## Rules with interesting dynamics

For discussion of other cellular automata.

### Re: Rules with interesting dynamics

x = 23, y = 7, rule = B2ci3ai4ci8/S02ae3eijkq4iz5a6i7e3bo15bo$b5o11b5o$bo3bo3b2o6bo3bo$2obob2ob2obo4b2obob2o$bo3bo3b2o6bo3bo$b5o11b5o$3bo15bo!

90-degree turner:
x = 7, y = 11, rule = B2ci3ai4ci8/S02ae3eijkq4iz5a6i7e2b2o$3bo$2b2o2$3bo$b5o$bo3bo$2obob2o$bo3bo$b5o$3bo! Doubler: x = 41, y = 29, rule = B2ci3ai4ci8/S02ae3eijkq4iz5a6i7e12bo15bo$10b5o11b5o$10bo3bo6b2o3bo3bo$9b2obob2o4bob2ob2obob2o$10bo3bo6b2o3bo3bo$10b5o11b5o$12bo15bo14$12bo15bo$10b5o11b5o$3bo6bo3bo6b2o3bo3bo6bo$b5o3b2obob2o4bob2ob2obob2o3b5o$bo3bo4bo3bo6b2o3bo3bo4bo3bo$2obob2o3b5o11b5o3b2obob2o$bo3bo6bo15bo6bo3bo$b5o29b5o$3bo33bo!

It seems like the doubler could be used for a stable 180-degree reflector.

Fuses:
x = 44, y = 52, rule = B2ci3ai4ci8/S02ae3eijkq4iz5a6i7e16bo15bo$14b5o11b5o$14bo3bo11bo3bo$8bo4b2obob2o4bo4b2obob2o4bo$6b5o3bo3bo3b5o3bo3bo3b5o$b2o3bo3bo3b5o3bo3bo3b5o3bo3bo$ob2ob2obob2o4bo4b2obob2o4bo4b2obob2o$b2o3bo3bo11bo3bo11bo3bo$6b5o11b5o11b5o$8bo15bo15bo14$8bo$6b5o$b2o3bo3bo$ob2ob2obob2o$b2o3bo3bo$6b5o$8bo4bo$11b5o$11bo3bo$10b2obob2o$11bo3bo$11b5o3bo$13bo3b5o$17bo3bo$16b2obob2o$17bo3bo$17b5o$19bo4bo$22b5o$22bo3bo$21b2obob2o$22bo3bo$22b5o3bo$24bo3b5o$28bo3bo$27b2obob2o$28bo3bo$28b5o$30bo!

It seems like with the current tech, all that is needed is a 2-cell pull+reflect reaction to create large ships of arbitrary slow speeds.

EDIT: This rule also has some big 2x2-like oscillators, but with 1x2 blocks.
she/they // Please stop using my full name. Refer to me as dani.

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

danny

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### Re: Rules with interesting dynamics

I don't even know how to wrap my head around this one:
x = 95, y = 122, rule = B2k3/S23-a4eitz91b2o$91b3o$85b2o6b2o$84bo8bo$71b2o11bo2bo4bo$72b2o11b3o$72b2o2$74b3o2$3o9b3o9b3o9b3o9b3o9b3o9b2ob2o$75b2o57$30bo8b4o$28bo2bo3b2o2b2obo$28b2ob2o7bo2b2o$28bo2b2o4b2o5bo$30bo7b7o$31b3obo$33bobobob6o$35bobobo4bo$34bo2bo6bo$38b2o3bo$40bo6$2b3o$2b2obo$5b2o3b2o$2bo2bobob3o$b4o4b3o$2b2o5bo$10b2o$4b3o3b2o$4bo2bo2b2o$7bo$5bo2bo$6bob2o$6b3o5$6bo$3bo2bo$4b3o7$85bo$77bo7b2o$76b3o5bob2o$63bo11bobobo4bobo$63b2o9b2o2b2o4b2o$64bo10bo2b2o$63b2obo8bo2bo$63b2obo9b3o$66b2o$64bobo$3b3o9b3o9b3o9b3o9b3o11b2o$65bo!

It makes a diagonal checkerboard which gradually fills up on the right.
she/they // Please stop using my full name. Refer to me as dani.

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

danny

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Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA

### Re: Rules with interesting dynamics

danny wrote:I don't even know how to wrap my head around this one:
rle

It makes a diagonal checkerboard which gradually fills up on the right.

That's a nice example of an MMMS breeder and an illustration of why cubic growth is impossible. Great find!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

A for awesome

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### Re: Rules with interesting dynamics

gmc_nxtman wrote:B3-cej/S234eijkrw5cry6ik7:

