Pi-R-Squared spaceship: Difference between revisions
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{{Glossary}} | {{Glossary}} | ||
The '''Pi-R-Squared spaceship''' is a fictituous [[spaceship]] due to [[Dave Greene]], supposedly consisting of two [[pi grandparent]]s and two [[R-pentomino]] | The '''Pi-R-Squared spaceship''' is a fictituous [[spaceship]] due to [[Dave Greene]], supposedly consisting of two [[pi grandparent]]s and two [[R-pentomino]]es, with a population of 20 in a {{times|55|34}} [[bounding box]], moving at [[speed]] [[c]]/137.<ref group="n" name="fine" /> | ||
It was claimed to have been "seen briefly in 1974 on a PDP-12 display by Tony Honcho Jarnow" (an anagram of "[[John Horton Conway]]"), arising from the [[ash]] of a random 128 | It was claimed to have been "seen briefly in 1974 on a PDP-12 display by Tony Honcho Jarnow" (an anagram of "[[John Horton Conway]]"), arising from the [[ash]] of a random {{times|128|80}} [[soup]], "just before an unfortunate power outage due to tripping on a power cable".<ref name="post57860" /> | ||
== | ==Generalisations== | ||
The idea is that the R-pentomino and the five-cell pi grandparent are each fairly [[common]] and therefore likely to pop up in general, regardless of what the pattern was like tens or hundreds of generations earlier (as long as it had not already adopted a stable/repeating configuration). If one of the many initial patterns that could lead to this also had two R-pentominoes and two pi grandparents (in the same configuration), then it would result in a spaceship. In August {{year|2013}}, [[Martin Grant]] discovered a near-miss spaceship | The idea is that the R-pentomino and the five-cell pi grandparent are each fairly [[common]] and therefore likely to pop up in general, regardless of what the pattern was like tens or hundreds of generations earlier (as long as it had not already adopted a stable/repeating configuration). If one of the many initial patterns that could lead to this also had two R-pentominoes and two pi grandparents (in the same configuration), then it would result in a spaceship. Near-miss examples of this include: | ||
* In August {{year|2013}}, [[Martin Grant]] discovered a near-miss spaceship, where an R-pentomino descendant moves at a speed of 14c/65 [[orthogonal]] with a dot [[spark]].<ref name="post8872" /> | |||
* In December {{year|2020}}, [[Tanner Jacobi]] found a mechanism where two blocks and two traffic light predecessors, aided by a line of [[gutter]] symmetry, happened to form from the same arrangement shifted by one cell 61 generations later minus one dot spark on each side due to their sheer commonness.<ref name="post116246" /> | |||
* An [[angel]] happens to form from a glide-reflected (or, because it has reflection symmetry, rotated) copy of itself with one extra cell after nineteen generations.<ref name="post116829" /> | |||
* Adding a cell to a block and honey farm predecessor interacting happens to result in the block and honey farm predecessor forming again (due to their commonness) with the same relative position, resulting in a near-miss glide-reflective 2c/120 spaceship.<ref name="post116746" /> | |||
* The [[two-glider octomino]], which is a fairly common pattern, happens to form again from itself 39 generations later in a different position when placed on an {{times|11|11}} [[torus]].<ref name="post4819" /> An [[R-pentomino]] exhibits similar behavior on a {{times|16|31}} [[Klein bottle]], appearing glide-reflected after 590 generations (although there is some other junk that dies eighteen generations later without interacting with the R-sequence).<ref name="post107332" /> | |||
==Notes== | |||
<references group="n"> | |||
<ref name="fine">The coefficient <tt>1/137</tt> is likely a reference to the {{LinkWikipedia|Fine-structure_constant|name=fine-structure constant|nobullet=nobullet|nosuffix=nosuffix}}, a physical constant independent on the system of units in which it is measured. It was thought to be exactly <tt>1/137</tt>, but more accurate measurements have found its denominator to be more precisely <tt>137.035999206</tt>. (See {{OEIS|A005600}}.)</ref> | |||
</references> | |||
==References== | ==References== | ||
<references> | <references> | ||
<ref name="post4819">{{LinkForumThread | |||
|format = ref | |||
|p = 4819 | |||
|title = Re: New ideas for pattern types | |||
|author = Emerson J. Perkins | |||
|date = July 4, 2011 | |||
}}</ref> | |||
<ref name="post8872">{{LinkForumThread | |||
|format = ref | |||
|p = 8872 | |||
|title = Re: Thread For Your Accidental Discoveries | |||
|author = Martin Grant | |||
|date = August 27, 2013 | |||
}}</ref> | |||
<ref name="post57860">{{LinkForumThread | <ref name="post57860">{{LinkForumThread | ||
| | |format = ref | ||
| | |p = 57860 | ||
|title | |title = Re: Thread for basic questions | ||
