Height map based automata

[Goutte]

A height map contains one real (float) value for each cell, and is provided as a sort of invariant fixture/environment for the automaton.

It can be thought of as the map of the altitude of each cell.
Some Perlin noise that provides terrain looking like a bunch of hills works great.


Example: Sisyphus

The story of Sisyphus pertains to someone rolling a boulder up a hill only for it to roll down once at the top.
To simplify the model, we consider that sisyphus climbs hills and the boulder rolls down, instead of having one push the other.

This ruleset is heavily inspired by Wireworld.

Nothing -> Sisyphus
if it has at least one SISYPHUS neighbor that's lower

Sisyphus -> Nothing
if it has at least one NOTHING neighbor that's higher

Sisyphus -> Boulder
if it has no neighbor that's higher

Nothing -> Boulder
if it has at least one BOULDER neighbor that's higher

Boulder -> Nothing
if it has at least one NOTHING neighbor that's lower

Boulder -> Sisyphus
if it has no neighbor that's lower

Works "best" (æsthetically?) with :

• Strict height conditions, meaning that height equality is rejected.
• Von Neumann neighborhood (4 adjacent cells)

I have so many questions !

Is there a way to use the forum viewer to represent such automata ?

Is it possible to express the rules as one of them short, sweet & arcane strings ? (like b3s23 ?)

What are the keywords I'm missing to find previous work about such automata ? (height map, environment, fixtures, ?)

I've explored dozens of variations, but there's so much more to explore !

I'm not uploading a preview image as per forum rules, but here's a link to a game (there's a HTML5 build) that runs the Sisyphus automaton in the background of its main menu. (you don't need to play the game to see it)
Please forgive the game quality if you end up playing it, it's the very first build, it's a jam, and I got totally sidetracked by automata – I'm sure most of you know what it feels like to fall in the depths of this marvelous discipline.

[confocaloid]

A height map contains one real (float) value for each cell, and is provided as a sort of invariant fixture/environment for the automaton.

It can be thought of as the map of the altitude of each cell.
Some Perlin noise that provides terrain looking like a bunch of hills works great.
[...]
Is there a way to use the forum viewer to represent such automata ?
[...]

If I understand right, in the example above there are three types of cells ("Nothing", "Sisyphus", "Boulder"), the cell's type can change during evolution, and additionally each cell has a real-valued height that doesn't change during evolution and can be chosen independently from the type of the cell.

I think it is possible to implement an "approximate" version of such CA (where the height is made integer-valued instead) in the form of a RuleLoader ruletable that can be loaded into Golly/LifeViewer. The state of a cell with height H and type T could be encoded by the number (3 H + T), where H could range from 0 through 84, and T would range from 0 through 2 (T = 0 means "Nothing", T = 1 means "Sisyphus", T = 2 means "Boulder"). Then the rules defining the behaviour of the CA can be written one-by-one, in terms of the resulting cellstate values.

[unname4798]

A height map contains one real (float) value for each cell, and is provided as a sort of invariant fixture/environment for the automaton.

It can be thought of as the map of the altitude of each cell.
Some Perlin noise that provides terrain looking like a bunch of hills works great.
[...]
Is there a way to use the forum viewer to represent such automata ?
[...]

If I understand right, in the example above there are three types of cells ("Nothing", "Sisyphus", "Boulder"), the cell's type can change during evolution, and additionally each cell has a real-valued height that doesn't change during evolution and can be chosen independently from the type of the cell.

I think it is possible to implement an "approximate" version of such CA (where the height is made integer-valued instead) in the form of a RuleLoader ruletable that can be loaded into Golly/LifeViewer. The state of a cell with height H and type T could be encoded by the number (3 H + T), where H could range from 0 through 84, and T would range from 0 through 2 (T = 0 means "Nothing", T = 1 means "Sisyphus", T = 2 means "Boulder"). Then the rules defining the behaviour of the CA can be written one-by-one, in terms of the resulting cellstate values.

The RuleLoader rule can also be 1D. There are 4 states.
None, "Nothing", "Sisyphus", "Boulder".
Higher is to the left, lower is to the right.

[pifricted]

Hmmm...

[...]

Nothing -> Sisyphus
if it has at least one SISYPHUS neighbor that's lower

Sisyphus -> Nothing
if it has at least one NOTHING neighbor that's higher

Sisyphus -> Boulder
if it has no neighbor that's higher

Nothing -> Boulder
if it has at least one BOULDER neighbor that's higher

Boulder -> Nothing
if it has at least one NOTHING neighbor that's lower

Boulder -> Sisyphus
if it has no neighbor that's lower

[...]

I think the “Nothing neighbor” means “the cell higher(or lower ) than ground without Boulder or Sisyphus”.

Hmmmm...Sisyphus has four or eight pairs of arms because he can push many Boulders in one go.

It is explosive.

[breaker's glider gun]

Or... you could just use ready. Make chemical "a" 0/sisyphus/boulder* and chemical "b" be height, and maybe chemical "c" to view what's going on.

*you could even use the float value to tell the direction of movement, if you don't want it to explode.

[Goutte]

Thank you all for the savant replies.