x = 16, y = 16, rule = B3-cej/S234eijkrw5cry6ik79bo2bob2o$o5bob2o4b2o$3ob2obo2bob2obo$2bo3bo2bo2bo$2ob2o2bob5obo$3o2b2ob4obobo$2ob2obob2o$o3b2obo5b2o$3b4ob3ob2o$4ob2ob5o2bo$2b2o3bob2obobo$3bo3bob2ob4o$ob4obo3b2o$4bobob6obo$4b2obob2o2b3o$o4b2obo4b2o! Takes a long time to stabilize for sure. Here's a 2c/8 diagonal from that rule: x = 4, y = 5, rule = B3-cej/S234eijkrw5cry6ik73o$2o$3bo$obo$bo! x = 4, y = 3, rule = B3-q4z5y/S234k5j2b2o$b2o$2o! LaundryPizza03 at Wikipedia LaundryPizza03 Posts: 337 Joined: December 15th, 2017, 12:05 am Location: Unidentified location "https://en.wikipedia.org/wiki/Texas" ### Re: Rules with interesting dynamics Another odd variant of the "crystallographic defect" rule, with some weird phenomena: x = 64, y = 4, rule = B2cn3-eqry4ckr/S01c2c3c4c6o2bob2o3b2o3bo2b3o3bob2o2b4o2bobob5o2bob3o2b2o2bo$bo2bob3o2bo3b2ob9o8bobobobo2b2o2b5o4bo2b2obo$4b3obo2bo7b7o2b2o2b3o2b2o2bo5b2ob6o2bo2bo$2b2o3b2ob2o2b2o2bo3bob2ob2o3b3o2bobobo2b2o3b2obob2ob7o!

Things crystallise slightly differently in this rule. There are multiple oscillating "wicks" that crystallise in the defects that seem to move in a random way. that I originally thought there was only one rule with the phenomenon, but Saka later proved me wrong, and there may be even more weird things lurking in this set of rules.

EDIT: Spacefiller in another variant:

x = 208, y = 5, rule = B2cn3-eqry4ckr/S01c2cn3c4cq2b3ob3ob2o2bobo3b3o5b2o2bo5bo3bob2o2b3o2b2o4b2o2bo2b4o3b2ob2o7b2obobobo2b2ob5obobobo2b2obob7o2b2ob4o2bo3bo10b2ob2ob6ob2obob4o2bobobo4b2ob3ob4ob2ob3obobo2bo$b2ob2obobo2bob2ob2o2bob7obob3obob2obo3b2o3b3o2bo2bo3b2o3bob6ob2o3bo2bob2o2bobo2bo2bob2ob2obobobob4o3bo4bobo4bob2obo5bo2bob3o3b2o2b4o2b3o2bob2ob2ob2ob2o3b2ob2ob2o2bob4obob3o$2bo2bob2o4b3o4bo2bobo2bo3bobobobobob4obo3bo2bob4ob2o2bo3b2o4b3o5b2o2b4o2bo5b2o2bo2bobob2o3b2ob8o2b2obo4b2ob6ob5o7b2obo3bob3obobo7b5obob2o2bo2b2ob3o3b2o$2bo3bo2b6o2b3obo3b2obo2b3o2bob3obo3b3ob3ob3o2bo2bo2bo2bo3bobo3b5obo2bob2obob3ob2ob5obob2o6bo2b7ob3ob3o2bobo6bob3obob2o2bo2bo2bobo3b4o2b2o3b2ob2o4bob2o2b5o3bob2o$o5b4obo3b2o3bo2b7o2bobobo3bobob2o4bo4b2ob3o2b2o3b3o3bo2bobo3bo2bob7o2bobo2bo6bob2o2bobob3o2b2obobo3bob3obobobob2o7bo2bob3ob2obob3o2b3obo3bobo2bo2bo3bo2b2o3b2o2b3o!

gmc_nxtman

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### Re: Rules with interesting dynamics

danny wrote:EDIT: This rule also has some big 2x2-like oscillators, but with 1x2 blocks.

Very interesting -- so this variant Snowflakes rule has the same exact set of even-length Sierpinski-triangle XOR oscillators again:

x = 72, y = 1, rule = B2ci3ai4ci8/S02ae3eijkq4iz5a6i7e72o!#C [[ STOP 174762 ]]

The odd lengths look like they're going to do the same thing, but they reliably collapse. I guess that's one way to tell even from odd --

x = 73, y = 1, rule = B2ci3ai4ci8/S02ae3eijkq4iz5a6i7e73o!

To look up what period an oscillator will be, add two to the length and look up that value in the WolframIndex column in the table.

dvgrn
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### Re: Rules with interesting dynamics

Something that I realized about these XOR oscillators: They're all actually 2x2 block oscillators, it's just that the 2x2 blocks have different contents. For the original 2x2 rule, the 2x2 blocks are completely full; for B2c/S and analogues, the blocks consist of one on cell and 3 off cells; and for rules such as that in the above post, the blocks look like this:
oo..

Obviously, they aren't all Margolus automata (at least range 1) — unlike 2x2 — but I feel like they still classify as 2x2 block oscillators, if not automata.

Here are two more families I've found based on this idea:
x = 96, y = 2, rule = B2c/S2cobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo! x = 90, y = 2, rule = B2c3i5i/S3i4i90o$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo!

Unfortunately, patterns in rules supporting the latter family cannot escape their bounding box.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

A for awesome

Posts: 1816
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: Rules with interesting dynamics

A for awesome wrote:Something that I realized about these XOR oscillators: They're all actually 2x2 block oscillators, it's just that the 2x2 blocks have different contents. For the original 2x2 rule, the 2x2 blocks are completely full; for B2c/S and analogues, the blocks consist of one on cell and 3 off cells; and for rules such as that in the above post, the blocks look like this:
oo..

Yup, and clearly the dynamics of all these rules have to be exactly isomorphic in some sense, or the recognizable behavior couldn't happen.

