Wick symmetry

Wicks and waves, patterns which are periodic in time and in one dimension of space but not both, are subject to symmetries in some sense, much like finite patterns.

Space symmetries

It is not known if the following list is comprehensive.

C1

The wick has no symmetry; it is only periodic in space and time.

x = 42, y = 39, rule = B3/S23:T42,42-7 40b2o$40bo3$40b2o$34b2o5bo$34bobob3o$36bobo$36b2o$34b2o$28b2o5bo$28bob ob3o$30bobo$30b2o$28b2o$22b2o5bo$22bobob3o$24bobo$24b2o$22b2o$16b2o5bo $16bobob3o$18bobo$18b2o$16b2o$10b2o5bo$10bobob3o$12bobo$12b2o$10b2o$4b 2o5bo$4bobob3o$6bobo$6b2o$4b2o$5bo$ob3o$obo$2o! [[ THEME 6 GRID GRIDMAJOR 0 ZOOM 8 WIDTH 320 HEIGHT 320 NOGUI ]]
Asymmetric wick

C2

There are points on the wick with 180 degree rotational symmetry. There are seven possibilities:

• Two points of C2_1 symmetry
• One point of C2_1 symmetry, one point of C2_2 symmetry
• One point of C2_1 symmetry, one point of C2_4 symmetry
• Two points of C2_2 symmetry, parallel
• Two points of C2_2 symmetry, perpendicular
• Two points of C2_4 symmetry
• One point of C2_4 symmetry, one point of C2_2 symmetry

x = 17, y = 17, rule = B3/S23:T20+12,18 10b7o$10bo5bo$11b3o$8bo5bo$8b7o2$6b7o$6bo5bo$7b3o$4bo5bo$4b7o2$2b7o$2b o5bo$3b3o$o5bo$7o! [[ THEME 6 GRID GRIDMAJOR 0 ZOOM 8 WIDTH 320 HEIGHT 320 NOGUI ]]
Two C2_1 points

x = 8, y = 20, rule = B3/S23:T20-5,20 bo$o$4o$3bo$2bo$bo$b4o$4bo$3bo$2bo$2b4o$5bo$4bo$3bo$3b4o$6bo$5bo$4bo$ 4b4o$7bo! [[ THEME 6 GRID GRIDMAJOR 0 ZOOM 8 WIDTH 320 HEIGHT 320 NOGUI ]]
C2_1 and C2_2

x = 14, y = 28, rule = B3/S23:T20+12,28 12bo$12b2o$13bo$10b3o$9bo$9b2o$10bo$9bo$9b2o$10bo$7b3o$6bo$6b2o$7bo$6b o$6b2o$7bo$4b3o$3bo$3b2o$4bo$3bo$3b2o$4bo$b3o$o$2o$bo! [[ THEME 6 GRID GRIDMAJOR 0 ZOOM 8 WIDTH 320 HEIGHT 320 NOGUI ]]
C2_1 and C2_4

x = 40, y = 34, rule = B3/S23:T40,40+20 b2o$obo$o4b2o$o3bobo$4bo4b2o$o2b2o3bobo$bo6bo4b2o$bob2o2b2o3bobo$bobob o6bo4b2o$bobobob2o2b2o3bobo$2b2obobobo6bo4b2o$5bobobob2o2b2o3bobo$2b2o 2b2obobobo6bo4b2o$2bo6bobobob2o2b2o3bobo$obo3b2o2b2obobobo6bo4b2o$2o4b o6bobobob2o2b2o3bobo$4bobo3b2o2b2obobobo6bo4b2o$4b2o4bo6bobobob2o2b2o 3bobo$8bobo3b2o2b2obobobo6bo4b2o$8b2o4bo6bobobob2o2b2o3bobo$12bobo3b2o 2b2obobobo6bo$12b2o4bo6bobobob2o2b2o$16bobo3b2o2b2obobobo$16b2o4bo6bob obob2o2bo$20bobo3b2o2b2obobobo$20b2o4bo6bobobobo$24bobo3b2o2b2obobo$ 24b2o4bo6bobo$28bobo3b2o2b2o$28b2o4bo$32bobo3b2o$32b2o4bo$36bobo$36b2o ! [[ THEME 6 GRID GRIDMAJOR 0 ZOOM 8 WIDTH 320 HEIGHT 320 NOGUI ]]

