Difference between revisions of "OCA:Flock"
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|b = 3 | |b = 3 | ||
|s = 12 | |s = 12 | ||
|ruleinteger = 3080 | |||
|reversal = B0123458/S01234678 | |||
}} | }} | ||
'''Flock''' is a [[cellular automaton]] | '''Flock''' is a [[Life-like cellular automaton]] in which cells survive from one generation to the next if they have 1 or 2 neighbours, and are born if they have 3 neighbours. Its rulestring is B3/S12. It differs very strongly from [[Conway's Game of Life]] and similar automata. It is the fourth most searched rule on [[Catagolue]] in terms of the total number of objects censused from asymmetric soups as of August 2022. | ||
==Patterns== | ==Patterns== | ||
Due to the missing S3 survival condition and addition of the S1 survival condition, almost no patterns from Life are compatible with Flock and vice versa. Random starting [[soup]]s rapidly degenerate into [[domino]]es and still [[duoplet]]s. [[Tub]], [[beehive]], [[loaf]] and [[mango]] still work as expected, as do the infinite family of [[lake]]s (including [[small lake]] and its extended derivatives). | Due to the missing S3 survival condition and addition of the S1 survival condition, almost no patterns from Life are compatible with Flock and vice versa. Random starting [[soup]]s rapidly degenerate into [[domino]]es and still [[duoplet]]s. [[Tub]], [[beehive]], [[loaf]] and [[mango]] still work as expected, as do the infinite family of [[lake]]s (including [[small lake]] and its extended derivatives). | ||
The rule, however, does share many features with rules such as | The rule, however, does share many features with rules such as {{rl|2×2}}, {{rl|HighFlock}}, {{rl|EightFlock}}, {{rl|Pedestrian Flock}} and {{rl|Goat Flock}}. | ||
There are small p2 [[oscillators]] which resemble the [[ship]], [[long ship]] and [[very long ship]] when played, one of which looks like a [[bipole]] in one phase. This family of oscillators does not appear to be extendable. | There are small p2 [[oscillators]] which resemble the [[ship]], [[long ship]] and [[very long ship]] when played, one of which looks like a [[bipole]] in one phase. This family of oscillators does not appear to be extendable. | ||
===Familiar fours=== | ===Familiar fours=== | ||
Despite the vastly different behaviour of patterns, some patterns can still settle naturally into [[familiar fours]] and related constellations. One, for example, is called ''flock'', a constellation of four duoplets, which evolves from a | Despite the vastly different behaviour of patterns, some patterns can still settle naturally into [[familiar fours]] and related constellations. One, for example, is called ''flock'', a constellation of four duoplets, which evolves from a {{times|3|3}} square of cells as in the [[traffic light]] sequence. | ||
{{gallery top}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 1, y = 1, rule = B3/S12 | |||
3o$obo$3o! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ]] | |||
|position = center | |||
|caption = ''Flock'' predecessor | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 5, y = 5, rule = B3/S12 | |||
bobo$o3bo2$o3bo$bobo! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ]] | |||