I had this rule confused with Snowflakes for a while there, and posted the following in the wrong thread. Putting it here now with appropriate edits, so as not to waste it --

There seem to be oscillators out there with period (2^N-2)*2^k for any N>2 and k>=0. And then there are the exceptions-that-prove-the-rule ones at 174762 and 45 billion [one third of "standard" numbers, both -- (2^19-2)/3 and (2^37-2)/3 ]...

#C period 45812984490 oscillatorx = 188, y = 1, rule = B2ci3ai4ci8/S02ae3eijkq4iz5a6i7e188o!

... So can the pointy ends of these diamonds make gliders and suchlike, the way AbhpzTa did with the horiship guns in B2cek3i/S12cei?

dvgrn
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### Re: Rules with interesting dynamics

variable-period replicator world:
......

Thought I saw a mandelbrot at around 969,000
freaked my out
Failed Replicator!
x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8bo$obo$bobo$2bo! (That I wish was not failed D:) jimmyChen2013 Posts: 131 Joined: December 11th, 2017, 3:28 am ### Re: Rules with interesting dynamics A for awesome wrote:Something that I realized about these XOR oscillators: They're all actually 2x2 block oscillators, it's just that the 2x2 blocks have different contents. For the original 2x2 rule, the 2x2 blocks are completely full; for B2c/S and analogues, the blocks consist of one on cell and 3 off cells; and for rules such as that in the above post, the blocks look like this: I found this out a good few months ago. I tried looking for a rule where the last family worked though, with no success. Here's more: x = 23, y = 6, rule = B2e/So3bo5bo6bo$bo3bo5bo6bo$6bo5bo6bo$7bo5bo6bo$14bo6bo$22bo!

The thread also mentioned this one:
x = 65, y = 32, rule = B2-a3/S01c5io19bo19bo19bo$21bo19bo19bo$22bo19bo19bo$43bo19bo$64bo16$2o18b2o18b2o18b2o$2o18b2o18b2o18b2o$2o18b2o18b2o18b2o$2o18b2o18b2o18b2o$20b2o18b2o18b2o$20b2o18b2o18b2o$20b2o18b2o18b2o$20b2o18b2o18b2o$40b2o18b2o$40b2o18b2o$60b2o$60b2o!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with interesting dynamics

A type R(?) replicator, which fits in at least six of the seven rules:

x = 1, y = 1, rule = B1c2n3c4c/So!

x = 2, y = 1, rule = B1c2a3q6i/S2o!

x = 2, y = 2, rule = B1c2n/S1c2n4cbo$o! x = 2, y = 2, rule = B1c2a3aq4qw8/S2a3q6i2o$bo!

x = 2, y = 2, rule = B1c2a4w/S3a4q82o$2o! x = 1, y = 1, rule = B1e2i3e4e/So! Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3310 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Rules with interesting dynamics It also appears that the "off" block state can be replaced under some circumstances allowing for oscillators that are similar if not exactly the same: x = 15, y = 15, rule = B4c/S02en3ce4ci5e15o$obobobobobobobo$2obobobobobob2o$obobobobobobobo$2obobobobobob2o$obobobobobobobo$2o9bob2o$obobobobobobobo$2obobobobobob2o$obobobobobobobo$2obobobobobob2o$obobobobobobobo$2obobobobobob2o$obobobobobobobo$15o! x = 15, y = 15, rule = B4t5ey6ci/S2ek3cnr4cy5e4b2o3b2o$b2obobobobob2o$bobobobobobobo$2bobobobobobo$2obobobobobob2o$obobobobobobobo$bob2obobobo2bo$2bobobobobobo$bobobobobobobo$obobobobobobobo$2obobobobobob2o$2bobobobobobo$bobobobobobobo$b2obobobobob2o$4b2o3b2o! x = 17, y = 17, rule = B3a5i8/S3i4i6ci7e8bobobobobobobobo$17o$bobobobobobobobo$17o$bobobobobobobobo$17o$bobobobobobobobo$17o$b13obo$17o$bobobobobobobobo$17o$bobobobobobobobo$17o$bobobobobobobobo$17o$bobobobobobobobo! x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce A for awesome Posts: 1816 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Rules with interesting dynamics This one seems to work for any even number not divisible by 4: x = 36, y = 16, rule = B2e3a4w/S1c3a4q2o5b2o11b2o$2o5b2o11b2o$2b2o5b2o11b2o$2b2o5b2o11b2o$11b2o11b2o$11b2o11b2o$13b2o11b2o$13b2o11b2o$28b2o$28b2o$30b2o$30b2o$32b2o$32b2o$34b2o$34b2o!

Also, bilateral rules can allow for this:

x = 31, y = 31, rule = B3i6i/S2i5i2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo9$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Rules with interesting dynamics

