B3458/S05678

[Hektor]

I discovered this rule watching in the Eppstein's Glider Database, in the 'slowest spaceships' page.
It has a very interesting behaviour, the most of the pattern at first seem to grow indefinitely, but always (?) end in a stable 'filled' shape.
This one became stable after 1319 generations:

Code: Select all

x = 67, y = 42, rule = B3458/S05678
39b2o$37b2o$33b4o$31b2o$30bo$28b2o$26b2o$23b3o$21b2o$48b2o$46b2o$9o33b
4o$40b2o$39bo$37b2o$35b2o$32b3o$7b2o21b2o$6bo21b2o$4b2o20b2o6b18o$3bo
5b25o$23bo39b2o$22bo38b2o$20b2o35b4o$19bo35b2o$18b2o34bo$16b2o34b2o$
15bo34b2o$13b2o32b3o$12bo32b2o$43b2o$41b2o6b18o$24b25o$38bo$37bo$35b2o
$34bo$33b2o$31b2o$30bo$28b2o$27bo!

A lot of patterns end to be a p2 or mostly a p4, but I also found this p12:

Code: Select all

x = 9, y = 3, rule = B3458/S05678
$2ob3ob2o$bobobobo!

Found also this ladder maker, similar to the "Life without death" one:

x = 60, y = 66, rule = B3458/S05678

Code: Select all

b58o$60o$b58o$60o$b58o$60o$b58o$60o$b58o$60o$b58o$60o$b58o$60o$b58o$
60o$b58o$60o$b58o$60o$b58o$60o$b58o$60o$b58o$60o$b58o$60o$b58o$60o$b
58o$60o$b58o$60o$b58o$60o$b58o$60o$2b57o$2b58o$4b55o$4b56o$6b53o$6b54o
$8b51o$7b53o$9b50o$9b51o$11b48o$11b49o$13b46o$13b47o$15b43o$15b43o$17b
39o$17b39o$19b35o$18bob35o$20b33o$20b33o$22b29o$22b29o$24b21obobo$24bo
bobob2obobobobobobo$28bo4bo$30b2o!

And this one, generated from a 110 cells line:

Code: Select all

x = 110, y = 1, rule = B3458/S05678
110o!

These are the known spaceships on the database http://fano.ics.uci.edu/ca/rules/b3458s05678/
Can someone tell me how to measure the ladder's speed?

[Hektor]

Another laddermaker with a big slope on the top:

Code: Select all

x = 281, y = 182, rule = B3458/S05678
15$46b2o$44bo4bo$42bobob2obobobobobobo$40b21obobobobobo$40b32obobobobo
bo$38b45obobobobobo$38b56obobobobobo$36b69obobobobobo$36b80obobobobobo
$34b93obobobobobo$35b103obobobobobo$33b116obobobobobo$33b127obobobobob
o$31b140obobobobobo$31b151obobobobobo$29b164obobobobobo$29b175obobobob
obo$27b188obobobobobo$27b199obobobobobo$25b212obobobobobo$25b223obobob
obobo$23bob234obobobobobo$24b244o$22b248o$22b248o$20b252o$20b252o$18b
256o$18b256o$16b260o$16b260o$14b263o$14b262o$12b265o$13b263o$11b266o$
11b265o$9b268o$9b267o$7b270o$7b269o$5b272o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o$5b271o$4b273o
$5b271o!

[Wojowu]

Both ladders are c/11, calculated by hand, waiting for repetition of leading part of pattern. From all patterns I was generating, all lead into filled block or some number of ladders with same leading pattern

Glider 12066 (c/141) can eat dots

Code: Select all

x = 13, y = 35, rule = B3458/S05678
8bo$4bo$8bo$4bo$8bo$4bo$8bo$4bo$8bo$4bo$8bo$4bo$8bo$4bo$8bo$4bo5$6bo$
4bo3bo$4bobobo$2bobobobobo$2b3obob3o$2o2bo3bo2b2o$2b3o3b3o$2o2bo3bo2b
2o$2b9o$2o3bobo3b2o$6bo$5bobo$4b5o2$5bobo!

p14!