|position = center | |||
|caption = ''Flock'' | |||
|style = width:300px; | |||
}}}} | |||
{{gallery bottom}} | |||
Another familiar four is known as ''radiator'', composed of four dominoes. | |||
{{gallery top}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 13, y = 6, rule = B3/S12 | |||
bo$bobo$11bo$o8b2obo$b2o5bo$7bo! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ]] | |||
|position = center | |||
|caption = Two radiator predecessors with different sequences | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 5, y = 3, rule = B3/S12 | |||
2ob2o2$2ob2o! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ]] | |||
|position = center | |||
|caption = Radiator | |||
|style = width:300px; | |||
}}}} | |||
{{gallery bottom}} | |||
===Spaceships=== | ===Spaceships=== | ||
Both orthogonal and diagonal spaceships exist in this rule | Both orthogonal and diagonal spaceships exist in this rule. [[David Eppstein]] lists two orthogonal period-4 c/4 ships and a diagonal period-8 c/4 ship; additionally, [[Josh Ball]] found a c/5 orthogonal ship in 2016, [[LaundryPizza03]] found a 2c/5 orthogonal ship in 2020, and DroneBetter found a c/6 diagonal ship in 2023. | ||
{|class="wikitable" style="text-align: center" | |||
{| style=" | !speed!!period!!first known!!discoverer!!minimal known!!discoverer | ||
|- | |||
|c/4||4||{{LinkCatagolue|xq4_0o8211i606i1128ozxh13j909j31hz4cgf3y33fgc4|b3s12|name=54P4H1V0|style=raw}}||unknown||{{LinkCatagolue|xq4_0g80i9570759i08gzc1g0g1cxc1g0g1czx1y51|b3s12|name=40P4H1V0|style=raw}}||unknown | |||
|- | |||
|c/5||5||{{LinkCatagolue|xq5_y342248y6gggg048o5g9gogzogo2pvc61w4228gwgce71h03s0c11cghj5wgzpmp0pgwf066660g96py0pwgy1ggg9wg96z10149f368w2441y037eoogs303o8j0osqzy324421yb211a0901|b3s12|name=184P5H1V0|style=raw}}||[[Josh Ball]], 2016<ref name="post27169" />||{{LinkCatagolue|xq5_y2gghtfz3o120j811z0h148gz0so40ovuz0120c1hjggzw8k622d18h0kzxo530a44442zy23wuxgzy3p5tw13j64zy5oki2a3022|b3s12|name=126P5H1V0|style=raw}}||DroneBetter, 2023<ref name="post174254" /> | |||
|- | |||
|2c/5||5||{{LinkCatagolue|xq5_y2250224664gyegzc8gwo01goabg0144xca19oo06h8gghggvzwc2649q51y037702hoigoj3348w1ee1googzy3mfy59gvgggg9w9099xgggg6zwj46i95qowg0cee0481401ssc2h0gonnog11z31x108015dw8i2x3589110681w80gfzy24a0442662|b3s12|name=242P5H2V0|style=raw}}||[[LaundryPizza03]], 2020<ref name="post97187" />||{{LinkCatagolue|xq5_gosw42g33zfh11rhlg040g80cszy5haarwhzuhggrhl104012067z137w481oo|b3s12|name=82P5H2V0|style=raw}}||DroneBetter, 2023<ref name="post174254" /> | |||
|- | |||
|c/6||6|| || ||{{LinkCatagolue|xq6_4ah2gq131o0o131qg2ha4zy279bxb97zy318hch81|b3s12|name=58P6H1V0|style=raw}}||DroneBetter, 2024<ref name="post175578" /> | |||
|- | |- | ||
| | |rowspan="2"|c/4d||4|| || ||{{LinkCatagolue|xq4_y1goo061o0f9j3z0g805p158gwu011zgr44o122g1824og2kg0gxs20hqg0oz1y11y1140k217cnog0jp7240342gg8gzy8o4wtne401310104i11h7207bgozy725sd088p7i90sy2132zya2w43ps4ase31zyf1x4ac|b3s12|name=206P4H1V1|style=raw}}||DroneBetter, 2023<ref name="post174254" /> | ||
|- | |- | ||
| | |8|| || ||{{LinkCatagolue|xq8_y1842ve4z8sqp821zw1|b3s12|name=18P8H2V2|style=raw}}||unknown | ||
|- | |- | ||
