Smolder

This is still a work in progress. It may be changed in the future.

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 $b_{t}$, $g_{t}$ and $r_{t}$.
• 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.
  • $\Delta _{b}=b_{c}-b_{t}$
  • $\Delta _{g}=g_{c}-g_{t}$
• Update the channels of the cell according to these formulas:
  • $b_{c}=(b_{t}+\Delta _{b}-\Delta _{g})\ \mathrm {mod} \ 4$
  • $g_{c}=(g_{t}-\Delta _{b}+\Delta _{g})\ \mathrm {mod} \ 4$
  • $r_{c}=(r_{t}-\Delta _{b}-\Delta _{g})\ \mathrm {mod} \ 4$

Single-cell example

As an example, consider this setup:

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The rightmost cell, 10, calculates this:

• $b_{t}=1,\ g_{t}=0,\ r_{t}=1$
• $\Delta _{b}=1-1=0,\ \Delta _{g}=0-0=0$
• $b_{c}=(1+0-0)\ \mathrm {mod} \ 4=1$
• $g_{c}=(0-0+0)\ \mathrm {mod} \ 4=0$
• $r_{c}=(1-0-0)\ \mathrm {mod} \ 4=1$

The board updates to this state:

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This is a basic example of flood-fill.

Multi-cell example

In this example:

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The middle cell adds all the cells neighboring it together, modulo 4. With the total, it computes:

• $b_{t}=(1+1+1)\ \mathrm {mod} \ 4=3,\ g_{t}=(1+1+1)\ \mathrm {mod} \ 4=3,\ r_{t}=(2+2+2)\ \mathrm {mod} \ 4=2$
• $\Delta _{b}=0-3=-3,\ \Delta _{g}=1-3=-2$
• $b_{c}=(3-3+2)\ \mathrm {mod} \ 4=2$
• $g_{c}=(3+3-2)\ \mathrm {mod} \ 4=0$
• $r_{c}=(2+3+2)\ \mathrm {mod} \ 4=3$

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Interactions

Decay

Certain wires when flood-filling can undergo decay, where the red channel slowly decreases.

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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.

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Oscillation

Similarly, certain wires may oscillate between a set of values.

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In this scenario, the total difference is zero, allowing the red channel to remain unaffected.

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