When there are two or more natural spaceships that travel at different speeds in the same direction, it is sometimes possible for islands of debris/chaos to form:
x = 64, y = 64, rule = B2ek3eikqr4aejr6k/S02ack3aknry4aknb2obobob2obo2b5o2bo5b5ob3o3bo2b2obo2bob2obob2o3b3o$3bobo2b3ob4o3bob2obobo2b8obo5b5o2bobo3b4ob2o$2bob2o2bo4bobo3b2ob2o7bo2b2ob3ob3o2b4o2b3o2b2o3b2o$3bo3bobo4b2o2b2ob2o2b2o2bo2bo8b2obo2bo2b2o4b4ob2o$b2ob3obob3ob2ob2ob5ob2ob3o4bo2b2ob3o2b2obob3ob2o2b4o$o2b3o2bo2bo2bo2b4ob2o2bobob2obobo3bobob2obob2o2b5obob3o$bo2bo4b3o3bobo4b3o3b2o3bo4b5ob2o2bo2bob2obo3bo2bo$4obo5b5o2b3o2bo2bo2bo2b2o3bobo4b2o2b4o2b3ob3o$2ob7o4b2o2bo2bobo3b2ob5obob2o5b2ob5obo2bo3b3o$2o3bob6obo2bo2b7obob2ob2obobob4obo6bo2bobob3obo$o2b4ob3ob2ob2ob2ob2o4b4obob2o2bob2o2bob3o10bo2bo$b4obobo2b4obob2obobobo2bobo2b3obo2bo6b4obo5b2o$2bo7bo3bo2bo3b3o2b3o4bobobob2o7b2o2bo2b3o2b3o$2obobo2bo3bo3b3obob3o2bo4bobo3b2o4b2o4bo2b3o3b2obo$5obo2b2o2bobobo5bo2bobo2bo3b4o3bo3bobobob2ob2obob2o$b6o4bob3obo2bob2ob2obobo3b2obo4b2o7bob2o2b2o$2obo4b3obo2bob4obo3bo3bob2o2bo2bo4b3obob7ob2o2bo$2bo4bobob3o3b5obob2o3bo3bobo2bo3bobo3b4o2bo6b2o$obo2b2o3b3obob4o3bo2b4o3b2o2b2o4bo6b2ob2o2bob3o$3o2b2obo4b2ob2o2b2obo3b2obob2o2bob2obob2o5b2ob3o2bo2bobo$6b4obo3bo2b2obob2o4b2obob3o2b2o3bob2o4b2o2b2o3bobo$bob2obo3bobo2bo5b2obo7bo2bo2b5obo3b3obobo3b3o$2ob4o2bo3bo3bobobo3bob4ob2ob3o3bo3b2obob3o7bob2o$5bo2bo4bo5b2o2bobo2bo2b3obob4o2bob2o3b3o2b4o3b2o$5bo3bobob2ob3obo2b6ob2ob2o4b2o5bo2bo2bo7bo$obo3bo2b2o2b4obo3bobo4b2o2b2o2bob2obob3ob6ob2o2b4o$5b4ob2o2bob3ob2o2bo2bob2obo6bobob2obobo4b5o2b4o$2b2ob2o2bob2ob2obob4obo2b4obo2bobob4o3bobo3bo2bob2obo2bo$3ob3o3bo3bobo6b2ob3obob4obobob4o2bo2b4ob2obo2bo$2b3ob2o4b2o3b2obob2o6b3obo2bo2b2ob2obo2b2o2b7obobo$2bo2bob2obob2obob2o3b2obo4b3ob2o2bo2b2o2b3o2b2o3bo2b2obobo$2b4o2b2obobo3bob6o5b2ob3obo4bo4b2obobo4b2o2bobo$o4b3obobob6o3b2o2bo2b2o5bob2o4bo4bob7ob4o$b2o2bob7ob2obob2ob3o2b2obobo3b4obo2b2o2b2obob2ob7o$o5bo2bob2o3b3o2bo3b5ob2ob2ob2o3bo4bo2b3o2bo3bob2o$bo2bobo6bob3ob5ob3obo2b3o2b2o2b2o3bo2b2o2bo2bo2b2o$obobo3bobobob5o2bob3ob4obobob2o2bo2b4obo2b9ob2o$3bo4b3ob5ob2o3b3ob8obob3obob2ob2o2b2ob3ob5o$bo2b2obo2bo3bo2b2o3bo2b3ob4ob7o3bobo4b2obo2bob3obo$4o7bobob2o2b2o3bob2o2bo2b3ob2o5bobob3o4b2o3bo2bo$5o4b2ob4o10bobob2ob2o3b2obo2b7ob2ob5ob2o$2bo3bobob2o3bobo2bob3o4bo3b3o4b2obo4bo5b2o6bo$3b4o2bo3b3obobo6bobo4bobo2bobob7obo2bob3obo2b2o$2b3ob5ob3o2b2o2bob3o2b3o2bo2bo4b6o6b6o3bo$5bob6obobobo3bo2bobo2b3obo3bob2ob2ob2obo2b4obob4o$2ob2obobo3b2obob2o7b2ob3ob2obo2bo2b2o2b3o4b2o5bobo$obo3b2ob4o2bob2o2b2ob3obobob4o4b5o8b3obob5o$2bo3bo3b2ob3o2bo4bob3obo2bobobob2o2b2o2b5obobobob2o2b2o$o3bo4bob2ob2obo2b3o3b3obo2b4ob3o3b3obobo2b2obob3o$o2bob2ob2o2b2o4b2ob2o3bob2ob2o2bo2bo2bo5b2obobob2obo4b2o$6o2bo2bobobo3bo2b3o2bob4ob2obo3b7obo2bob2obob2o2bo$bobobob2o3bobobo2bob4obob2ob3o5b2o2b2o3b3ob2ob5o$2bobo3b7o2bobob3o2b3ob2o2b2ob2o4bob5o3bob3o3bobo$bobobobo2b3o3b3o5bo3b2obo2b7ob3ob4o3b6ob2obo$o2b2o3bobo2b4o7b3o5b3obo2bo2b4o2bo4b3ob7o$o5bobobob2obo2bob2ob2obo2b2o8b2ob2o3bobo5b2o3b4o$bob2ob3obob2ob3obo2b3ob2o2b5obobo5bob4obo3bo3bobobo$o3b4obobob2o3b3o4bob2o2bob3obob2obob4o2bob2obo2b2ob3o$o4b2obob2obo6bo2bo2b2ob2ob4o6bob2o4bobo3b4o2bo$3b3o2b3o3bo3bo8b2ob2o3bob2ob4ob4ob4o2bo2bo3bo$bobobo5b6ob3o2b2o3bob2o7b3obo2b4o3bo4bobo$2o3bo3b2ob7o3b3o2b2obobo3bobob3obob2obob2o5b3obo$obob2o3b2obo4b2o2bob4o2bo4bob2o3b4ob2obo2bo3bo2b2ob2o$bo4b3o2b2obobob2obo4bo2bo2b3obo2bob2ob3o4b2obo2b4obo! A