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A to-scale, physically grounded model of the universe — from the Big Bang to a billion years beyond the present day — that you fly around in real time.
240,000 individually evolving stars and 60,000 galaxies at a locked 60 fps.
Nothing here is a texture or a fitted curve. Star colours are the CIE colours of their Planck spectra, the expansion history is a numerical integration of the Friedmann equation, and a black hole's shadow, accretion disc and jets all follow from its mass, spin and accretion rate.
pip install ursina numpy
python3 main.pyTested on Python 3.12, Ursina 8.3, NumPy 1.26, Panda3D with OpenGL 3.2+. Runs at 60 fps on integrated graphics (Intel Iris Xe).
W A S D |
fly · R / F up and down · Q / E roll |
SHIFT / CTRL |
faster (×10) / finer (×0.08) |
| mouse | look · ESC releases the cursor |
1 2 3 4 |
jump +1 / +10 / +100 Myr, +1 Gyr (SHIFT to go back) |
B / P |
Big Bang / present day |
SPACE |
pause · T / G time rate up and down |
X |
detonate the nearest massive star |
N |
cycle nearby luminous stars · C travel to the selected one |
V |
travel to another galaxy |
M / K |
travel to a black hole / an active quasar |
TAB / H |
hide the HUD / the control list · F10 quit |
Travel speed scales with the distance to the nearest object, so the same key
crosses a planetary system and intergalactic space. Star to star is about eight
seconds with SHIFT held.
The Friedmann equation is integrated numerically at import, building a table that links scale factor, cosmic time, redshift, comoving distance and lookback time. Everything downstream is a lookup.
| quantity | this model | published |
|---|---|---|
| Age of the universe | 13.786 Gyr | 13.787 |
| Particle horizon | 14.16 Gpc | ~14.2 |
| Deceleration parameter q₀ | −0.533 | −0.53 |
| Growth factor D(z=1) | 0.609 | ~0.61 |
| Recession velocity at 100 Mpc | 6,766 km/s | ~6,770 |
Also modelled: the thermal history from the Planck epoch through nucleosynthesis, recombination and reionisation; the CMB temperature as 2.7255 K / a(t); and the primordial fireball, which really does fill the sky before the universe turns transparent.
Sampled from the Kroupa initial mass function with formation times following the Madau–Dickinson cosmic star formation history, which peaks at z ≈ 1.9.
Main-sequence lifetimes come from the nuclear timescale — available core mass times 0.7% of mc² divided by luminosity — not from a fitted exponent. Temperature is the Stefan–Boltzmann inversion of luminosity and radius, so L, R and T stay mutually consistent when a star swells into a giant.
| mass | lifetime here | published |
|---|---|---|
| 1 M☉ | 10.2 Gyr | ~10 |
| 2 M☉ | 1.47 Gyr | ~1.2 |
| 25 M☉ | 5.9 Myr | ~6.4 |
| 40 M☉ | 3.7 Myr | ~4.3 |
Colour is the CIE tristimulus integral of the star's Planck spectrum over 360–830 nm, using the Wyman–Sloan–Shirley colour matching fits, converted to sRGB and gamut-mapped. The Sun comes out very slightly warm white; M dwarfs orange; O stars blue-white.
How blinding a resolved star looks is set by its temperature alone. Surface brightness is σT⁴ and, unlike flux, does not fall off with distance — only angular size does — so one expression covers a 2,500 K red dwarf and a 40,000 K O star. The disc is limb-darkened by I(μ)/I(0) = 1 − 0.62(1 − μ), and the glare around it grows with the logarithm of the apparent flux, the same law the distant star field uses, so a star looks continuous as it crosses from a point sprite to a resolved disc.
Remnants follow the Kalirai initial–final mass relation for white dwarfs (cooling by Mestel's law), the TOV limit for neutron stars, and fallback or direct collapse for black holes.
Types Ia, II and Ib/c, hypernovae and pair-instability explosions, classified by progenitor mass and metallicity. Light curves are powered by the actual ⁵⁶Ni → ⁵⁶Co → ⁵⁶Fe decay chain, with the right half-lives and specific decay powers, plus a hydrogen recombination plateau for Type II and shock breakout for core collapse.
| type | peak M_bol here | observed |
|---|---|---|
| Ia | −19.0 | −19.3 |
| II | −16.1 | −17.0 |
| Pair-instability | −21.7 | −21.5 |
Press X and the nearest star massive enough for core collapse will oblige. A
red dwarf will not, however hard you ask.