Code: Select all

x = 9, y = 9, rule = B3458/S05678
3bobo$2bobobo$2bo3bo$2o5b2o$2b5o$2o5b2o$2b2ob2o2$4bo!

[Hektor]

Found a p4 that can be extended both on the x and the y axis:

Code: Select all

x = 90, y = 22, rule = B3458/S05678
bobobobo13bobobobo13bobobobobobobobobobo10bobobobobobobobobobo2$b7o13b
7o13b19o10b19o$bo5bo13bo5bo13bo17bo10bo17bo$b7o13b7o13b19o10b19o2$o7bo
11bo7bo11bo19bo8bo19bo2$b7o13b7o13b19o10b19o$bobobobo13bo5bo13bobobobo
bobobobobobo10bo17bo$21b7o42b19o2$20bo7bo40bo19bo2$21b7o42b19o$21bo5bo
42bo17bo$21b7o42b19o2$20bo7bo40bo19bo2$21b7o42b19o$21bobobobo42bobobob
obobobobobobo!

Two p6

Code: Select all

x = 6, y = 5, rule = B3458/S05678
ob2obo$obobo$o4bo$obobo$ob2obo!

And p8!

Code: Select all

x = 11, y = 11, rule = B3458/S05678
2bobobobo2$ob7obo$2bo5bo$obo5bobo$2bo5bo$obo5bobo$2bo5bo$ob7obo2$2bobo
bobo!

[Tropylium]

The less dense areas generated by this rule seem to be basically the same as B345/S0, which is a slow chaotic growth rule (as are many other rules in its vicinity). It's fairly clear than an area of solidity is always bound to rise from chaos, and is bound to keep growing within it. Less obvious is why it generally gets "stuck" in a solid shape, though this seems common for many B345/D123 rules.

Some patterns with only one phase of zebra stripes work rather like LongLife. This is p28, for example:

Code: Select all

x = 18, y = 19, rule = B3457/S05678
7b4o2$5b8o2$3b12o2$b16o2$18o2$18o2$b16o2$3b12o2$5b8o2$7b4o!

Diamonds with odd width don't behave well due to the S0. For example, the previous osc is generated from a line of length 22; a line of length 23 will however die out to 9 dots…

[Drelectron8]

This rule is called Mystery if wanted to know.

Code: Select all

x = 12, y = 40, rule = B3458/S05678
2bo6bo2$3o6b3o2$ob2o4b2obo2$b4o2b4o$4bo2bo$b3o4b3o$3bo4bo$b2o6b2o$3bo4bo$b2o6b2o$3bo4bo$b2o6b2o$3b6o$
b2o6b2o$3b6o$b2o6b2o$3b6o$b2obo2bob2o$2bo2b2o2bo$5o2b5o2$ob2o4b2obo2$2bo6bo$o2b6o2bo$2b2o4b2o$4bo2bo
$4o4b4o$4b4o$3o6b3o$3bo4bo$b2o6b2o$3bob2obo$ob3o2b3obo$5b2o$b4o2b4o$5b2o!

Here is a spaceship.

[May13]

New speed, c/4 orthogonal spaceship:

Code: Select all

x = 35, y = 23, rule = B3458/S05678
17bo$13bobobobobo$9bobob2ob3ob2obobo$5bobobobob9obobobobo$3bobo4b4ob5o
b4o4bobo$bo3bo2b5ob7ob5o2bo3bo$6ob21ob6o$2b7ob2obob5obob2ob7o$6o2bob2o
2b7o2b2obo2b6o$bob5ob2ob2ob5ob2ob2ob5obo$bobobob5o2bob3obo2b5obobobo$b
ob2obob4o2b7o2b4obob2obo$4bo4b5ob5ob5o4bo$4bo2b7obobobob7o2bo$7bob5o2b
obo2b5obo$8b4o11b4o$9bob2o9b2obo$9bo15bo$7bobo15bobo$7bobobobo7bobobob
o$6b2obobob3obob3obobob2o$7bobobobobobobobobobobo$8bo3bob2o3b2obo3bo!