Two C2_2 points, parallel

x = 10, y = 27, rule = B3/S23:T20+9,27 8bo$8b2o$9bo$7bo$7b2o$8bo$6bo$6b2o$7bo$5bo$5b2o$6bo$4bo$4b2o$5bo$3bo$ 3b2o$4bo$2bo$2b2o$3bo$bo$b2o$2bo$o$2o$bo! [[ THEME 6 GRID GRIDMAJOR 0 ZOOM 8 WIDTH 320 HEIGHT 320 NOGUI ]]
Two C2_2 points, perpendicular

x = 14, y = 18, rule = B3/S23:T18-6,18 13bo$10b4o$10bo$11bo$8b4o$8bo$9bo$6b4o$6bo$7bo$4b4o$4bo$5bo$2b4o$2bo$ 3bo$4o$o! [[ THEME 6 GRID GRIDMAJOR 0 ZOOM 8 WIDTH 320 HEIGHT 320 NOGUI ]]
C2_2 and C2_4

x = 12, y = 20, rule = B3/S23:T20+10,20 bo$2o$2b2o$2bo$3bo$2b2o$4b2o$4bo$5bo$4b2o$6b2o$6bo$7bo$6b2o$8b2o$8bo$ 9bo$8b2o$10b2o$10bo! [[ THEME 6 GRID GRIDMAJOR 0 ZOOM 8 WIDTH 320 HEIGHT 320 NOGUI ]]
Two C2_4 points

D2

The wick is mirror symmetric across two parallel lines, perpendicular to the direction of periodicity. There are four possibilities:

To sort

These are to be placed in viewers.

-c and -c x = 32, y = 11, rule = B3/S23:T32,20 3bo7bo7bo7bo$2bobo5bobo5bobo5bobo$3bo7bo7bo7bo2$b5o3b5o3b5o3b5o$o2bo2b obo2bo2bobo2bo2bobo2bo2bo$2o3b2ob2o3b2ob2o3b2ob2o3b2o$2b3o5b3o5b3o5b3o $2o3b5o3b5o3b5o3b3o$2bobo2bo2bobo2bo2bobo2bo2bobo2bo$b2ob2o3b2ob2o3b2o b2o3b2ob2o!

-c and -e x = 35, y = 7, rule = B3/S23:T35,20 o3b2o3b2o3b2o3b2o3b2o3b2o3bo$bobo2bobo2bobo2bobo2bobo2bobo2bobo$2ob4ob 4ob4ob4ob4ob4ob2o2$2ob4ob4ob4ob4ob4ob4ob2o$bobo2bobo2bobo2bobo2bobo2bo bo2bobo$2bo4bo4bo4bo4bo4bo4bo!

-e and -e x = 36, y = 7, rule = B3/S23:T36,20 2b2o4b2o4b2o4b2o4b2o4b2o$bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$b4o2b4o2b 4o2b4o2b4o2b4o2$b4o2b4o2b4o2b4o2b4o2b4o$bo2bo2bo2bo2bo2bo2bo2bo2bo2bo 2bo2bo$o4b2o4b2o4b2o4b2o4b2o4bo!

/ and / x = 31, y = 31, rule = B3/S23:T31,31 29bo$28bobo$27bo2bo$26bob2o$25bobo$24bo2bo$23bob2o$22bobo$21bo2bo$20bo b2o$19bobo$18bo2bo$17bob2o$16bobo$15bo2bo$14bob2o$13bobo$12bo2bo$11bob 2o$10bobo$9bo2bo$8bob2o$7bobo$6bo2bo$5bob2o$4bobo$3bo2bo$2bob2o$bobo$o 2bo$b2o!

+c and +c x = 7, y = 36, rule = B3/S23:T35,36 2bobo$obobobo$2obob2o$3bo$2obob2o$obobobo$2bobo$obobobo$2obob2o$3bo$2o bob2o$obobobo$2bobo$obobobo$2obob2o$3bo$2obob2o$obobobo$2bobo$obobobo$ 2obob2o$3bo$2obob2o$obobobo$2bobo$obobobo$2obob2o$3bo$2obob2o$obobobo$ 2bobo$obobobo$2obob2o$3bo$2obob2o$obobobo!

+c and +e x = 7, y = 35, rule = B3/S23:T35,35 2obob2o$3bo$3bo$2obob2o$obobobo$2bobo$obobobo$2obob2o$3bo$3bo$2obob2o$ obobobo$2bobo$obobobo$2obob2o$3bo$3bo$2obob2o$obobobo$2bobo$obobobo$2o bob2o$3bo$3bo$2obob2o$obobobo$2bobo$obobobo$2obob2o$3bo$3bo$2obob2o$ob obobo$2bobo$obobobo!