stable example: x = 64, y = 64, rule = B2ekn3ceir4ajrtw5a6ce7c/S02-ei3akn4az5c6aen7eb2obobob2obo2b5o2bo5b5ob3o3bo2b2obo2bob2obob2o3b3o$3bobo2b3ob4o3bob2obobo2b8obo5b5o2bobo3b4ob2o$2bob2o2bo4bobo3b2ob2o7bo2b2ob3ob3o2b4o2b3o2b2o3b2o$3bo3bobo4b2o2b2ob2o2b2o2bo2bo8b2obo2bo2b2o4b4ob2o$b2ob3obob3ob2ob2ob5ob2ob3o4bo2b2ob3o2b2obob3ob2o2b4o$o2b3o2bo2bo2bo2b4ob2o2bobob2obobo3bobob2obob2o2b5obob3o$bo2bo4b3o3bobo4b3o3b2o3bo4b5ob2o2bo2bob2obo3bo2bo$4obo5b5o2b3o2bo2bo2bo2b2o3bobo4b2o2b4o2b3ob3o$2ob7o4b2o2bo2bobo3b2ob5obob2o5b2ob5obo2bo3b3o$2o3bob6obo2bo2b7obob2ob2obobob4obo6bo2bobob3obo$o2b4ob3ob2ob2ob2ob2o4b4obob2o2bob2o2bob3o10bo2bo$b4obobo2b4obob2obobobo2bobo2b3obo2bo6b4obo5b2o$2bo7bo3bo2bo3b3o2b3o4bobobob2o7b2o2bo2b3o2b3o$2obobo2bo3bo3b3obob3o2bo4bobo3b2o4b2o4bo2b3o3b2obo$5obo2b2o2bobobo5bo2bobo2bo3b4o3bo3bobobob2ob2obob2o$b6o4bob3obo2bob2ob2obobo3b2obo4b2o7bob2o2b2o$2obo4b3obo2bob4obo3bo3bob2o2bo2bo4b3obob7ob2o2bo$2bo4bobob3o3b5obob2o3bo3bobo2bo3bobo3b4o2bo6b2o$obo2b2o3b3obob4o3bo2b4o3b2o2b2o4bo6b2ob2o2bob3o$3o2b2obo4b2ob2o2b2obo3b2obob2o2bob2obob2o5b2ob3o2bo2bobo$6b4obo3bo2b2obob2o4b2obob3o2b2o3bob2o4b2o2b2o3bobo$bob2obo3bobo2bo5b2obo7bo2bo2b5obo3b3obobo3b3o$2ob4o2bo3bo3bobobo3bob4ob2ob3o3bo3b2obob3o7bob2o$5bo2bo4bo5b2o2bobo2bo2b3obob4o2bob2o3b3o2b4o3b2o$5bo3bobob2ob3obo2b6ob2ob2o4b2o5bo2bo2bo7bo$obo3bo2b2o2b4obo3bobo4b2o2b2o2bob2obob3ob6ob2o2b4o$5b4ob2o2bob3ob2o2bo2bob2obo6bobob2obobo4b5o2b4o$2b2ob2o2bob2ob2obob4obo2b4obo2bobob4o3bobo3bo2bob2obo2bo$3ob3o3bo3bobo6b2ob3obob4obobob4o2bo2b4ob2obo2bo$2b3ob2o4b2o3b2obob2o6b3obo2bo2b2ob2obo2b2o2b7obobo$2bo2bob2obob2obob2o3b2obo4b3ob2o2bo2b2o2b3o2b2o3bo2b2obobo$2b4o2b2obobo3bob6o5b2ob3obo4bo4b2obobo4b2o2bobo$o4b3obobob6o3b2o2bo2b2o5bob2o4bo4bob7ob4o$b2o2bob7ob2obob2ob3o2b2obobo3b4obo2b2o2b2obob2ob7o$o5bo2bob2o3b3o2bo3b5ob2ob2ob2o3bo4bo2b3o2bo3bob2o$bo2bobo6bob3ob5ob3obo2b3o2b2o2b2o3bo2b2o2bo2bo2b2o$obobo3bobobob5o2bob3ob4obobob2o2bo2b4obo2b9ob2o$3bo4b3ob5ob2o3b3ob8obob3obob2ob2o2b2ob3ob5o$bo2b2obo2bo3bo2b2o3bo2b3ob4ob7o3bobo4b2obo2bob3obo$4o7bobob2o2b2o3bob2o2bo2b3ob2o5bobob3o4b2o3bo2bo$5o4b2ob4o10bobob2ob2o3b2obo2b7ob2ob5ob2o$2bo3bobob2o3bobo2bob3o4bo3b3o4b2obo4bo5b2o6bo$3b4o2bo3b3obobo6bobo4bobo2bobob7obo2bob3obo2b2o$2b3ob5ob3o2b2o2bob3o2b3o2bo2bo4b6o6b6o3bo$5bob6obobobo3bo2bobo2b3obo3bob2ob2ob2obo2b4obob4o$2ob2obobo3b2obob2o7b2ob3ob2obo2bo2b2o2b3o4b2o5bobo$obo3b2ob4o2bob2o2b2ob3obobob4o4b5o8b3obob5o$2bo3bo3b2ob3o2bo4bob3obo2bobobob2o2b2o2b5obobobob2o2b2o$o3bo4bob2ob2obo2b3o3b3obo2b4ob3o3b3obobo2b2obob3o$o2bob2ob2o2b2o4b2ob2o3bob2ob2o2bo2bo2bo5b2obobob2obo4b2o$6o2bo2bobobo3bo2b3o2bob4ob2obo3b7obo2bob2obob2o2bo$bobobob2o3bobobo2bob4obob2ob3o5b2o2b2o3b3ob2ob5o$2bobo3b7o2bobob3o2b3ob2o2b2ob2o4bob5o3bob3o3bobo$bobobobo2b3o3b3o5bo3b2obo2b7ob3ob4o3b6ob2obo$o2b2o3bobo2b4o7b3o5b3obo2bo2b4o2bo4b3ob7o$o5bobobob2obo2bob2ob2obo2b2o8b2ob2o3bobo5b2o3b4o$bob2ob3obob2ob3obo2b3ob2o2b5obobo5bob4obo3bo3bobobo$o3b4obobob2o3b3o4bob2o2bob3obob2obob4o2bob2obo2b2ob3o$o4b2obob2obo6bo2bo2b2ob2ob4o6bob2o4bobo3b4o2bo$3b3o2b3o3bo3bo8b2ob2o3bob2ob4ob4ob4o2bo2bo3bo$bobobo5b6ob3o2b2o3bob2o7b3obo2b4o3bo4bobo$2o3bo3b2ob7o3b3o2b2obobo3bobob3obob2obob2o5b3obo$obob2o3b2obo4b2o2bob4o2bo4bob2o3b4ob2obo2bo3bo2b2ob2o$bo4b3o2b2obobob2obo4bo2bo2b3obo2bob2ob3o4b2obo2b4obo!
x = 4, y = 3, rule = B3-q4z5y/S234k5j2b2o$b2o$2o!

