2.5 million cubes of real planet, weighed and smashed live in a web page · worked examples: Earth, Moon, Mars · 1 unit = 1 cm · TL = 0.136899099984016
HIGHTISTIC (Russell Vernon Trent III) · SNSFT Foundation uuia.app/imatter · [9,9,3,27]
WORKED EXAMPLES
Mars core density (InSight range)6.00 g/cm³
Slide the core density across the InSight seismic range and watch the moment of inertia in the THREE-BODY CHECK move toward the measured 0.3644.
Each world is filled with tiny cubes called TL-cells. Each cube takes the density of the rock or metal at its spot, from the standard model seismologists use. Count the cubes, add up their weight, and the total has to match the real Earth.
Each TL-cell of edge h takes the Preliminary Reference Earth Model (PREM) density at its center. Mass, mean density, polar moment of inertia and the gravity profile are sums over cells, compared with the measured values.
PLANET BUILDER
Radius5,000 km
Stack layers from the center out. Each layer reaches to a share of the radius; the top layer always reaches the surface. The page works out the exact answer from formulas, then counts the cells, and the two have to agree.
Layers are constant density. Exact: M = Σ ρ·(4/3)π(r₁³ − r₀³), I = Σ ρ·(8/15)π(r₁⁵ − r₀⁵); a uniform ball gives I/MR² = 0.4 exactly. Material densities at surface conditions: iron 7.87, granite 2.70, basalt 3.00, water 1.00, ice 0.92 g/cm³; mantle rock 3.30 and compressed iron-nickel core 11.0 are typical planetary values.
TL-CELLS
Cells across Earth96
TOOLS
Brush2 cells
Material
DIG removes cells, PLACE adds cells on the face you touch, PAINT changes what cells are made of. With a tool on, one finger or the left mouse button works the tool; turn the view with two fingers or the right mouse button. Every number updates after each stroke.
Edits change cell occupancy and density directly; mass, I/MR², gravity and the layer table are recounted from the cells after each stroke. Keys: O orbit, D dig, P place, A paint, Ctrl+Z undo, [ and ] brush.
IMPACT
Impactor diameter—
Material
Speed20 km/s
Angle from horizontal45°
Pick a size, material, speed and angle, then FIRE. AIM lets you click the spot to hit; otherwise it strikes the side facing you. Small impacts dig a crater and throw out debris that falls back as a blanket; big enough impacts blow part of the planet away.
Crater: Collins, Melosh & Marcus (2005) π-group scaling, transient D = 1.161 (ρᵢ/ρₜ)^⅓ L^0.78 v^0.44 g^−0.22 sin^⅓θ; final simple 1.25 D, complex 1.17 D^1.13 / D_c^0.13 (D_c = 3.2 km). Bowl depth D/2√2. Disruption: Leinhardt & Stewart (2012) universal law, M_lr/M_tot = 1 − Q_R / 2Q*_RD, c* = 1.9, μ̄ = 0.36. Ejecta speeds follow a power law (Housen & Holsapple 2011); debris below escape speed falls back ballistically and builds a blanket.
CUTAWAY
Show layers from depth0 km
Peel the planet: slide right to strip away the outer layers and look at the core.
VIEW
ORBIT: drag to turn, scroll to move in, all the way inside if you like; double-click any cell to circle around that spot. FLY: drag to look around, scroll or W/S to move forward and back, A/D to slide sideways, Q/E down and up, hold Shift to go faster. On a phone, drag to look and pinch to move.
Orbit camera: target point, distance and two angles; double-click sets the target to a cell. Fly camera: free position with yaw and pitch, Z up. In fly mode the tool hotkeys are off; W/A/S/D/Q/E and the arrow keys move the camera.
EXPORT
SCALE
1 unit = 1 cm (Unreal Engine convention; glTF, Blender and Unity divide by 100 for meters). Geometry is stored as dimensionless TL-cell counts; one declared edge length per scene converts every count to physical units.