Drawn from a cold dark matter halo mass function, with stellar masses from Moster abundance matching, sizes from the observed size–mass relations, and central black holes from the Magorrian relation. Positions trace a cosmic web of filaments, sheets and voids.
The morphology mix lands where a deep survey does: 71% spiral, 12% elliptical, 13% irregular, 5% lenticular. A Milky Way–mass halo gets r_vir = 211 kpc, σ = 101 km/s, M★ = 3.4 × 10¹⁰ M☉; a 10¹⁵ M☉ cluster gets σ = 1,010 km/s.
Mergers fire at the observed rate, which rises as (1+z)^2.5, and a major merger destroys the disc.
Built by core accretion: a minimum-mass-solar-nebula disc, a snow line at 2.7 √L AU, and isolation masses that only exceed the ~10 Earth-mass threshold for gas capture beyond the ice line. Giant planet occurrence rises with host metallicity, as it does in the real exoplanet census.
Orbits are exact. Kepler's equation is solved by Newton iteration, and the relativistic perihelion precession comes out at 42.98 arcsec/century for Mercury's parameters.
Planets are lit by their own star, so a world on the far side of its orbit shows as a crescent.
- Shadow at √27 GM/c² — what a distant observer sees, not the Schwarzschild radius.
- Accretion disc coloured by the Shakura–Sunyaev temperature profile, which peaks at 1.36 r_isco, with Keplerian velocities and relativistic Doppler beaming as the Doppler factor cubed.
- Jets powered by Blandford–Znajek, length scaling as P^⅓ (≈3 kpc at 10³⁸ W), collimated within ~12 gravitational radii then opening at ~1.3°.
- Gravitational lensing of everything behind, using the exact Schwarzschild point-lens equation β = θ − θ_E²/θ, with the true magnification μ = 1/|1 − (θ_E/θ)⁴|. The far side of the disc is lifted up over the top of the hole, and a faint secondary image of its underside hugs the shadow.
Quasar activity follows a duty cycle peaking at cosmic noon: ~150 active nuclei at z = 2, five today. A few per cent of stellar-mass black holes are accreting X-ray binaries. Sanity checks: radiative efficiency 0.057 at a = 0 and 0.32 at a = 0.998; Salpeter time 50 Myr; an equal-mass merger leaves spin 0.686 and radiates 5% of the mass. The Crab pulsar's spin-down reproduces to within 1%.
Three ideas do most of the work.
State is a function of cosmic time, not an accumulation. A star's phase follows from comparing t − t_formation against two fixed timescales. Nothing integrates, so time travel is exact in both directions, there is no drift, and jumping a billion years costs the same as advancing one frame.
Almost nothing changes between frames. Every transition a star will ever make is precomputed into one sorted event schedule. Stepping forward is a binary search plus a walk over the few thousand stars that actually crossed a threshold — not a pass over the population. A rolling slice keeps slowly cooling remnants current, and a full O(N) evaluation handles jumps and running backwards.
Nothing is a scene graph node. Each population is a single interleaved GPU vertex buffer drawn as one point primitive. The logarithmic distance compression happens in the vertex shader against a camera-position uniform, so crossing the universe uploads nothing — it is three floats.
Heavy work (rebuilding a galaxy's stars, redrawing the short-lived stellar population) runs on worker threads, planned for where the clock will be when it lands. Anything paced by simulated time is also rate-limited in real time: at a trillion years a second, 300 Myr elapses in a third of a millisecond.
On an Intel Iris Xe at 1600×900:
| mean | frames under 16.7 ms | |
|---|---|---|
| Default view | 122 fps | 99.1% |
| Black hole, with lensing | 107 fps | 98.1% |
| With vsync (normal play) | 60.1 fps | locked |
Resident memory settles at ~290 MB and stays flat under sustained travel.