LaundryPizza03 at Wikipedia

LaundryPizza03

Posts: 337
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

### Re: Rules with interesting dynamics

The island effect occurs pretty frequently with gliders in Life (and especially tlife) for that matter. At least in huge soups

Majestas32

Posts: 524
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

### Re: Rules with interesting dynamics

B2c3-kqry6-k78/S2c4ace5678, another rule that generates crystal-like structures:

x = 224, y = 5, rule = B2c3-kqry6-k78/S2c4ace5678b3o3b2ob2ob3o4bob4obob7ob4o2bobob4o2b3ob4o3b2ob6obobo2b2ob11obob6o2bobob2ob2ob2ob6obo2b5ob7ob2ob4ob2ob3o3b7obobob4ob7ob6obob5ob4ob2ob7ob2obob4o$2ob14o2b4ob4ob2o2b3ob7obob5ob5ob6o3b2obob3ob9ob10ob9ob21ob2ob5ob2obob2o2bobob9ob10obo2b5ob4obobob11o2bobob16o$bob2o2b2ob4obob2o3b2ob2ob2ob14obobo4b3o2b5o2bob7o2b2ob14ob3o2b3ob4ob2obo3b2ob17obob6ob7obobob2ob2ob7ob9ob13ob2obo2b7ob2o2bo2b5obo$5ob2ob3ob3ob2o2b2ob13o2bob10ob2obo2b3ob2ob4o2b4ob15ob4ob2ob6obob4ob2o2b3ob6ob5o3bob3o2b3obob2ob2ob2ob5o4bob15o2bob2o2b4obobo2b4o2b2ob3o3bob4o$ob3obobob4ob4ob2ob6ob4o2b3o4bo4bob5o4b2obob7obob3obob5ob2obobob3ob3o2bob6ob2ob6o3b5obo2b2ob3ob4obobobob3ob8ob2ob19obobo2b2obo3b4ob2ob10ob4obo!

