The Chemistry

Twenty digital atoms: fifteen role-atoms that live in the grid below, and five backbone atoms that deliberately do not. Every number on this page was authored by us, and every number is shown.

This is not physical chemistry. It is an artificial chemistry, which is an established line of work in artificial life rather than a metaphor we are borrowing. An artificial chemistry is usually given as a triple: a set of possible molecules, a set of reaction rules, and an algorithm deciding how the rules get applied. This page specifies the first of those three and part of the second. The reaction grammar and the reactor algorithm do not exist yet, and until they do there is an alphabet here but not yet a chemistry. What follows is laid out so that where an atom sits determines what it is, which means the design can be argued with instead of taken on trust.

How to read the table

Two axes, and each one is doing a job.

Columns are jobs. Each column is a role an atom plays for its neighbours. The column is also a hypothesis about interchangeability: the compression machinery only ever proposes swapping an atom for another in the same column, because a spacer standing in for another spacer is plausible and a donor standing in for an acceptor is not, since it would reverse the direction of a reaction.

Rows are reactivity, rising downward. Nothing is exactly interchangeable with anything else, which is deliberate: a chemistry with exact duplicates would hand the compression machinery a free answer.

We expect row distance to be the leakage axis, so that two atoms one row apart are good candidates to stand in for each other while two atoms three rows apart are not. That expectation is not paid for by anything above it. As currently specified, reactivity sets cost and nothing else, which makes it a price coordinate wearing a reactivity label. So it is written down here as a claim that can fail rather than as a property of the design: substitution error should increase with row distance. If a run shows it does not, the row axis is wrong and the table needs rebuilding.

Cost is derived, not chosen per atom. Cost is a function of reactivity, with a base and a slope set once per column. So an atom's price follows from where it sits.

Fifteen atoms in thirty cells. The empty cells are not gaps in the design, they are room: a new atom can be added by filling a reserved cell, and nothing already placed has to move or be renumbered.

The rules that produce those numbers

There are three of them and they are the whole derivation. Valence is set per column; reactivity is set by row; cost follows from reactivity.

reactivity(row) = 0.10 + 0.15 x (row - 1)
cost(col, row)  = base[col] + slope[col] x reactivity(row)
valence(col)    = 1 for Inert, Acceptor, Donor
                  2 for Binding and Catalytic

                 base   slope   valence
  Inert          0.10    0.4      1     filler is cheap by design
  Binding        0.60    1.2      2     an interface has to be held, so it is paid for
  Catalytic      1.20    2.0      2     catalysts are precious, so this column is short
  Acceptor       0.50    1.4      1     completing a reaction costs less than driving one
  Donor          0.60    1.6      1     driving a reaction is the expensive half

Only two things are set by hand rather than derived: polarity, because it governs which atoms prefer to bond with which and deriving it would make the bonding graph too regular to be interesting, and tags, which mark the two atoms that carry an interface and the two that catalyse.

Why each column earns its place

The backbone

Five atoms sit outside the grid, because they do not belong to a job column and are not freely swappable by role. Swapping the scaffold changes everything hanging off it.

If the backbone ever starts forming interchangeable groups in a run, the tolerance has been set too loose. That is a deliberate control.

What can bond with what

Two gates, and no more. An atom carries a valence, which is how many bonds it can hold at once, and a polarity, which is a signed preference. Opposite polarities attract, like polarities resist, and neither can exceed its valence budget. Those two numbers are the entire bonding grammar; a molecule is whatever falls out of applying them.

Next: What's Inside of a Cell?, which is what you would build out of this alphabet.