| | |c/6d||4|| || ||{{LinkCatagolue|xq6_y0u0h8ccoqaz26ahgh0guy3goz0884x1c1icca201zy36044|b3s12|name=57P6H1V1|style=raw}}||DroneBetter, 2023<ref name="post174254" /> | ||
|} | |} | ||
Currently, the p8 c/4 diagonal spaceship is the only [[natural]] one, and has only occurred naturally once.<ref group="n">{{cata|hashsoup/C1/l_K96fC38Dz5ri12898942/b3s12|the soup in question}}</ref> | |||
{{gallery top}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 38, y = 14, rule = B3/S12 | |||
b3o9b3o$o2bo9bo2bo9b3ob3o$25bo2bobo2bo$o2b2o7b2o2bo10b2ob2o$6bo3bo12bo2bo5bo2bo$2bo4bobo4bo7bo2bo7bo2bo$22bo3bo5bo3bo$5bo5bo$3bo2b2ob2o2bo7bo5bo3bo5bo$2bobo7bobo6bo5bo3bo5bo$b2ob2o5b2ob2o7bobo7bobo$4bo2bobo2bo11bo9bo$4b2obobob2o$4bo7bo! | |||
|imgname = Flockorthogonalships | |||
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 4 TRACK 0 -1/4 ]] | |||
|position = center | |||
|caption = Two orthogonal c/4 ships (Eppstein's 14679 and 14839) | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 42, y = 50, rule = B3/S12 | |||
9bo4bo15bobo$8bo2b2o2bo13bo2bo$7b2o6b2o11b4o$6bobo6bobo6b2obo$8bobo2bobo$5bobobo4bobobo5b4o5bo$5b2o10b2o5b2o6b3o$4bo14bo$b2o4bo3b2o3bo4b2o3b2o3bo$3bo3b2obo2bob2o3bo7b2o3bo$3bo6bo2bo6bo12b2o$3b2o14b2o6bo5bo$2b2o2b2ob2o2b2ob2o2b2o8bobobo$8bobo2bobo17b2o$33b2o$7bo2b4o2bo15b2o2b2o$32bo2b4o$8bo6bo14bobo2bo$8b3o2b3o13bo4b2o$7b2o6b2o19bo$6bo2bo4bo2bo11bo6bobo$5bo4b4o4bo10b4ob3o2bo$4bo14bo10bo4b2o$9b2o2b2o22bobo$3bobo12bobo10bo2bo$6bo10bo14bobo$3bo4b2o4b2o4bo15bo$35b3o$bobo3bo8bo3bobo12bo3bo$4bob3o6b3obo15bo4bo$o4b3o8b3o4bo11bo$o2bo3bo8bo3bo2bo11bo3b2o$bobo4bo6bo4bobo12bo4bo$2b3o3bo6bo3b3o13bob2o$5bobo3b2o3bobo16bob3o$6bobo2b2o2bobo20b2o$7b2ob4ob2o20b3o2$10b4o$9b6o25bo$9bo4bo22b2obo$36b4o$34bobob2o$36bo2b3o$33bo2bo3bo$32bob2o$31bo$31bo$32bo$31bobo! | |||
|imgname = Flockc5orthogonal | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 448 AUTOSTART GPS 5 TRACK 0 -1/5 ]] | |||
|position = center | |||
|caption = <!--An orthogonal c/5 ship found by Josh Ball, and smaller one found by DroneBetter-->The smallest known even-symmetric and asymmetric c/5's | |||
|style = width:300px; | |||
|apgcode = xq5_y342248y6gggg048o5g9gogzogo2pvc61w4228gwgce71h03s0c11cghj5wgzpmp0pgwf066660g96py0pwgy1ggg9wg96z10149f368w2441y037eoogs303o8j0osqzy324421yb211a0901/b3s12 | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 59, y = 40, rule = B3/S12 | |||
16b2o22bo11bo$14bo4bo17b3ob3o5b3ob3o$13b2o4b2o15bo4bo9bo4bo$13b2o4b2o19bo11bo$5b5o4bo4bo4b5o9bob4o5b4obo$4bo4b2o12b2o4bo6bo19bo$9bob3o6b3obo10bo3bobobo5bobobo3bo$5bo3bob3o6b3obo3bo10b3obo5bob3o$9b2o4bo2bo4b2o9bo4b3o9b3o4bo$9bo5bo2bo5bo9b2o5bo2bo3bo2bo5b2o$8bo16bo19bobo$5bo3bo3bobo2bobo3bo3bo14bobobobo$6b2o4bo8bo4b2o14bo2bobo2bo$10b2o10b2o$8b4o3bo2bo3b4o15bo9bo$8b4o2bo4bo2b4o15bob2o3b2obo$5bo2bo4b2o4b2o4bo2bo$5bo8bo4bo8bo$6bobo2bo2bo4bo2bo2bobo$7b2o4b8o4b2o$10bo3bo4bo3bo$11bo3bo2bo3bo2$7bo2b3o8b3o2bo$4bo2bo2b3o8b3o2bo2bo$2bo2bo4b2o10b2o4bo2bo$b2o28b2o$b2o6bo14bo6b2o$2bo2b2obo16bob2o2bo$bo4bobo16bobo4bo$bo6b3o12b3o6bo$9b2obo2b4o2bob2o$obo2bo5bob2ob2ob2obo5bo2bobo$bo8bo2bo6bo2bo8bo$8b2o2bo8bo2b2o$11b2o8b2o$11bo10bo$9bo2b2o6b2o2bo$8bo16bo$7b2o16b2o! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 392 AUTOSTART GPS 5 TRACK 0 -2/5 ]] | |||
|position = center | |||