EDIT: Rules like this generate vein-like structures:

x = 8, y = 6, rule = B3ai5i6a/S3-i4ar5aci6ac78bo$b6o$8o$b6o$bo2b3o$5b2o! gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm ### Re: Rules with interesting dynamics Weird growth: x = 100, y = 3, rule = B2-a3aey4in5ae6i/S12i3-aij4akr5iy6i2o$99bo$2o97bo! she/they // Please stop using my full name. Refer to me as dani. "I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D. danny Posts: 951 Joined: October 27th, 2017, 3:43 pm Location: New Jersey, USA ### Re: Rules with interesting dynamics B2ci3-ij4air5ain678/S2aei3-ijn4air5aiy6ac78 and nearby rules are highly chaotic rules with wicks and fuses that "sets things on fire" x = 30, y = 30, rule = B2ci3-ij4air5ain678/S2aei3-ijn4air5aiy6ac784o4bo3b8o6bobo$o3bo2bo3bo3b2o4bob2ob3o$2o2b5obob2o4b2obo2b2ob3o$o2b3o2b5obob3o2bo4b4o$3bo2b5o2bo2bobo3bobo2b3o$4obob3ob2o6bo5bobobo$ob9ob2obob2o3b2o3b2o$o2bob3obo4bo3bo2b2o5b2o$b3obobo2bo2bob2o4b2ob4obo$4bobob2obo2b5obo2bob2obo$2b2o3b3ob3obo2b6o4b2o$2obo5bob3o3bob2o2b3obobo$ob3o2bobobo5bo2b2o2bo3b2o$2b2obob3o2b3obo4b4o2bobo$4o3b2obob2ob3o2b2o2bob2obo$2b3o3b3ob2obo2bobobo2b2obo$o7b2obo2b6obobobob2o$b2obob3o2b2obobo2bo2b4ob3o$obo5bobobob3ob3o2bo2bob2o$b2o3b2obo2bob5o2b4ob2obo$2bobo3bob2o3bo3b2obobo3bo$o4bo2b3o2b2o2b2ob3o4b2o$b3obob4o2bobo2bo2b2o4b2o$2b2ob3obo2b2o2bo2bo2b2ob2o$ob2o3bo2b2ob3obo2bob5obo$o6b2ob2obo2b2o3bo3b2o$4b2o3b3o2b3o3b2o2bobo2bo$b2o2b5o2b3ob3obo3bob3o$4ob2o2bo2bob6o2bob2ob2o$2bob5o5bobo3b6obobo!
If you're the person that uploaded to Sakagolue illegally, please PM me.
x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo! (Check gen 2) Saka Posts: 2998 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Rules with interesting dynamics B2-ai3cj4i5678/S125678 and some nearby rules are very difficult to predict, forming large yet temporary structures with 100% density, and meandering over the place. Small patterns sometimes wander all over the place before growing. x = 3, y = 4, rule = B2-ai3cj4i5678/S1256782bo$obo$2bo$2o!

EDIT: Nearby rule has a fascinating p124 oscillator:

x = 3, y = 5, rule = B2-ai3cj4i5678/S124j5678o$b2o$b2o$b2o$o!

EDIT2: Very odd fluctuating diamond:

x = 16, y = 4, rule = B2c3aijn45aiy6acn78/S3inq4aiqr5aiy6acn7816o$16o$16o$15o! gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm ### Re: Rules with interesting dynamics B2-cn/S1e2e3e4e5e6e7e8 Lost of fascinating waves. Also spaceships with tagalongs. x = 74, y = 32, rule = B2-cn/S1e2e3e4e5e6e7e86$44b5o$49b2o$51b3o$54b2o$56bo$57bo$31b15o12bo$31bo14bo11bo$31b2o13bo11bo$33b2o10bo11b2o$6bo28b2o7bo10b2o$7bo29b2o2b3o6b5o$8b2o28b12o$10b2o22b4o$12b4o13b5o$16b13o! The triangles on the wave on the bottom-left appear to travel superluminously for some reason. Optical illusion? On a related note, B2aei/S1e2e3e4e5e6e7e8: x = 11, y = 9, rule = B2aei/S1e2e3e4e5e6e7e87o$7bo$7bo$7b2o$8b3o$4b7o$4bo3bo$4bob2o$4b3o! Large swathes of still lives and oscillators. A backrake! x = 9, y = 7, rule = B2aei/S1e2e3e4e5e6e7e8$6bo$7bo$b3ob3o$b3o! KittyTac Posts: 533 Joined: December 21st, 2017, 9:58 am ### Re: Rules with interesting dynamics This rule doesn't work very well with small starting configurations, but it has the capability to stabilize with very large final populations and lacks linear growth. Case in point, a pattern that stabilizes with 983,823,576 cells: x = 48, y = 48, rule = B2c3an4a5ai6a78/S3i4a5ai6ac7811ob5ob7ob21o$b14ob3ob28o$2ob10ob5ob28o$18ob29o$20ob27o$b20ob25o$48o$19ob28o$48o$48o$48o$48o$48o$48o$48o$45o2bo$ob44obo$2ob45o$46obo$48o$48o$48o$48o$48o$47o$45ob2o$ob46o$48o$47o$48o$48o$48o$12ob35o$48o$b2obob7o2b33o$5ob42o$ob10ob35o$2ob10ob30ob2o$2ob45o$b10ob34obo$48o$10ob37o$5ob3ob38o$7ob40o$9ob38o$12ob17ob17o$4ob3o2b19ob14ob3o$14ob33o!

