The Web on the Field: Cluster Glows, Swirls, Patches and Voids

The BPT law

BPT Part 3.12 (The Character of the First Ripples) says what the web is: the ripples a universe begins with "are a random field: at every scale, waves of every direction with random phases", with the Primordial Ripple Spectrum Δ²(k) = A⊚ · (k / k⊚)^(n⊚ − 1), "nearly equally strong on every scale". "Because the phases are random, the web that grows from such ripples is a tangle of sheets, filaments and knots in every direction, the cosmic web of Bond, Kofman & Pogosyan (1996), and never a grid. In Binary Pulse Theory the ripples are the unevenness of the data on the scaffold (Part 3.6): the data falls on the lattice unevenly, cell by cell, and that unevenness is the random field; the lattice shapes it, as the dark matter shapes ours, but does not draw it." Its Game's Reading says the game's ripples are that random field, "so the web is a tangle that follows the lattice loosely". BPT Part 2.9 (Gas, Stars, and the Stellar Road to the Null Well), through its Data–Matter Equivalence N⚛ = m_H · 𝒞→² / (k_B · T · ln(2)), makes every particle "an enormous coherent swarm of data", and says what the game shows of it: "the data falls in toward the matter and turns about it as the matter turns, so that every forming cluster of stars, and not only every well, is wrapped in its own spiral of data." (This is the BPT part cited at app.js:825.)

BPT does not state how many clusters glow or swirl, the glow's reach, or the patch test; these are game methods. The game computes no clumping statistic of the web (no correlation function, no filament finder): the web is marked only by the measures below.

The established physics

• The orbital speed round a mass falls as 1/√k with distance k (Kepler); the data brightens with it.
• A void holds 10 to 20% of the mean density (Sheth & van de Weygaert 2004, A hierarchy of voids).
• The web of sheets, filaments and knots grown from random-phase ripples (Bond, Kofman & Pogosyan 1996, as BPT Part 3.12 cites it).

The game's math

The cluster glow on the field (drawFieldTexture() app.js:336–347):

reach = max(2, min(24, ⌊min(rows, cols)/4⌋))       24 cells on a desktop, 16 on a phone
big = the 24 heaviest bodies of drawn mass m ≥ 16
for each, at k ≤ reach cells:  w = √(1/max(1, k)) · (1 − k/reach);  glow = max over clusters

The data's brightness under the stars is then intensity × (base + (CLUSTER_GLOW − base)·glow), CLUSTER_GLOW = 0.8, base 0.08 from the 4th harmonic on, 0.35 before (app.js:385).

The cluster swirls (stepWells() app.js:827–832): the same 24 heaviest bodies of m ≥ 16 are handed to the data dynamics (gravity.js) as swirl-only wells, turning the data round them at their Kepler rate √(G·M/k³) without swallowing it. The dynamics' cache is cleared past 40,000 entries.

The cluster patches (setMatter() scene3d.js:822–836, used only when the starlight skin is off): mass is summed in 8 × 8-cell patches; a patch above 2.5 times the mean patch mass, not inside a drawn galaxy, is a cluster, and glows with g = min(1, log₂(mass/mean)/4).

The void floor (scene3d.js:920–922, the starlight skin): every patch gets 12% of the mean star and gas weight added, "so the web reads as filaments in a dim sea".

In the game

The web is narrated as it grows. Three toasts mark its stages by the scale factor a (app.js:670–673), each shown once in a life:

• at a ≥ 0.25, "a quarter grown": "The universe is a quarter of its final size · the ripples are growing: the first clumps gather along the lattice's lines";
• at a ≥ 0.5, "half grown": "Half its final size · filaments are forming along the scaffold, stars igniting in them", with the count of stars shining;
• at a ≥ 0.9, "the web stands": "Nearly full size · the cosmic web stands on the scaffold: clusters where filaments cross, voids between", with the supernovae so far.

On the torus the player sees the web three ways. The starlight skin paints the light of all the stars each cell's bodies stand for, so a deep universe glows end to end along its filaments, with the 12% floor keeping the voids a dim sea rather than black; before the skin is first painted, the dense 8 × 8 patches glow as violet points instead. Under the stars, the data of the field is dark except round the heaviest clusters, where it brightens toward each one as its orbital speed does, and the same clusters turn the data round them: with Flow colours on (the default: "every new cell takes the colour of the data that lit it, so the spin, the flow and the wells' swirl show as moving colour", index.php:214) the data is seen to spiral round the heaviest clumps of matter as it does round the wells, the "spiral of data" BPT Part 2.9 describes. All of this is in the 3D view; the glow under the stars is drawn only while the scene draws the matter as stars.

The scale model

The glow, the swirl and the patches mark drawn bodies and drawn patches; their reach is in cells and does not change with the level. The void floor is a share of the mean, scale-free.

Where the game and the theory differ

• BPT wraps "every forming cluster of stars" in its spiral of data. The game glows and swirls the data round the 24 heaviest bodies of drawn mass 16 or more, whatever their number: a desktop field with 400 bodies above m = 16 marks only 24 of them, a phone field with 10 marks all 10, and the same 24 glow at level 28, where a body holds a few stars, and at level 202, where it holds a galaxy's worth.
• The glow's reach is a share of the field (a quarter, between 2 and 24 cells), not a law.
• The game shows the web BPT describes but does not measure it: no statistic of sheets, filaments and knots is computed, so the narration's stages are tied to the scale factor, not to what the matter has done.
• A patch above 2.5 times the mean counts as a cluster with no source given.

Fixed numbers