Karel's p15

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Karel's p15
x = 10, y = 11, rule = B3/S23 2bo4bo$2b6o$2bo4bo4$2b6o$bo6bo$o8bo$bo6bo$2b6o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 24 GPS 8 LOOP 15 ]]
Pattern type Oscillator
Number of cells 28
Bounding box 16 × 14
Period 15
Mod 15
Heat 34.9
Volatility 1.00
Strict volatility 1.00
Discovered by Karel Suhajda
Year of discovery 2002

Karel's p15 is a period-15 oscillator discovered by Karel Suhajda on December 11, 2002.[1] In this oscillator, a pentadecathlon hassles an unnamed active reaction. A pentadecathlon can support 2 Karel's p15s.

It provides accessible sparks that can be used to perturb reactions; the advantage of Karel's p15 over a pentadecathlon is that the pentadecathlon's long end reaches its maximum extent on two separate occasions, while Karel's p15 does only once, allowing its use as a T-nose. The p15 bouncer mechanism is an example. In the same month of its discovery, Mark Niemiec found an 18-glider synthesis of this oscillator.[2]

This oscillator first appeared semi-naturally in March 2015.[3]

A glider stream with period divisible by 5 but not 15 can be filtered with a Karel's p15 to triple the period.

x = 112, y = 61, rule = B3/S23 52b2o14bo25bo$27b2o24bo14b3o21b3o$28bo13b2o6b3o18bo19bo9bo$28bobo11b2o 6bo19b2o19b2o6b5o$14b2o13b2o67bo5bo$14b2o57bo24bob2o2bo$42bo54b2obobob 3obo$40bo3bo44bo12bo4b2o$8b2o30bo3bo43b3o10b2ob2o$8b2o30b2o3bo41b2obo 8bo2bobob5o$12b2o29b2o15b2o36bobo3bo6bo$12b2o25bo3b2o15b2o36bob2ob5o2b 2o$90bob2o4b2o$39bo2bo47bo7b3o4b2o$40bob2o39bobo7bo4b3o4b2o$7b2o33b3o 38bobo3bo3bo4b2o$7b2o34b2o34b2o3bo4bo2bo5bob2ob5o2b2o$57b2o20b2o8b3o6b obo3bo6bo$27bo3b2o24bo41bo2bobob5o$26bobo3bo5b2o3b2o13bo42b2ob2o$26b2o 3bo7bo3bo13b2o43bo4b2o$30bo5b3o5b3o50b2obobob3obo$26b5obo3bo9bo51bob2o 2bo$26bo4b2o65bo5bo$27b3o69b5o$29bob2o68bo$30bobo$79bobo$10bo68b2obo$ 8b5o69b3o$7bo5bo65b2o4bo$7bo2b2obo51bo9bo3bob5o$3bob3obobob2o50b3o5b3o 5bo$3b2o4bo43b2o13bo3bo7bo3b2o$6b2ob2o42bo13b2o3b2o5bo3bobo$b5obobo2bo 41bo24b2o3bo$o6bo3bobo6b3o8b2o20b2o$2o2b5ob2obo5bo2bo4bo3b2o34b2o34b2o $12b2o4bo3bo3bobo38b3o33b2o$5b2o4b3o4bo7bobo39b2obo$5b2o4b3o7bo47bo2bo $12b2o4b2obo$2o2b5ob2obo36b2o15b2o3bo25b2o$o6bo3bobo36b2o15b2o29b2o$b 5obobo2bo8bob2o41bo3b2o30b2o$6b2ob2o10b3o43bo3bo30b2o$3b2o4bo12bo44bo 3bo$3bob3obobob2o54bo$7bo2b2obo82b2o$7bo5bo22b2o43b2o13b2o$8b5o6b2o40b o6b2o11bobo$10bo9bo7bo30b3o6b2o13bo$17b3o7b3o5bo22bo24b2o$17bo8b2ob2o 3b3o21b2o$25b3ob3o$25b3ob3o2b3o$25b3ob3o2b3o$25b3ob3o$26b2ob2o3b3o$27b 3o5bo$28bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ MAXGRIDSIZE 9 WIDTH 750 HEIGHT 430 THUMBSIZE 2 ZOOM 6 AUTOSTART LOOP 435 ]]
Period 435 gun shows how this pattern thins out the glider stream and triples the period
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RLE: here Plaintext: here

As a catalyst

Karel's p15 can be used to push a beehive with a much smaller footprint than the beehive push catalyst. Even though it is a periodic catalyst, it works in 13 of 15 generations, with the two that fail being consecutive.

x = 58, y = 48, rule = B3/S23 49bo$49bo$41b3o$49bo$40bo3bo3bobo$41b3o$48b3o3$48b3o$21b2o18b3o$15bob 2obobo17bo3bo3bobo$6b2o7b2obobo28bo$2b2obobo11b2o20b3o$3bobo43bo$3bob 2o35bo6bo$2obo28b2o7bobo$o2b4o25bo3bo4bobo$b2o3bo23bobo2bobo4bo$3b3o 24b2o4bo$3bo15b3o$bobo15bo$b2o16bo$20b2obo9b2o$23b2o9bob2o$38bo16b2o$ 38bo15bobo$36b3o15bo$21bo4b2o24b3o$15bo4bobo2bobo23bo3b2o$14bobo4bo3bo 25b4o2bo$14bobo7b2o28bob2o$8bo6bo35b2obo$8bo43bobo$14b3o20b2o11bobob2o $8bo28bobob2o7b2o$7bobo3bo3bo17bobob2obo$14b3o18b2o$7b3o3$7b3o$14b3o$ 7bobo3bo3bo$8bo$14b3o$8bo$8bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 23 THUMBSIZE 2 ZOOM 6 ]]
A period-345 LCM oscillator. The base reaction is p69. As 69 is a multiple of 3, Karel's p15 can push the beehive back in generations that are multiples of 3, avoiding the two in a row that cause it to fail. No non-LCM completion of this p69 is known.
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x = 23, y = 23, rule = B3/S23 8o$ob4obo$8o4$o6bo4bo$2bo2bo4b3o$2bo2bo4b3o$2bo2bo$o6bo6b3o$14b2o$14b 2o3$12bo3bo3b3o$20bobo$13b3o4b3o$20b3o$20b3o$13b3o4b3o$20bobo$12bo3bo 3b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 GPS 2 ZOOM 20 LOOP 15 HEIGHT 600 AUTOSTART ]]
Two Karel's p15s hassle blinkers and rephase them (occurred seminaturally in tetramer form in a soup by Charity Engine on 2022-02-13)[4]
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See also


External links