagon 3|5 can support two reactions simultaneously,[4] with the 3 side being the same as the reaction the conventional T-nosed p4 uses.
Two p4 T-nose reactions on an Octagon 3|5 (click above to open LifeViewer) RLE: here Plaintext: here |
The blocked p4 t-nose uses a third reaction (click above to open LifeViewer) RLE: here Plaintext: here |
The asymmetric reduced version uses a fourth (click above to open LifeViewer) RLE: here Plaintext: here |
Reactions for p5, p6, p7 and p8 are known and all have been stabilised as of August 2022. The pi-heptomino also produces a T-pentomino in generation 15, allowing for hasslers containing it to be T-nosed. Other true t-nose reactions of this period and true t-nose reactions of any other period are unknown.
No still life (allowing for a "T-nosed p1") can contain a T-pentomino within itself due to the central cell immediately dying of overpopulation and the tip dying of isolation, and no period-2 T-nose can exist because those two cells cause the oscillator to recede two cells, which cannot be made up in a single generation. It seems very likely that no true t-nose reaction can exist for period 3.
See also
- T-noses (category)
References
- ↑ Dave Greene (August 26, 2016). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
- ↑ Moosey (February 13, 2019). Re: Thread For Your Useless Discoveries (discussion thread) at the ConwayLife.com forums
- ↑ hotcrystal0 (March 28, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Entity Valkyrie (November 29, 2020). Re: Thread For Your Useless Discoveries (discussion thread) at the ConwayLife.com forums