Smolder
Smolder is a cellular automaton invented by User:Aadenboy created from a failed attempt at recreating Burn.
Structure
Smolder is held on a 2D space of cells. Each cell has three channels, blue, green, and red, however the red channel can be left empty. Channels can range from 0 to 3. Cells with a value in the red channel are immutable.
Each step, cells that aren't 00 without a red channel and next to any other cell with a red channel follow these rules:
- Keep track of running totals , and .
- Check all four of your orthogonally adjacent neighbors. If they have a red component greater than zero, add each of their channels to the total, modulo 4.
- Store the difference between the total and the cell.
- Update the channels of the cell according to these formulas:
Single-cell example
As an example, consider this setup:
The rightmost cell, 10, calculates this:
The board updates to this state:
This is a basic example of flood-fill.
Multi-cell example
In this example:
The middle cell adds all the cells neighboring it together, modulo 4. With the total, it computes:
State network
For this section, a "transformation" is one cell turning into another via interaction with a single cell, and a "combination" is one cell turning into another via interaction with two cells.
The rules provided make it impossible for certain states to turn into any other, even when attempting to use combinations. If we create a map of these states, where nodes are connected through directed edges defined by transformations and combinations (which will be solid and dashed respectively). When doing this for every cell, it reveals that there are eight distinct clusters of states, which are mostly independent of one another.
This cluster is the only one where both transformations and combinations allow traversal within it, making it optimal for computations.
Interactions
Decay
Certain wires when flood-filling can undergo decay, where the red channel slowly decreases.
In this scenario, the difference between either channel equates in a total difference of 1, leading to the red channel decreasing by one each step.
Oscillation
Similarly, certain wires may oscillate between a set of values.
In this scenario, the total difference is zero, allowing the red channel to remain unaffected.
Logic
NAND
Where X and Y are either 202 or 00.
Computational class
Without infinite tiling and arbitrary modification after tiling the grid, Smolder is Total, since performing any useful computation (ex: NAND gate) must irreversibly turn some of the mutable cells used in it immutable, making any kind of loop impossible.
The computational class of unbounded Smolder with arbitrary modification after tiling the grid is unknown.