Make chemical "a" 0/sisyphus/boulder* and chemical "b" be height, and maybe chemical "c" to view what's going on.

So that's how they generically categorized multi-layered automata : chemicals ! Thanks, this word's pretty handy.

I think the “Nothing neighbor” means “the cell higher(or lower ) than ground without Boulder or Sisyphus”.

Exactly right ; please forgive my ambiguous definition, I'm quite new to this.

If I understand right, in the example above there are three types of cells ("Nothing", "Sisyphus", "Boulder"), the cell's type can change during evolution, and additionally each cell has a real-valued height that doesn't change during evolution and can be chosen independently from the type of the cell.

That's it. In my shader implementation, "Nothing" is what's neither "Boulder" nor "Sisyphus", but that's just for practical purposes, so I can "prettify" the initial fixtures that kickstart the automaton, and let the automaton "eat" those extra, decorating pixels, as if they were nothing.

Hmmmm...Sisyphus has four or eight pairs of arms because he can push many Boulders in one go.
It is explosive.

It is explosive, but a carefully crafted height map with "plateau"s (adjacent cells with identical height) can "contain" the automaton, or even shape it.
I'm observing that eventually the automaton stabilizes in an endless loop, but that's inevitable in finite terrains due to the determinism of the automaton.

On plateaus, Sisyphus and Boulder will alternate on each tick, due to the strict nature of height comparisons.
I tried various tweaks to the automaton to try and mitigate the phenomenon (make it less epileptic), but what worked best for me was to carefully craft a height map without plateaus, or just very little.

The RuleLoader rule can also be 1D. There are 4 states.
None, "Nothing", "Sisyphus", "Boulder".
Higher is to the left, lower is to the right.

I'm sorry, I tried, but I don't get it. What's the purpose of None ?

you could even use the float value to tell the direction of movement, if you don't want it to explode

Oooooh… Juicy ! I've implemented Langton's Ant just yesterday, so I happen to have the shader toolkit for this.
I guess it will require a little more effort when crafting the initial fixtures, though. We'll see.

[pifricted]

...
It is explosive, but a carefully crafted height map with "plateau"s (adjacent cells with identical height) can "contain" the automaton, or even shape it.
I'm observing that eventually the automaton stabilizes in an endless loop, but that's inevitable in finite terrains due to the determinism of the automaton.

On plateaus, Sisyphus and Boulder will alternate on each tick, due to the strict nature of height comparisons.
I tried various tweaks to the automaton to try and mitigate the phenomenon (make it less epileptic), but what worked best for me was to carefully craft a height map without plateaus, or just very little.

...
I'm sorry, I tried, but I don't get it. What's the purpose of None ?

The “None” is the state 0 cell in CAs.In Life,it means “dead cell”.In this CA ,it means “the ground”

In many explosive rule ,the patterns always live a long time in a loop room.

Code: Select all

x = 20, y = 20, rule = B2/S:T20,20
o4b3obo2b3o2b2o$obobobobob2ob2o3b2o$o4b2ob4ob2obob2o$5o2bo4bobo2b2o$3b
o4bob4ob2obo$3b2ob3o2b2o3bobo$o4b3ob3ob3obo$2o2bo2b2o3bobo2b2o$4bo3b3o
bo2bo3bo$bob5o4bo3bo2bo$b2obobo2bo2b4obobo$obobo5bo4b2obo$4b3ob5obo2b
2o$2o2bo6bo3b5o$3o4bobo2b2obobo$3bob2obo4b3obobo$2obo3bo2bobobo2b3o$2o
b2obo3b2o2bobobo$5b3o2bo8bo$2o2b3ob2o4b4o!

Code: Select all

x = 20, y = 20, rule = Iceballs:T20,20
o4b3obo2b3o2b2o$obobobobob2ob2o3b2o$o4b2ob4ob2obob2o$5o2bo4bobo2b2o$3b
o4bob4ob2obo$3b2ob3o2b2o3bobo$o4b3ob3ob3obo$2o2bo2b2o3bobo2b2o$4bo3b3o
bo2bo3bo$bob5o4bo3bo2bo$b2obobo2bo2b4obobo$obobo5bo4b2obo$4b3ob5obo2b
2o$2o2bo6bo3b5o$3o4bobo2b2obobo$3bob2obo4b3obobo$2obo3bo2bobobo2b3o$2o
b2obo3b2o2bobobo$5b3o2bo8bo$2o2b3ob2o4b4o!

Code: Select all

x = 20, y = 20, rule = B34/S34:T20,20
o4b3obo2b3o2b2o$obobobobob2ob2o3b2o$o4b2ob4ob2obob2o$5o2bo4bobo2b2o$3b
o4bob4ob2obo$3b2ob3o2b2o3bobo$o4b3ob3ob3obo$2o2bo2b2o3bobo2b2o$4bo3b3o
bo2bo3bo$bob5o4bo3bo2bo$b2obobo2bo2b4obobo$obobo5bo4b2obo$4b3ob5obo2b
2o$2o2bo6bo3b5o$3o4bobo2b2obobo$3bob2obo4b3obobo$2obo3bo2bobobo2b3o$2o
b2obo3b2o2bobobo$5b3o2bo8bo$