|caption = <!--An orthogonal 2c/5 ship found by LaundryPizza03, and smaller one found by DroneBetter-->The smallest known even- and odd-symmetric 2c/5's | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 21, y = 15, rule = B3/S12 | |||
2bo3b3o3b3o3bo$bobobobo5bobobobo$o19bo$bo3bo3bobo3bo3bo$2bob2o3bobo3b2obo$6b | |||
3o3b3o$6bobo3bobo$6bo7bo$7b2o3b2o2$7bobobobo2$10bo$8bobobo$9bobo! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 HEIGHT 336 AUTOSTART GPS 6 TRACK 0 -1/6 ]] | |||
|position = center | |||
|caption = The only known c/6 | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 52, y = 39, rule = B3/S12 | |||
23bo2b4o$22bo3bob2o$22bo3bo$19b2o3bob2o$18b3o3bo3bo$17b4o6b2o$25bo$17bo2bo4bo$15bo2bo2bo3bo$14bo3bo3bo2bo$14bo3bo3bo16bo$14bo4b2o3bo3bo8bo2bo$15b2o8bo3bo6bo$14bo2bo5bo2bo9bo3bo2bo$13b2o2bo3bo4b2ob2obo3bo2b3obo$13bo5bo5bo4b2obo3b3o3bo$6b4o19bobobo3bob2o2bobo$5bo4bo15bobo2b3o5bobo2bo$8bo23bobo3bo9bo$4bo23bo4b3ob2o7b2obo$3bo25b2o3b3obo3b4o2b2o$bo6bo21b2o3bo5bo3b2ob2o$o25bo2b4o7bo4bo2bo$o24bo3bobo17bobo$obo2bo19bo3b2o10bo2bo5b2o$o24bobo3b2obo8b2o$bo22bo7b2o10b2o$25b3o4bo3bo$26b2ob3o2bobo$26bo4bobo2bo$31b2o5b2o$27bo3bo3bob2o$30bo2b2ob2o$32b2ob3o$32b2o2bo$32bo$37bo$36bobo$37b2o! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 336 AUTOSTART GPS 4 TRACK -1/4 -1/4 ]] | |||
|position = center | |||
|caption = c/4 diagonal ships, of periods 8 (Eppstein's 10618) and 4 | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 18, y = 17, rule = B3/S12 | |||
7b4o$9b2o2$5b3o$4bo2b3o5b2o$3bo3b3o4b2o$3b7o$3o5bob2obo$8bo2b4o$2o6bo4b3o$8b3o6bo$9bo7bo$12b5o$5bo3b3o2bo$5bo7b2o$10bob3o$5b2o5b2o! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 HEIGHT 336 AUTOSTART GPS 6 TRACK -1/6 -1/6 ]] | |||
|position = center | |||
|caption = The only known c/6 diagonal | |||
|style = width:300px; | |||
|apgcode = xq6_y0u0h8ccoqaz26ahgh0guy3goz0884x1c1icca201zy36044/b3s12 | |||
}}}} | |||
{{gallery bottom}} | |||
====Linear growth==== | |||
Linear growth is known in the form of 2c/5 domino puffers and c/4 diagonal linestretchers.<ref name="post174254" />{{gallery top}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 51, y = 37, rule = B3/S12 | |||
6bo11bo13bo11bo$3b3ob3o5b3ob3o7b3ob3o5b3ob3o$2bo4bo9bo4bo5bo4bo9bo4bo$6bo11bo13bo11bo$4bob4o5b4obo9bob4o5b4obo$2bo19bo5bo19bo$bo3bobobo5bobobo3bo3bo3bobobo5bobobo3bo$5b3obo5bob3o11b3obo5bob3o$o4b3o9b3o4bobo4b3o9b3o4bo$2o5bo2bo3bo2bo5b2ob2o5bo2bo3bo2bo5b2o$11bobo23bobo$9bobobobo19bobobobo$8bo2bobo2bo17bo2bobo2bo2$7bo9bo15bo9bo$7bob2o3b2obo15bob2o3b2obo3$14bobo23bobo$16bo25bo$15bobo23bobo$16b2o24b2o2$16b2o24b2o3$43b4o$41bo5bo$41bo$41b2o$39b2o$41bo2bobo$38bo4bo$45bo2$40bo$42b2o! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 392 AUTOSTART GPS 5 TRACK 0 -2/5 ]] | |||
|position = center | |||
|caption = A domino-pulling tagalong for the 2c/5 and additional tagalong with backward heavyweight sparks, that become stable dominoes | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 78, y = 63, rule = B3/S12 | |||