+e and +e x = 7, y = 36, rule = B3/S23:T35,36 2bobo$b2ob2o$o5bo$o5bo$b2ob2o$2bobo$2bobo$b2ob2o$o5bo$o5bo$b2ob2o$2bob o$2bobo$b2ob2o$o5bo$o5bo$b2ob2o$2bobo$2bobo$b2ob2o$o5bo$o5bo$b2ob2o$2b obo$2bobo$b2ob2o$o5bo$o5bo$b2ob2o$2bobo$2bobo$b2ob2o$o5bo$o5bo$b2ob2o$ 2bobo!

+e and +k x = 8, y = 35, rule = B3/S23:T36,35 bob2obo$2o4b2o$2b4o$2o4b2o$bob2obo$bob2obo$2o4b2o$2b4o$2o4b2o$bob2obo$ bob2obo$2o4b2o$2b4o$2o4b2o$bob2obo$bob2obo$2o4b2o$2b4o$2o4b2o$bob2obo$ bob2obo$2o4b2o$2b4o$2o4b2o$bob2obo$bob2obo$2o4b2o$2b4o$2o4b2o$bob2obo$ bob2obo$2o4b2o$2b4o$2o4b2o$bob2obo!

+k and +k x = 12, y = 24, rule = B3/S23:T24,24 2obob2obob2o$3bo4bo$2obo4bob2o$bobob2obobo$bobob2obobo$2obo4bob2o$3bo 4bo$2obob2obob2o$2obob2obob2o$3bo4bo$2obo4bob2o$bobob2obobo$bobob2obob o$2obo4bob2o$3bo4bo$2obob2obob2o$2obob2obob2o$3bo4bo$2obo4bob2o$bobob 2obobo$bobob2obobo$2obo4bob2o$3bo4bo$2obob2obob2o!

xc and xc x = 24, y = 24, rule = B3/S23:T24,24 10b2ob2o$9bo2bo$8bobobo$8bo2bo$6b2ob2o$5bo2bo$4bobobo$4bo2bo$2b2ob2o$b o2bo$obobo$o2bo$b2o19b2o$o20bo$o19bobo$20bo2bo$18b2ob2o$17bo2bo$16bobo bo$16bo2bo$14b2ob2o$13bo2bo$12bobobo$12bo2bo!

xc and xk x = 20, y = 20, rule = B3/S23:T20,20 19bo$18bo$17bo$16bo$15bo$14bo$13bo$12bo$11bo$10bo$9bo$8bo$7bo$6bo$5bo$ 4bo$3bo$2bo$bo$o!

xk and xk x = 24, y = 24, rule = B3/S23:T24,24 14b2obo2bo$9bo3bobobobo$8bobobobo3bo$7bo2bob2o$8b3o$11b3o$8b2obo2bo$3b o3bobobobo$2bobobobo3bo$bo2bob2o$2b3o$5b3o$2b2obo2bo$bobobobo13bo$obo 3bo13bobo$2o17bo2bo$20b3o$2o21bo$2bo17b2obo$bo13bo3bobobo$o13bobobobo$ 13bo2bob2o$14b3o$17b3o!

n glide c x = 24, y = 13, rule = B3/S23:T24,24 6b2o6b2o6b2o$7bo7bo7bo$6bo7bo7bo$6b2o6b2o6b2o$o2bo4bo2bo4bo2bo$o2b6o2b 6o2b5o2$5o2b6o2b6o2bo$4bo2bo4bo2bo4bo2bo$2b2o6b2o6b2o$2bo7bo7bo$3bo7bo 7bo$2b2o6b2o6b2o!

n glide e x = 24, y = 6, rule = B3/S23:T24,24 4b2o4b2o4b2o4b2o$bo2bo2bo2bo2bo2bo2bo2bo$2o3b3o3b3o3b3o3bo$2b3o3b3o3b 3o3b3o$bo2bo2bo2bo2bo2bo2bo2bo$b2o4b2o4b2o4b2o!

n glide / x = 67, y = 64, rule = B3/S23 65b2o$62bo3bo$62b4o$60b2o$56b2obobo2b2o$56b2obo4b2o$59bo$59b2o$57b2o$ 54bo3bo$54b4o$52b2o$48b2obobo2b2o$48b2obo4b2o$51bo$51b2o$49b2o$46bo3bo $46b4o$44b2o$40b2obobo2b2o$40b2obo4b2o$43bo$43b2o$41b2o$38bo3bo$38b4o$ 36b2o$32b2obobo2b2o$32b2obo4b2o$35bo$35b2o$33b2o$30bo3bo$30b4o$28b2o$ 24b2obobo2b2o$24b2obo4b2o$27bo$27b2o$25b2o$22bo3bo$22b4o$20b2o$16b2obo bo2b2o$16b2obo4b2o$19bo$19b2o$17b2o$14bo3bo$14b4o$12b2o$8b2obobo2b2o$ 8b2obo4b2o$11bo$11b2o$9b2o$6bo3bo$6b4o$4b2o$2obobo2b2o$2obo4b2o$3bo$3b 2o!