gmc_nxtman

Posts: 1147
Joined: May 26th, 2015, 7:20 pm

### Re: Rules with interesting dynamics

x = 11, y = 7, rule = B2ae4i/S1e2n7ob3o2$7ob3o2$7ob3o2$7ob3o! x = 75, y = 22, rule = B2ae4i/S1e2n2$14bo$13bo9bo7bo7bo7bo7bo4bo$13bo2bo7bo7bo7bo7bo7bo4bo$8bo7bo7bo7bo7bo7bo7bo$7bo4bo10bo7bo7bo7bo7bo$7bo3bo$8bo2bo$12bo$5bo$4bo$4bo21bo$5bo19bo$25bo$18bo7bo$17bo$17bo$18bo!
Includes crystal growth:
x = 8, y = 8, rule = B2ae4i/S1e2n2bobobo$o2b4o$2obo$3b5o$2bo$2o2bo$2o2b2o$o2b3o! Oblique crawler!!!!!!! x = 285, y = 310, rule = 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Appears naturally eventually:
x = 8, y = 8, rule = B2ae4i/S1e2n2b4obo$2b2obobo$2obobo$3o$bobo2bo$o3b4o$3ob4o$5b2o! SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI what is “sesame oil”? Rhombic Posts: 1056 Joined: June 1st, 2013, 5:41 pm ### Re: Rules with interesting dynamics KittyTac wrote:B2-cn/S1e2e3e4e5e6e7e8 Nice. It's got the definite B2 feel to it, but it's a lot less chaotic than Seeds or any other totalistic B2 rule that I can think of. Looks more like Brian's Brain or something similar, but with only two states. KittyTac wrote:The triangles on the wave on the bottom-left appear to travel superluminously for some reason. Optical illusion? I see what you mean. The apparent motion is indeed superluminal, with the pattern reappearing shifted 2 cells right and 4 down in 2 cycles. It's not causal, of course: if you perturb the pattern by toggling a cell on/off, the perturbation only spreads at 1c or slower. Here's a simpler pattern that exhibits a similar effect: x = 5, y = 5, rule = B2-cn/S1e2e3e4e5e6e7e8o$o$bo$2bo$3b2o! The waves behind the advancing diagonal again appear to move subluminally, although the effect is a bit less clear because they have an (apparent) period of 4. But what's actually happening is that they're just following the diagonal at lightspeed; if you delete a cell from one of the waves, the disturbance (in this particular case, creating a puffer) clearly moves behind the front wave: x = 129, y = 129, rule = B2-cn/S1e2e3e4e5e6e7e864b2o$63bo2bo5$58b2o$57bo2bo5$52b2o$51bo2bo5$46b2o$45bo2bo5$40b2o$39bo2bo5$34b2o$33bo2bo5$28b2o$27bo2bo5$22b2o$21bo2bo5$16b2o$15bo2bo5$10b2o$9bo2bo5$4b2o6bobo11bo11bo27bobo$o24bo11bo$o3bobo5bobo51bobo58bo$bobobobo3bobo114bo$2bobobobobo51bobo63bo$3bobo5bobo113bo$4bobo5bobo37bo9bobo$5bobo5bobo37bo$6bobo3bobobo3bobobo96bo$7bobobobobo7bo98bo$8bobobobo5bobo99bo$9bobo9bo99bo$10bobo$11bobo$12bobo3bo96bo$13bobobobo3bo7bo29bo54bo$14bobobobobobo37bo53bo$15bobo5bobo89bo$16bobo5bobo$17bobo5bobo7bo$18bobo3bobobo5bobo72bo$19bobobobobo7bo74bo$20bobobobo7bobo73bo$21bobo9bobo73bo$22bobo$23bobo$24bobo3bo72bo$25bobobobo72bo$26bobobobobo69bo$27bobo9bo63bo$28bobo7bo29bo$29bobo3bobo29bo$30bobo13bobo48bo$31bobobobo7bobobo48bo$32bobo5bo5bobo49bo$33bobo9bo51bo$34bobo3bo$35bobo3bo11bo$36bobobobo48bo$37bobobo50bo$38bobo7bo43bo$39bobo5bobo41bo$40bobo3bobobo17bo$41bobo3bobobo15bo$42bobobobobobo7bo24bo$43bobobo3bobo5bo26bo$44bobo5bo5bobo25bo$45bobo9bo27bo$46bobo3bo5bobo$47bobo3bo$48bobobobo24bo$49bobobo26bo$50bobo7bo19bo$51bobo5bobo17bo$52bobo3bobobo3bobo$53bobo3bobobobo$54bobobobobo3bobo4bo$55bobobo3bobo8bo$56bobo5bo9bo$57bobo13bo$58bobo3bo$59bobo3bo$60bo3bobo$61bobobo2bo$62bobobobo$63bobo$64bo$65bo$66b2o! vyznev Posts: 27 Joined: April 23rd, 2016, 4:08 am ### Re: Rules with interesting dynamics Let's call it Dense Brain. KittyTac Posts: 533 Joined: December 21st, 2017, 9:58 am ### Re: Rules with interesting dynamics Really weird explosion: x = 128, y = 39, rule = B2ac3nq5ey/S01e4i48bo$48bo$48bo$49bo$49bo$10b6o33bo$6b4o6b8o25bo$5bo18b6o19bo$4bo44bo$3bo45bo$3bo44bo$2bo45bo$2bo45bo$bo45bo$bo45bo$bo45bo76bob2o$bo45bo78b2o$o45bo79b2o$o45bo78bo$o45bo79b2o$o44bo80b2o$bo43bo78bob2o$bo43bo$2bo41bo$3bo40bo$3bo40bo$4bo38bo$5bo37bo$6b2o34bo$8bo33bo$9bo31bo$10bo29bo$11bo27bo$12b2o25bo$14b2o22bo$16b3o18bo$19b3o14bo$22b4o8b2o\$26b8o!
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere

Posts: 1019
Joined: July 1st, 2016, 3:58 pm

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