New ideas for pattern types

[wintersolstice]

I've been thinking about patturns with an infinite population (defined by a lattice) either in one dimensions like a wick: call that "linear" or in 2 dimensions like an agar: call that "planar"

Now if a patturn is finite it could be called "0 dimensional" and the catorgaries are:

Still life
Oscillator
Space ship
Puffer
Gun
Breeder
Replicator
Sawtooth
Methuselah
Garden of Eden

Now "0D" patturns come in all ten varieties

Now a "linear still-life/oscillator" is a type of wick
a "planar still-life/oscillator" is an agar

now planar patturn can only be: still life, oscillator, Methuselah, Space ship, Garden of Eden

linear pattern could be all 5 of those but also: Gun, Puffer, Replicator* or Sawtooth**

*a simple example of a linear replicator is the infinite line
**this is only possible by altering the definition: mark out the repeating unit an extend to the infinity in the other direction (perpendicular to the pattern) making an infinite rectangle/parallelogram(for diagonal patturns)

Then the up and down population is the population contained inside the rectangle/parallelogram.

Given that "linear/planar still-life/oscillator" have been counted (wicks and agars) the ten types of patturn are:

"Planar Methuselah"
"Planar Space Ship"
"Planar Garden of Eden"
"Linear Methuselah"
"Linear Space Ship"
"Linear Garden of Eden"
"Linear Gun"
"Linear Puffer"
"Linear Replicator"
"Linear Sawtooth"

Now I have no idea if any of these are feasible, there all just theories, and all from 2D Life (with 3D you could have even more!!! such as "Realmic Methuselah", "Planar Puffer", "Linear Breeder" or "Super Breeders", ) OK yes I do know of a "Linear Replicator" but not any others

I also don't know how to even investigate infinite patturns

Any thoughts and criticisms welcome (I have said this before I am still only a beginner at all this!!!)

[ebcube]

Hmm. Interesting.

Well, a linear spaceship would be a growing spaceship; those already exist. Most linear replicators are linear sawtooths as well, I guess. A planar spaceship, that is, a growing 2D spaceship, already exists too; I'm thinking of the c/4 to c/5 growing oblique spaceship, which, I guess, would fit your definition.

I'm not sure if I understand your concept (or what are we supposed to do with it, for that matter)

[wintersolstice]

Hmm. Interesting.

Well, a linear spaceship would be a growing spaceship; those already exist. Most linear replicators are linear sawtooths as well, I guess. A planar spaceship, that is, a growing 2D spaceship, already exists too; I'm thinking of the c/4 to c/5 growing oblique spaceship, which, I guess, would fit your definition.

What do you mean "growing spaceship"
I'm talking about patterns whose "initial population" in "infinity" so it can't grow(unless it was linear).

Hmm. Interesting.
I'm not sure if I understand your concept (or what are we supposed to do with it, for that matter)

I got interested in "agars" the only patterns to be i"nfinite lattices" as opposed to finite patterns (which is a pattern with a bounding box) a type of wick is a linear infinite pattern, the infinite line is a replicator but it's infinite (in population) but wicks and agars are only ocsillators(or still life) and the infinite replicator is one of many new patterns that can be studied so I just wanted to share my ideas. New ideas.

[ebcube]

Well, what would a linear spaceship be? This all sounds timecubic to me...

[wintersolstice]

Well, what would a linear spaceship be? This all sounds timecubic to me...

A linear patternis a pattern that has an infinite number of cells (but it can be contained inside either a paralellogram/rectangle in which one of the dimensions of them is "infinite" the other is "finite")

For planar it means that both dimensions of the paralellogram/rectangle are infinite.

A agar is a planar still life/oscillator and a wick (or an infinite wick) is a linear still life/oscillator So a linear spaceship is a wick-like pattern (of an infinite number of cells) that travels in a direction other than the one that is infinitly long.

It is very hard to describe. but the genearl idea is to have a pattern that has an "infinite" number of living cells (that are defined by a repeating unit) either in one dimension (linear) or two (planar)

wicks and agars seem to be the only ones that are so far (one type of wick anyway) and it's only the oscilators that apply to these terms, so I thought why not go further and consider "infinite" patterns that are not still lifes/oscillators.

An "infinite pattern" is a pattern whose "initial population" (number of living cells at the beginning) is not a finite number and the pattern stretches to infinity but repeating unit (one that can tile the space periodically like a space filling tesselation either the whole plane (planar) or just one dimensions but it has thickness (linear))

I hope that answers your question!!

In terms of what I wanted others to do with all this, I was interested in sharing it so it can be investigated and add a whole new range of patterns to the game.

[knightlife]

I also don't know how to even investigate infinite patturns

One way is using a cylindrical universe to find "linear spaceships" quite easily with Golly 2.2 or higher.
The existing name for this type of pattern is "superstring" (if velocity is c).
This one might be the simplest:

Code: Select all

x = 2, y = 16, rule = B3/S23:T0,16
bo$2o$2o$bo$bo$2o$2o$bo$bo$2o$2o$bo$bo$2o$2o$bo!

(This could also exist in a T0,4 universe, although not much else will.)

Other superstrings show up quickly if random cells are placed next to a vertical line.

