T-nose

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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 (Catagoluehere), 15 (Karel's p15), 16 (Rich's p16), 20 (Catagoluehere), 28 (Catagoluehere), 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.

x = 3, y = 16, rule = LifeHistory .E$.A$3A3$3A$.A$.A$.A$.A$3A3$3A$.A$.A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 500 HEIGHT 300 COLOR MARKOFF 255 255 255 COLOR MARK2 255 0 0 LABEL 15 14 4 "#G" GPS 4 AUTOSTART LOOP 15 ]]
See generations 4 and 5
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 23, y = 12, rule = LifeHistory 9.E$9.A$8.3A2$2.2A14.A$2.A14.A.A$3.12A2.A.A$3A2.10A.A2.A.2A$A2.A2.9A 4.A.2A$.2A16.A$8.2A.2A4.A.A$8.2A.2A4.2A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 500 HEIGHT 300 COLOR MARKOFF 255 255 255 COLOR MARK2 255 0 0 LABEL 25 12 4 "#G" GPS 4 AUTOSTART LOOP 8 ]]
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.

x = 17, y = 19, rule = B3/S23 7b3o2$6bo3bo$7bobo2$6b5o$5bo5bo$4bo7bo$o2bo9bo2bo$2obo9bob2o$o2bo9bo2b o$4bo7bo$5bo5bo$6b5o2$7bobo$6bo3bo2$7b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 500 HEIGHT 400 GPS 4 AUTOSTART LOOP 4 ]]
Two p4 T-nose reactions on an Octagon 3|5
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 25, y = 11, rule = B3/S23 11b3o2$10bo3bo$4bo3bo7bo3bo$3bobo13bobo$3bobo13bobo$2obobob11obobob2o$ 2obo17bob2o$3bo17bo$3bobo4b2ob2o4bobo$4b2o4b2ob2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 500 HEIGHT 400 GPS 4 AUTOSTART LOOP 4 ]]
The blocked p4 t-nose uses a third reaction
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 10, y = 12, rule = B3/S23 4b3o2$3bo3bo2$3bo2bo$2bo2b2o$bobobo2bo$bob3o3bo$2bobobobo$3bo$3o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 WIDTH 500 HEIGHT 400 GPS 4 AUTOSTART LOOP 4 ]]
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

References

  1. Dave Greene (August 26, 2016). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
  2. Moosey (February 13, 2019). Re: Thread For Your Useless Discoveries (discussion thread) at the ConwayLife.com forums
  3. hotcrystal0 (March 28, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  4. Entity Valkyrie (November 29, 2020). Re: Thread For Your Useless Discoveries (discussion thread) at the ConwayLife.com forums