11bo2bobo37b2ob3o$10b4o2bo35b2o5bo$9b3o39bo$13bo41bobo$5b6o3b2o34bo2bobo$4bo4b3o3bo33bo5b2o2bo$9b2obo35bo2bo4b2obo$7b2o3bo34bo2bo5bo$3b3o3b3o33bo3bobobo5bo$2b2o6b2o32bo15b3o$b4o6bo32bo2bo3bobo8b2o$4b2o2b2o2b2o11b3o15bo15b4o2bo$2bo2bob4o2b4o7b3o16bo2b3o11bo5bo$bo2b2ob3o6bo6b2obo3bo17b3o16bo$o5bo7b2o3bo7bo2bo12bo2bo2bo10bo$o2bo2bo5bobobobobo3b2o2b2o13bo17bo$13b3obo2bo4bo3bo13b2o3b2obo2bo7bo$14bo3bo7bobo2b3o18bob2obo$19bobo11b3o16bobo3bo$15bo6bob2o10bo15b3o4bo$16bo4bo7b2obo3bo16bo$17b2o3bo3bo2bo2bo2bo$14bo4bo8bobobo2bo18bo$13b4o5bo5b4o6b2o15bo$12b3o2bobo9b2o4bobo18bo$21bo$11bo2bo4b2o10b2o6b2o$12bo10bo16b2o$14b3obo3bo17bo2bo$14bo2bo3b2o17bo2b3o$14b4o2b3o2bobo5b4o4bo4bo$15bo2bobo4bo6b4ob2obo4b3o$17bo2bo2bo3bo3b2o3bo6bob3o$20bo2bo10bobo6bo2bo$19bo3bo6bo3bobobo6bo$19bo10bo3b2o$24bo9b5o6bo$21bobo7bo2bo4bo4b2o$26bo3b3o7b2o3b2o$24b2o3bo10b2o$28b2o8b2o$32bo8b2ob2o$28bo15b2o$31bob2o6b4o$29b6ob3o8bobobo$36b2o6bo4bo$45b2o4bo$45b2o$51b3o$44bo10bo3bo$45b2o4bo6b2o$53bobob3o$56bo5b4o$55bo4b4ob2o$60b2o3bo3b3o2bobo$55bo2bo12b3o2bo$64b3o3bo$73b2o$73bo2$75bo$76bo$77bo! | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 WIDTH 700 HEIGHT 560 AUTOSTART GPS 4 TRACK -1/4 -1/4 ]] | |||
|position = center | |||
|caption = c/4 diagonal linestretchers (note that the smaller right one's internal p8 mechanism is p4 in {{rl|Pedestrian Flock}}) | |||
|style = width:300px; | |||
}}}} | |||
{{gallery bottom}} | |||
===Oscillators=== | ===Oscillators=== | ||
Line 34: | Line 157: | ||
Oscillators with higher periods have been known to occur naturally. One of the most common of these is the ''Tetris shuttle'', consisting of a tetromino (which is a [[beehive]] grandparent in normal Life) being hassled by two dominoes. There is also a p9 which is a bit less common, along with one occurrence of a p7. | Oscillators with higher periods have been known to occur naturally. One of the most common of these is the ''Tetris shuttle'', consisting of a tetromino (which is a [[beehive]] grandparent in normal Life) being hassled by two dominoes. There is also a p9 which is a bit less common, along with one occurrence of a p7. | ||
{{gallery top}} | |||
{| | {{gallery item|{{EmbedViewer | ||
| | |rle = x = 50, y = 5, rule = B3/S12 | ||
| [[ | 15b2o20b2o$7bo7bobo8bo6b2o3bo4b2obo$2o5bobo16bo6bo2b2o7b2o2bo$o7bo8bo | ||
|- | bo4bobobo5bo2bo6bobo2bo$b2o6b2o7b2o4bo2b2o6b2o10bo! | ||
| [[ | |imgname = Flockp2 | ||
|- | |viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]] | ||
| [[ | |position = center | ||
|} | |caption = Small period-2 oscillators | ||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 48, y = 6, rule = B3/S12 | |||
31bo4bo7bo$15b2o6b2o6bo4bo6bo$obo5b2o7bo4bo2bo7b2o6bobo3bo$o8b2o6bo5b | |||
3o7b2o6bobo3bo$bo8bo4bo15bo4bo6bo$2b2o4b2o5b2o8b2o4bo4bo7bo! | |||
|imgname = Flockp4 | |||
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 4 ]] | |||
|position = center | |||
|caption = Small period-4 oscillators | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 19, y = 9, rule = B3/S12 | |||
2bo9b2o2bo$2bo14bo$2obo2bo3bo3bo3bo$2bo2bo4bo4b2obo$12bo3b2o$3bo2bo6bo | |||
$2bo2bob2obo2b2o$6bo4bo2bo$6bo5b2o! | |||
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 5 ]] | |||
|position = center | |||
|caption = Seminatural period-5 oscillators, a D4_x1 one ({{LinkCatagolue|code=xp5_44b4084zw2102d22/b3s12|style=brief}}) and D2_x one ({{LinkCatagolue|code=xp5_c0h148picz248b6/b3s12|style=brief}}) | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 6, y = 8, rule = B3/S12 | |||