Code: Select all

x = 10, y = 16, rule = B3/S23:T0,16
3ob2o3bo$2ob4o2bo$2o2bo2b3o$o2b7o$o2b2o2bobo$o2bob3obo$obob3o2bo$o3b2o
3bo$3obo2b3o$o4bobobo$obobob4o$b9o$4bo2b3o$4obob3o$2b2ob2ob2o$obo2b3ob
o!

Code: Select all

x = 4, y = 16, rule = B3/S23:T0,16
3bo$ob2o$ob2o$3bo$3bo$3bo$3bo$3bo$3bo$3bo$3bo$3bo$3bo$ob2o$ob2o$3bo!

Usually debris is left behind though:

Code: Select all

x = 10, y = 16, rule = B3/S23:T0,16
obo5b2o$2o3b5o$b2o3bob2o$bobo3bobo$b3o2bob2o$2b2o3bobo$obo3bob2o$bo2b
3o2bo$4ob5o$4bobob2o$b3o3bobo$4b2o3bo$b2o2bobobo$2obo2bo2bo$bo2b2ob3o$
b3o4b2o!

This one is wide and contains a replicator that fails to grow infinitely:

Code: Select all

x = 82, y = 6, rule = B3/S23:T0,6
2o9b2o7bo5b2o3b3o10bobo13b3o6b2obo3bo3b2o$ob2ob3o2bob2o5b2o4b2obobo3bo
8bo3bo10bo3bo5bobobo3bobo2bo$b2o2bobo2bo2bo4bo6b2obobobob2o7bo3bo10bob
2o5b2o9bo2bo$ob2ob3o2bob2o5b2o4b2obobo3bo8bo3bo10bo3bo5bobobo3bobo2bo$
2o9b2o7bo5b2o3b3o10bobo13b3o6b2obo3bo3b2o$79b3o!

Wide but chaotic:

Code: Select all

x = 41, y = 6, rule = B3/S23:T0,6
o8bo6bob2o11bob2o5bo$3bo6bo5bob4o7bobob2o5bo$2obo6bo6bo22bo$3b3o3b2o
11bo10bo2bo3bo$o4bo30bo3bo$17bo4bo7bobo3bo3bo!

Blinkers disappear:

Code: Select all

x = 10, y = 16, rule = B3/S23:T0,16
bobob2ob2o$8obo$b3o2b4o$3bobo3bo$ob5ob2o$o3bo4bo$o3bob2obo$o2b2ob2obo$
3bobob3o$2bob2o3bo$2ob2o2b3o$3obobob2o$bo3b3obo$2b2obo2b2o$b2o2b2ob2o$
bobobobobo!

Other types:

Growing linear spaceship:

Code: Select all

x = 34, y = 16, rule = B3/S23:T0,16
30bo2bo$30bo2bo$32b2o$31b3o$31b3o$31b3o$32b2o$30bo2bo$33bo$6bo25b2o$2o
bobobobo21b3o$4o3b4o20b3o$11bob3ob3ob3ob3o3b3o$4o3b4o20b3o$2obobobobo
21b3o$6bo25b2o!

Infinite rake makes forward gliders:

Code: Select all

x = 10, y = 16, rule = B3/S23:T0,16
o2b3ob3o$b2o2bobobo$obo3b2obo$obob2ob3o$b2o2bo2b2o$o2b2obob2o$2obo2b4o
$b2ob2obobo$2obo3b3o$4o3bobo$4b2o2b2o$2o2b3ob2o$o3b3ob2o$5bo2b2o$bobo
2b4o$4ob3obo!

[ebcube]

Another growing linear spaceship:

Code: Select all

x = 49, y = 16, rule = B3/S23:T0,16
46b3o$45bob2o$48bo$48bo$3bo41bo2bo$2b3o42b2o$bo17bo27b2o$2o2b2o13bo28b
o$b2ob2o19bo22bo$2b2o21b2o3bo3bo3bo3bo5bo$15b3o3bobobobobobobobobobobo
bo4bo$16bo7b2o3bobobobobobobobo4bo$17bo3b2o5b3o3bo3bo3bo5bo$21b2o25bo$
21b2ob2o19bo2bo$47b2o!

[knightlife]

Found a "planar spaceship" that travels diagonally at a velocity of c/39:

Code: Select all

x = 4, y = 4, rule = B3/S23:T11,11
2bo$2b2o$3o$2o!

Every 39 generations the octomino is displaced by (1,1).
An entire infinite plane covered with these 11 x 11 tiles would appear to move diagonally at c/39.

[skomick]

Found a "planar spaceship" that travels diagonally at a velocity of c/39

I like it! Now if we could just tame it on the plane, you'd have a p1521 oscillator!
Edit: <slaps hand on forehead> why did I square 39?

[ebcube]

Wow, great discovery, knightship! I like where this is going.

I'm still not convinced about the definitions. For example, is an ant a linear spaceship at c velocity? You can easily see what I mean on a width 5 torus.

[knightlife]

The previously posted octomino pattern is simultaneously a p429 oscillator and a c/39 diagonal spaceship when it exists in the 11 x 11 toroidal universe. Oscar sees it as a spaceship.

Code: Select all

x = 32, y = 4, rule = B3/S23:T0,4
o5b3o12bo9bo$b2o2bo2bo11b2o8b2o$4bo2b2o12bo8b2o$b2o2bo2bo11b2o9bo!

Above are the only 3 lightspeed linear spaceships as far as I know in a size 4 cylindrical universe.