n glide /e x = 62, y = 56, rule = B3/S23 58b2o$49b2o5bo2bo$49bobo4b3o$51bo2b2o$50b2obobo2b3o$53bo4bo2bo$53b2o5b 2o$51b2o$42b2o5bo2bo$42bobo4b3o$44bo2b2o$43b2obobo2b3o$46bo4bo2bo$46b 2o5b2o$44b2o$35b2o5bo2bo$35bobo4b3o$37bo2b2o$36b2obobo2b3o$39bo4bo2bo$ 39b2o5b2o$37b2o$28b2o5bo2bo$28bobo4b3o$30bo2b2o$29b2obobo2b3o$32bo4bo 2bo$32b2o5b2o$30b2o$21b2o5bo2bo$21bobo4b3o$23bo2b2o$22b2obobo2b3o$25bo 4bo2bo$25b2o5b2o$23b2o$14b2o5bo2bo$14bobo4b3o$16bo2b2o$15b2obobo2b3o$ 18bo4bo2bo$18b2o5b2o$16b2o$7b2o5bo2bo$7bobo4b3o$9bo2b2o$8b2obobo2b3o$ 11bo4bo2bo$11b2o5b2o$9b2o$2o5bo2bo$obo4b3o$2bo2b2o$b2obobo2b3o$4bo4bo 2bo$4b2o5b2o!

-c glide c x = 24, y = 9, rule = B3/S23:T24,12 2bo7bo7bo$5o3b5o3b5o$5bobo5bobo5bobo$6ob7ob7obo2$2ob7ob7ob5o$bobo5bobo 5bobo$o3b5o3b5o3b4o$6bo7bo7bo!

-c glide e x = 24, y = 6, rule = B3/S23:T24,12 2ob2ob2ob2ob2ob2ob2ob2o$bobo3bobo3bobo3bobo$o3b3o3b3o3b3o3b2o$b3o3b3o 3b3o3b3o$o3bobo3bobo3bobo3bo$2ob2ob2ob2ob2ob2ob2ob2o!

-e glide c x = 24, y = 7, rule = B3/S23:T24,12 2b2o4b2o4b2o4b2o$bo2bo2bo2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo2bo2bo$ob2ob 2ob2ob2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo2bo2bo$o 4b2o4b2o4b2o4bo!

-e glide e x = 24, y = 4, rule = B3/S23:T24,8 2b2o4b2o4b2o4b2o$bo2bo2bo2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo2bo2bo$o4b2o 4b2o4b2o4bo!

/ glide / x = 23, y = 24, rule = B3/S23:T24,24 20b3o2$18b3o$15bo2bo2bo$14bobobobo$13bo2bo2bo$14b3o2$12b3o$9bo2bo2bo$ 8bobobobo$7bo2bo2bo$8b3o2$6b3o$3bo2bo2bo$2bobobobo$bo2bo2bo$2b3o2$3o$o 2bo17bo$obo17bobo$bo17bo2bo!

/ glide /e x = 24, y = 24, rule = B3/S23:T24,24 23bo$23bo$21b2o$20bo$20bo$18b2o$17bo$17bo$15b2o$14bo$14bo$12b2o$11bo$ 11bo$9b2o$8bo$8bo$6b2o$5bo$5bo$3b2o$2bo$2bo$2o!

/ and .c glide / x = 32, y = 32, rule = B3/S23:T32,32 $10b3o$9bo3bo$6bo2bo2bo$5bobobobo$4bo2bo2bo$3bo3bo$4b3o2$2b3o$bo3bo$bo 2bo25bo$bobo25bobo$2bo25bo2bo$27bo3bo$28b3o2$26b3o$25bo3bo$22bo2bo2bo$ 21bobobobo$20bo2bo2bo$19bo3bo$20b3o2$18b3o$17bo3bo$14bo2bo2bo$13bobobo bo$12bo2bo2bo$11bo3bo$12b3o!

/ and .e glide /e x = 22, y = 22, rule = B3/S23:T22,22 19b2o$18bo2bo$17bo2bo$16bob2o$15bobo$14bo2bo$14bobo$12b2obo$11bo2bo$ 10bo2bo$9bob2o$8bobo$7bo2bo$7bobo$5b2obo$4bo2bo$3bo2bo$2bob2o$bobo$o2b o$obo$bo!