obo$o$o2bo$b3o2$4b2o$2bob2o$4bo! | |||
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 6 ]] | |||
|position = center | |||
|caption = The only natural nontrivial period-6 oscillator | |||
|style = width:300px; | |||
|apgcode = xp6_789czw2073/b3s12 | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 9, y = 8, rule = B3/S12 | |||
2b2o$o2bo$3bo$obo4bo$bo4bobo$5bo$5bo2bo$5b2o! | |||
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 7 ]] | |||
|position = center | |||
|caption = Period-7 oscillator | |||
|style = width:300px; | |||
|apgcode = xp7_c9852zx4a193/b3s12 | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 20, y = 6, rule = B3/S12 | |||
4bo2bo$2bo2bobo8bo$5bo7bobo3bo$5bobo5bobo3bo$2o5bo$3obo! | |||
|imgname = Flockp9andp14 | |||
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 9 ]] | |||
|position = center | |||
|caption = Period-9<ref group="n">Note that the p9 has two variants ([[Catagolue]] links: {{LinkCatagolue|code=xp9_fvy18gzw12y1vu/b3s12|style=raw|name=variant 1}}, {{LinkCatagolue|code=xp9_3608xi4zw12y136/b3s12|style=raw|name=variant 2}}) naturally occurring with C2_2 symmetry and one variant ({{LinkCatagolue|code=xp9_0g29xi4z31y336/b3s12|style=brief}}) with D2_+1_gO1s1</ref> and period-14{{refn|group=n|Commonly referred to as the Tetris shuttle<ref name="post27531" />}} oscillators | |||
|style = width:300px; | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 14, y = 14, rule = B3/S12 | |||
6bo$5bo$5bo$6bo$6b2o$b2o3bo$o2b3o3bo$4bo3b3o2bo$7bo3b2o$6b2o$7bo$8bo$8bo$7bo! | |||
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 22 ]] | |||
|position = center | |||
|caption = [[Strictly volatile]] p22 found by [[Josh Ball]] on 2016-01-31<ref group="n">{{cata|attribute/xp22_y16pgz211262ho464884zy396/b3s12/D4_x4|the attribute page}}</ref> | |||
|style = width:300px; | |||
|apgcode = xp22_y16pgz211262ho464884zy396/b3s12 | |||
}}}} | |||
{{gallery item|{{EmbedViewer | |||
|rle = x = 9, y = 9, rule = B3/S12 | |||
b3ob3o$4bo$2o2bo2b2o$b7o2$b7o$2o2bo2b2o$4bo$b3ob3o! | |||
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 4 ]] | |||
|position = center | |||
|caption = The only known volatility-1 p4 | |||
|style = width:300px; | |||
|apgcode = xp22_y16pgz211262ho464884zy396/b3s12 | |||
}}}} | |||
{{gallery bottom}} | |||
<gallery> | <gallery> | ||
File:2x2_oscillator_rank1.gif| | |||
File:2x2_oscillator_rank4.gif| | |||
File:2x2_oscillator_rank5.gif| | |||
File:2x2_oscillator_rank8.gif| | |||
File:2x2_oscillator_rank9.gif| | |||
File:2x2_oscillator_rank10.gif| | |||
File:2x2_oscillator_rank12.gif| | |||
File:2x2_oscillator_rank14.gif| | |||
File:2x2_oscillator_rank15.gif| | |||
File:2x2_oscillator_rank16.gif| | |||
File:2x2_oscillator_rank18.gif| | |||
</gallery> | </gallery> | ||
==Notes== | |||
<references group="n"/> | |||
==See also== | |||
*rules named after Flock | |||
:*{{rl|HighFlock}} (B36/S12) | |||
:*{{rl|Pedestrian Flock}} (B38/S12) | |||
:*{{rl|EightFlock}} (B3/S128) | |||
:*{{rl|Goat Flock}} (B2in3/S123a) | |||
==References== | |||
<references> | |||