One double-precision frame keeps 1 cm out to about 9 × 10¹³ m. Larger scenes give each octree cell its own local origin, so 1 cm holds at any scale.
layers
—
— fps
COUNTING CELLS…
COUNT VS MEASURED
TL-cells inside Earth—
TL-cell edge—
Mass—
Mean density—
Moment of inertia I/MR²—
Surface gravity—
Peak gravity—
Escape velocity—
Core share of mass—
Teal numbers are within 1% of the measured value. The moment of inertia says how much weight sits near the middle: a uniform ball would read 0.400, and Earth reads 0.331 because its heavy iron core is packed in the center.
M = Σ ρᵢh³. ρ̄ = M / (4/3 πR³). I = Σ mᵢ(xᵢ² + yᵢ²). g(r) = G·M(<r)/r². Measured: M = GM/G with GM = 3.986004418 × 10¹⁴ m³/s² and G = 6.67430 × 10⁻¹¹ m³/(kg·s²); R = 6371.0 km; I/MR² = 0.3307; surface GM/R² = 9.820 m/s².
IMPACT RESULT
Impactor mass—
Energy—
Seismic magnitude—
Transient crater—
Final crater—
Crater in TL-cells—
Specific energy Q_R / Q*_RD—
Largest remnant—
Cells removed · escaped · fell back · still aloft (bound)—
EDITS
Cells dug0
Cells placed0
Cells painted0
Mass change0
Moment of inertia change0
Edits are measured against the world as it was built. The comparison column above still shows the original target, so you can watch your digging pull the numbers away from it.
THREE-BODY CHECK moment of inertia · 128 cells across
Body
Counted
Measured
Off by
counting…
The moment of inertia tells how much weight sits near the middle. It is never put in by hand: it comes out of the count, so matching it on three different worlds is a real test.
Earth uses PREM directly. For the Moon and Mars, the core and crust come from published seismic and gravity models, the mantle density is solved from the measured mass, and I/MR² is then predicted by the count. Measured values are C/MR²; normalization conventions (polar C against mean moment, mean against equatorial radius) differ by up to about 0.4%.
LAYERS
Layer
Cells
Mass %
ρ g/cm³
GRAVITY INSIDE EARTH
g from the cells against radius, center to surface. On Earth gravity rises going down and peaks at the core–mantle boundary; on the Moon and Mars, with lighter cores, it peaks at the surface. It falls to zero at the center on every world.
CONVERGENCE smaller cells → exact
Cells across
Edge km
Cells inside
mean ρ
vs measured
BUILT FROM
Dziewonski & Anderson (1981), "Preliminary Reference Earth Model," Physics of the Earth and Planetary Interiors 25: the density of every layer.
IERS Conventions (2010), Technical Note 36: GM⊕ = 3.986004418 × 10¹⁴ m³/s². CODATA 2018: G = 6.67430 × 10⁻¹¹. IUGG mean radius 6371.0 km.
Yoder (1995), "Astrometric and Geodetic Properties of Earth and the Solar System," AGU Reference Shelf 1: I/MR² = 0.3307.
Moon: Weber et al. (2011), "Seismic Detection of the Lunar Core," Science 331: core layers. Wieczorek et al. (2013), "The Crust of the Moon as Seen by GRAIL," Science 339: crust density 2.55 g/cm³, about 40 km thick. GM = 4902.80 km³/s² (GRAIL). I/MR² = 0.3929 ± 0.0009 (Williams et al. 1996, lunar laser ranging).
Mars: Stähler et al. (2021), "Seismic detection of the martian core," Science 373: core radius 1830 km, density 5.7–6.3 g/cm³. Knapmeyer-Endrun et al. (2021) and Khan et al. (2021), Science 373: crust and upper mantle. GM = 42828.37 km³/s²; I/MR² = 0.3644 ± 0.0005 (Konopliv et al. 2011, Icarus 211).
Collins, Melosh & Marcus (2005), "Earth Impact Effects Program," Meteoritics & Planetary Science 40: crater scaling, energy, seismic magnitude. Leinhardt & Stewart (2012), "Collisions between gravity-dominated bodies I," Astrophysical Journal 745: disruption threshold and largest remnant. Housen & Holsapple (2011), Icarus 211: ejecta speed scaling. Canup (2004), Icarus 168: the Moon-forming impact.
Laine & Karras (2010), "Efficient Sparse Voxel Octrees": cell storage at scale. Barnes & Hut (1986), Nature 324: gravity summed through the tree.