|date | |author = Dave Greene | ||
|date = March 13, 2018 | |||
}}</ref> | }}</ref> | ||
<ref name=" | <ref name="post107332">{{LinkForumThread | ||
| | |format = ref | ||
| | |p = 107332 | ||
|title | |title = Re: Agar discussion thread | ||
| | |author = MathAndCode | ||
| | |date = October 21, 2020 | ||
}}</ref> | }}</ref> | ||
<ref name="post116246">{{LinkForumThread | <ref name="post116246">{{LinkForumThread | ||
|format = ref | |format = ref | ||
|title = Re: Thread For Your Useless Discoveries | |p = 116246 | ||
|title = Re: Thread For Your Useless Discoveries | |||
|author = Tanner Jacobi | |author = Tanner Jacobi | ||
|date = December 17, 2020 | |date = December 17, 2020 | ||
}}</ref> | }}</ref> | ||
<ref name=" | <ref name="post116746">{{LinkForumThread | ||
|format = ref | |format = ref | ||
|title = Re: Thread for your | |p = 116746 | ||
|title = Re: Thread for your unsure discoveries | |||
|author = MathAndCode | |author = MathAndCode | ||
|date = December | |date = December 22, 2020 | ||
<ref name=" | }}</ref> | ||
<ref name="post116829">{{LinkForumThread | |||
|format = ref | |format = ref | ||
|title = Re: Thread for your | |p = 116829 | ||
|title = Re: Thread for your Trolls | |||
|author = MathAndCode | |author = MathAndCode | ||
|date = December | |date = December 23, 2020 | ||
}}</ref> | |||
</references> | </references> | ||
[[Category:Jokes]] | [[Category:Jokes]] | ||
[[Category:Mathematical miscellany]] | |||
Latest revision as of 07:08, 12 November 2023
The Pi-R-Squared spaceship is a fictituous spaceship due to Dave Greene, supposedly consisting of two pi grandparents and two R-pentominoes, with a population of 20 in a 55 × 34 bounding box, moving at speed c/137.[n 1]
It was claimed to have been "seen briefly in 1974 on a PDP-12 display by Tony Honcho Jarnow" (an anagram of "John Horton Conway"), arising from the ash of a random 128 × 80 soup, "just before an unfortunate power outage due to tripping on a power cable".[1]
Generalisations
The idea is that the R-pentomino and the five-cell pi grandparent are each fairly common and therefore likely to pop up in general, regardless of what the pattern was like tens or hundreds of generations earlier (as long as it had not already adopted a stable/repeating configuration). If one of the many initial patterns that could lead to this also had two R-pentominoes and two pi grandparents (in the same configuration), then it would result in a spaceship. Near-miss examples of this include:
- In August 2013, Martin Grant discovered a near-miss spaceship, where an R-pentomino descendant moves at a speed of 14c/65 orthogonal with a dot spark.[2]
- In December 2020, Tanner Jacobi found a mechanism where two blocks and two traffic light predecessors, aided by a line of gutter symmetry, happened to form from the same arrangement shifted by one cell 61 generations later minus one dot spark on each side due to their sheer commonness.[3]
- An angel happens to form from a glide-reflected (or, because it has reflection symmetry, rotated) copy of itself with one extra cell after nineteen generations.[4]
- Adding a cell to a block and honey farm predecessor interacting happens to result in the block and honey farm predecessor forming again (due to their commonness) with the same relative position, resulting in a near-miss glide-reflective 2c/120 spaceship.[5]
- The two-glider octomino, which is a fairly common pattern, happens to form again from itself 39 generations later in a different position when placed on an 11 × 11 torus.[6] An R-pentomino exhibits similar behavior on a 16 × 31 Klein bottle, appearing glide-reflected after 590 generations (although there is some other junk that dies eighteen generations later without interacting with the R-sequence).[7]
Notes
- ↑ The coefficient 1/137 is likely a reference to the fine-structure constant , a physical constant independent on the system of units in which it is measured. It was thought to be exactly 1/137, but more accurate measurements have found its denominator to be more precisely 137.035999206. (See
A005600.)
References
- ↑ Dave Greene (March 13, 2018). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
- ↑ Martin Grant (August 27, 2013). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
- ↑ Tanner Jacobi (December 17, 2020). Re: Thread For Your Useless Discoveries (discussion thread) at the ConwayLife.com forums
- ↑ MathAndCode (December 23, 2020). Re: Thread for your Trolls (discussion thread) at the ConwayLife.com forums
- ↑ MathAndCode (December 22, 2020). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
- ↑ Emerson J. Perkins (July 4, 2011). Re: New ideas for pattern types (discussion thread) at the ConwayLife.com forums
- ↑ MathAndCode (October 21, 2020). Re: Agar discussion thread (discussion thread) at the ConwayLife.com forums