The Scale Model of Matter

The BPT law

BPT does not state the scale model; it is a game method. BPT Part 6.10 (The Game's Reading, Formally) states the principle the code follows: "The simulation cannot reach the scale at which m_P and m_H are separate numbers: its cells are Pulse Lengths and its matter is counted in bits, so its universes are ratios of ours. It keeps every law above in its proportions." The same reading fixes the cloud the game measures by: gas "in 8 × 8-cell clouds denser than twice the mean (per real area of the torus) turns into stars". A ratio of a universe must keep its shares, not its cell counts, when it is drawn smaller, and this Part is how the game does that for matter.

The established physics

None: a game method.

The game's math

The drawn field is viewSide(Lm) = 4·2^Lm cells a side, Lm = min(L, MODEL_LEVEL), and MODEL_LEVEL() app.js:4244 is 6 on a desktop and 4 on a phone (isPhone() app.js:4243: the screen's short side at most 480 px, or a mobile user agent). The model level is documented in Chapter 1, Part 1.10; this Part is what matter does with it.

cloudCells() app.js:1167:

full = viewSide(min(L, 6))                    the level's full field (256 at L ≥ 6)
CL   = max(1, round(8 · cols / max(cols, full)))

setCloud(m) app.js:1168 sets m.cloud = CL and m.full = CL². Desktop: CL = 8, full = 64. Phone: CL = round(8·64/256) = 2, full = 4. At a level below 6 on desktop, cols = full, so CL = 8.

The rule. A cloud is a share of the universe, not a count of cells (ruling 2026-10-29, after a level-182 phone run formed 302 stars where the weighting drew 40,000). Everything measured in cells or flips that should be the same share of the universe scales by sk = CL/8:

• Star-forming clouds (stars.js, Chapter 5) and cooling clouds (Matter.cool()) are CL × CL cells.
• A planet's least mass is one cloud, CL² cells.
• applyFeedback() app.js:766 multiplies its reach (cells) and heating time (flips) by sk = (matter.cloud or 8)/8: "a scale model's cells are wider and its flips longer by the same share: reach and heat follow it, speeds stay" (Chapter 5, Part 5.12).

The heat's velocity correction 2^(Lm − 6) (Part 4.14) is the same rule for speeds against light.

In the game

The scale model is stated on screen wherever it applies. The HUD's Level line adds "· drawn at C cells across" when the model level is below the true one (app.js:2144), and its tooltip reads "The universe's level; deeper than level 6 (4 on a phone) the field and clock are a scale model" (index.php:81). The readout adds a "Drawn at" row, "No screen can draw a field this deep, so it is drawn on a smaller grid; its physics, stars, wells and harmonics all follow its own level" (app.js:2086), and the Wells line reads "N counted · M drawn · law P … at level L" (app.js:2142). The run's saved record keeps the device and the model level (device, model_level, app.js:2205). On a phone the same universe is drawn on a 64-cell field instead of 256, so its cells look four times coarser, its clouds are 2 × 2 cells instead of 8 × 8, and a planet's least mass, and the least mass that carries an accretion disk, is 4 cells instead of 64.

The scale model

This Part is the scale model. On a phone a cell is four times wider and a flip, against light, four times longer than on desktop. A desktop and a phone running the same universe should agree on shares (of matter in clouds, of gas in stars), not on cell counts.

Where the game and the theory differ

• Numbers the share rule does not reach. BPT Part 6.10 keeps every law in its proportions. These matter numbers do not follow the cloud's share: the mesh's block side B (Part 4.7) follows the device; the data drains' 24-ring reach (Part 4.13) is cells on any field; COOL_DENSITY, the 256-well switch, the merge radius of one cell and the six-step planet test are the same on every field.
• The device decides the model. The model level is 6 on a desktop and 4 on a phone, and a phone is any screen whose short side is at most 480 px, or a mobile browser (isPhone() app.js:4243). The same universe is therefore a different scale model on a phone, and the heat's speed correction (Part 4.14) and the cloud's share are what bring the two back into agreement.

Fixed numbers