Achim's p4

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Achim's p4
x = 11, y = 9, rule = B3/S23 2b2o3b2o$bo2bobo2bo$bob2ob2obo$2o7b2o$2bobobobo$2o7b2o$bob2ob2obo$bo2b obo2bo$2b2o3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 36 GPS 2 ]]
Pattern type Oscillator
Oscillator type Billiard table
Number of cells 40
Bounding box 11 × 9
Frequency class 29.0
Period 4
Mod 4
Heat 4
Volatility 0.17
Strict volatility 0.17
Discovered by Achim Flammenkamp
Year of discovery 1988
This article is about the p4 oscillator sometimes referred to as "cloverleaf". For other uses of "cloverleaf", see Cloverleaf (disambiguation).

Achim's p4 (or cloverleaf) is a period-4 oscillator that was found in a less compact form (using two sombreros) by David Buckingham in 1976. The form shown here was found by Achim Flammenkamp in 1988.[1] The rotor is two copies of the rotor of 1-2-3-4, so the oscillator is sometimes called the dual 1-2-3-4.

x = 15, y = 11, rule = B3/S23 3b2o5b2o$3bobo3bobo$5bo3bo$3bob2ob2obo$b3o7b3o$o3bobobobo3bo$b3o7b3o$ 3bob2ob2obo$5bo3bo$3bobo3bobo$3b2o5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 36 GPS 2 AUTOSTART ]]
The original, less compact form of Achim's p4
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RLE: here Plaintext: here
Catagoluehere

Occurrence

See also: List of common oscillators

Achim's p4 is about the twenty-third most common naturally-occurring oscillator in Achim Flammenkamp's census.[2] On Catagolue, it is the third most common period 4 oscillator, being less common than mazing.[3] Stator variants with one[4] and three[5] bits added respectively are the fourth and eighth most common period-4 oscillators,[3] and an inflected version has also occurred naturally.[6]

x = 15, y = 7, rule = LifeHistory 6.3A2$4.A5.A2.2A$D3.A5.A2.2A$4.A5.A2$6.3A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ THUMBSIZE 2 GPS 6 GRID THEME Book AUTOSTART T 0 PAUSE 2 PASTET 23 PASTE C! 0 3 T 23 PAUSE 1 T 45 PAUSE 1 GPS 4 LOOP 57 ]]
Achim's p4 forms when a traffic light + block sequence gets hit by a dot spark in a specific location and timing.
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Glider synthesis

An 8-glider synthesis of this oscillator was found by Jason Summers in September 2004.[7] In October 2010, Lewis Patterson found a predecessor of this oscillator that allows a 7-glider synthesis.[8][9] This was improved to 6 gliders by Chris Cain in March 2015,[10] and then to 5 gliders in July 2022.[11]

x = 42, y = 48, rule = B3/S23 8bo$9bo$7b3o11$bo$2bo$3o26$37bo$35b2o$25bo10b2o$26bo$24b3o12b2o$39bobo $39bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ THUMBSIZE 2 HEIGHT 600 Z 12 GPS 20 GRID THEME Book T 40 X 15 Y 20 Z 20 T 105 X 15 Y 13 Z 24 PAUSE 2 T 179 PAUSE 2 LOOP 180 ]]
The 5-glider synthesis shows an example of the required dot spark being delivered at the right time
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Trivia

One half of Achim's p4 (excluding the central row) may act as the stator component of a seminaturally-occurring variant of the T-nosed p4, or as part of the stator of a half-middleweight volcano, as found by Noam Elkies on March 15, 2000.

x = 11, y = 13, rule = B3/S23 5bo$5bo$4b3o4$3b5o$2bob3obo$2bo5bo$2o2bobo2b2o$bob2ob2obo$bo2bobo2bo$2b2o3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 36 GPS 2 AUTOSTART ]]
(click above to open LifeViewer)
Catagoluehere
x = 14, y = 15, rule = B3/S23 6bo$4bo$8bo$3bo$b3ob2obobo$o3bo2b2ob3o$2ob2o3b2o3bo$bobo7bobo$bo2bo2b 6o$2b2o2bo$3bob2obob3o$3bo2bo4bobo$4bo3b2o3bo$5b3o2b3o$7bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 3 ZOOM 24 GPS 2 AUTOSTART ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagoluehere

See also

References

  1. Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  2. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  3. 3.0 3.1 Adam P. Goucher. "Census". Catagolue. Retrieved on October 27, 2018.
  4. Tanner Jacobi (November 8, 2014). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  5. gameoflifeboy (August 21, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  6. praosylen (April 27, 2016). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  7. Jason Summers' jslife pattern collection. Retrieved on January 5, 2020.
  8. Lewis Patterson (October 17, 2010). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
  9. Matthias Merzenich (October 17, 2010). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
  10. Chris Cain (March 1, 2015). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
  11. Carson Cheng (July 4, 2022). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums

External links