<ref name="post27169">{{LinkForumThread | |||
|format = ref | |||
|f = 11 | |||
|t = 2026 | |||
|p = 27169 | |||
|title = Re: B3/S12 (Flock) | |||
|author = velcrorex | |||
|date = February 1, 2016 | |||
}}</ref> | |||
<ref name="post27531">{{LinkForumThread | |||
|format = ref | |||
|f = 11 | |||
|t = 2026 | |||
|p = 27531 | |||
|title = Re: B3/S12 (Flock) | |||
|author = muzik | |||
|date = February 18, 2016 | |||
}}</ref> | |||
<ref name="post97187">{{LinkForumThread | |||
|format = ref | |||
|f = 11 | |||
|t = 2026 | |||
|p = 97187 | |||
|title = Re: B3/S12 (Flock) | |||
|author = LaundryPizza03 | |||
|date = May 18, 2020 | |||
}}</ref> | |||
<ref name="post174254">{{LinkForumThread | |||
|format = ref | |||
|f = 11 | |||
|t = 2026 | |||
|p = 174254 | |||
|title = Re: B3/S12 (Flock) | |||
|author = DroneBetter | |||
|date = December 27, 2023 | |||
}}</ref> | |||
<ref name="post175578">{{LinkForumThread | |||
|format = ref | |||
|f = 11 | |||
|t = 2026 | |||
|p = 175578 | |||
|title = Re: B3/S12 (Flock) | |||
|author = DroneBetter | |||
|date = January 14, 2024 | |||
}}</ref> | |||
</references> | |||
==External links== | ==External links== | ||
{{LinkCatagolueRule|b3s12}} | * {{LinkCatagolueRule|b3s12}} | ||
{{LinkEppsteinRule|b3s12}} | * {{LinkEppsteinRule|b3s12}} | ||
{{LinkForumThread|t=2026|title= | * {{LinkForumThread|t=2026|title=Flock}} | ||
[[Category:Life-like cellular automata]] |
Latest revision as of 06:20, 13 January 2024
Flock | |
View static image | |
Rulestring | 12/3 B3/S12 |
---|---|
Rule integer | 3080 |
Character | Chaotic |
Black/white reversal | B0123458/S01234678 |
Flock is a Life-like cellular automaton in which cells survive from one generation to the next if they have 1 or 2 neighbours, and are born if they have 3 neighbours. Its rulestring is B3/S12. It differs very strongly from Conway's Game of Life and similar automata. It is the fourth most searched rule on Catagolue in terms of the total number of objects censused from asymmetric soups as of August 2022.
Patterns
Due to the missing S3 survival condition and addition of the S1 survival condition, almost no patterns from Life are compatible with Flock and vice versa. Random starting soups rapidly degenerate into dominoes and still duoplets. Tub, beehive, loaf and mango still work as expected, as do the infinite family of lakes (including small lake and its extended derivatives).
The rule, however, does share many features with rules such as 2×2, HighFlock, EightFlock, Pedestrian Flock and Goat Flock.
There are small p2 oscillators which resemble the ship, long ship and very long ship when played, one of which looks like a bipole in one phase. This family of oscillators does not appear to be extendable.
Familiar fours
Despite the vastly different behaviour of patterns, some patterns can still settle naturally into familiar fours and related constellations. One, for example, is called flock, a constellation of four duoplets, which evolves from a 3 × 3 square of cells as in the traffic light sequence.
Flock predecessor (click above to open LifeViewer) |
Flock (click above to open LifeViewer) |
Another familiar four is known as radiator, composed of four dominoes.
Two radiator predecessors with different sequences (click above to open LifeViewer) |
Radiator (click above to open LifeViewer) |
Spaceships
Both orthogonal and diagonal spaceships exist in this rule. David Eppstein lists two orthogonal period-4 c/4 ships and a diagonal period-8 c/4 ship; additionally, Josh Ball found a c/5 orthogonal ship in 2016, LaundryPizza03 found a 2c/5 orthogonal ship in 2020, and DroneBetter found a c/6 diagonal ship in 2023.
speed | period | first known | discoverer | minimal known | discoverer |
---|---|---|---|---|---|
c/4 | 4 | 54P4H1V0 | unknown | 40P4H1V0 | unknown |
c/5 | 5 | 184P5H1V0 | Josh Ball, 2016[1] | 126P5H1V0 | DroneBetter, 2023[2] |
2c/5 | 5 | 242P5H2V0 | LaundryPizza03, 2020[3] | 82P5H2V0 | DroneBetter, 2023[2] |
c/6 | 6 | 58P6H1V0 | DroneBetter, 2024[4] | ||
c/4d | 4 | 206P4H1V1 | DroneBetter, 2023[2] | ||
8 | 18P8H2V2 | unknown | |||
c/6d | 4 | 57P6H1V1 | DroneBetter, 2023[2] |
Currently, the p8 c/4 diagonal spaceship is the only natural one, and has only occurred naturally once.[n 1]
Two orthogonal c/4 ships (Eppstein's 14679 and 14839) (click above to open LifeViewer) |
The smallest known even-symmetric and asymmetric c/5's (click above to open LifeViewer) Catagolue: here |
The smallest known even- and odd-symmetric 2c/5's (click above to open LifeViewer) |
The only known c/6 (click above to open LifeViewer) |
c/4 diagonal ships, of periods 8 (Eppstein's 10618) and 4 (click above to open LifeViewer) |
The only known c/6 diagonal (click above to open LifeViewer) Catagolue: here |
Linear growth
Linear growth is known in the form of 2c/5 domino puffers and c/4 diagonal linestretchers.[2]
A domino-pulling tagalong for the 2c/5 and additional tagalong with backward heavyweight sparks, that become stable dominoes (click above to open LifeViewer) |
c/4 diagonal linestretchers (note that the smaller right one's internal p8 mechanism is p4 in Pedestrian Flock) (click above to open LifeViewer) |
Oscillators
Many oscillators occur naturally in this rule. There are many extremely common p2 and p4 oscillators. p3 oscillators are somewhat rare but have been observed.
Oscillators with higher periods have been known to occur naturally. One of the most common of these is the Tetris shuttle, consisting of a tetromino (which is a beehive grandparent in normal Life) being hassled by two dominoes. There is also a p9 which is a bit less common, along with one occurrence of a p7.
Small period-2 oscillators (click above to open LifeViewer) |
Small period-4 oscillators (click above to open LifeViewer) |
Seminatural period-5 oscillators, a D4_x1 one (Catagolue: here) and D2_x one (Catagolue: here) (click above to open LifeViewer) |
The only natural nontrivial period-6 oscillator (click above to open LifeViewer) Catagolue: here |
Period-7 oscillator (click above to open LifeViewer) Catagolue: here |
Period-9[n 2] and period-14[n 3] oscillators (click above to open LifeViewer) |
Strictly volatile p22 found by Josh Ball on 2016-01-31[n 4] (click above to open LifeViewer) Catagolue: here |
The only known volatility-1 p4 (click above to open LifeViewer) Catagolue: here |
Notes
See also
- rules named after Flock
- HighFlock (B36/S12)
- Pedestrian Flock (B38/S12)
- EightFlock (B3/S128)
- Goat Flock (B2in3/S123a)
References
- ↑ velcrorex (February 1, 2016). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
- ↑ 2.0 2.1 2.2 2.3 2.4 DroneBetter (December 27, 2023). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
- ↑ LaundryPizza03 (May 18, 2020). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
- ↑ DroneBetter (January 14, 2024). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
- ↑ muzik (February 18, 2016). Re: B3/S12 (Flock) (discussion thread) at the ConwayLife.com forums
External links
- Flock at Adam P. Goucher's Catagolue
- Flock at David Eppstein's Glider Database
- Flock (discussion thread) at the ConwayLife.com forums