There is no linear scale on which both a planet and a galaxy are visible, so every deep-space position is compressed logarithmically about the camera:
r_render = log10(1 + r / 1000 km) × 7
That puts a fifty-metre approach and the edge of the observable universe inside 143 render units. The compression preserves direction exactly and changes only range, so angular sizes are restored explicitly — a body of radius R at distance d is drawn with radius p·R/d at compressed distance p, which subtends exactly the angle it should.
| flag | |
|---|---|
--stars N --galaxies N |
population sizes (default 240,000 / 60,000) |
--seed N |
random seed |
--view V |
start at disc, galaxy, cosmic, system, star, planet, blackhole or quasar |
--standoff N |
viewing distance: stellar radii for star, gravitational radii for black holes |
--age GYR |
start at a cosmic age (0 is the Big Bang) |
--windowed WxH |
window size |
--benchmark N |
fly a fixed path, report frame times with a CPU breakdown, exit |
--stress SECONDS |
fly flat out logging memory, threads and frame time |
--selftest |
press every control in turn and report failures |
--screenshot PATH |
render a few frames, save an image, exit |
--memory-limit MB |
abort if resident memory runs away (default 3072, 0 disables) |
--no-vsync |
uncap the frame rate |
Examples:
python3 main.py --view quasar --age 3.3 # a quasar at cosmic noon
python3 main.py --view star --standoff 3 # three stellar radii from a star
python3 main.py --age 0.0003 # inside the primordial fireball
python3 main.py --benchmark 600 --no-vsync # measure itmain.py Ursina application: flight, HUD, input, viewpoints
simulation_kernel.py The clock, the observer, and everything they see
simulation_constants.py Physical constants and simulation sizes
cosmology/
expansion/ Friedmann integration, distances, growth factor
cosmictime/ The clock
hubbleflow/ Proper distances, recession, redshift
bigbang/ Thermal history and epochs
stellar_pop/
stellar_evolution/ Structure relations, blackbody colour,
the vectorised population, a scalar Star
star_birth/ Kroupa IMF, cosmic SFR, enrichment
remnants/ White dwarfs, neutron stars, black holes
supernovae/ Classification, energetics, light curves
galaxy_pop/
dark_matter_halos/ NFW haloes, abundance matching
galaxy_formation/ Catalogue, morphologies, cosmic web
mergers/ Merger rates and dynamical friction
compact_objects/
black_holes/ Horizons, ISCO, M–sigma, growth
neutron_stars/ Pulsar spin-down, magnetars
quasars/ Eddington accretion, disc profile, jets
planetary_systems/
formation/ Core accretion, planet types
orbital_mechanics/ Kepler solver, Hill radii, GR precession
collisions/ Stability and giant impacts
renderer/
__init__.py Distance compression, GPU point cloud
shaders.py Star, planet, disc, jet, shadow shaders
geometry.py Procedural spheres, annuli, jets
star_field/ galaxy_lod/ The two big point batches
nearby_objects/ Resolvable bodies, drawn as geometry
black_holes.py Shadow, accretion disc, jets
lensing.py Screen-space gravitational lensing
About 12,000 lines.
These are real and worth knowing before you go looking for them.
Stars are ~400× too far apart. 240,000 rendered stars stand in for roughly
10¹¹, so the median spacing between neighbours is 220 pc rather than a few light
years. Raising --stars barely helps, since spacing falls only as N^(−1/3). The
fix is a dense local shell at true stellar density around the observer, which
is not built yet.
The population is deliberately over-sampled at the bright end. Drawn purely from the IMF, a quarter of a million stars would contain no living massive stars at all and nothing could ever explode. The population is therefore a mixture — a true-IMF field component plus a young component uniform in log mass — and every star carries an importance weight so that weighted counts still reproduce the real galaxy. What is over-sampled is exactly what a telescope over-samples.
The accretion disc has a faceted dark boundary near the shadow. The dark annulus itself is correct — the primary lensed image cannot appear inside the Einstein radius — but its edge is polygonal, because the deflection is evaluated per vertex and the Einstein radius varies steeply across the inner disc. The fix is to solve the lens equation per fragment against an analytic disc plane rather than per vertex.
Close planetary viewing needs the clock stopped. Four planetary radii from a
world, that world is moving tens of km/s along its orbit, so at any rate fast
enough to watch the orbit it leaves the frame. --view planet pauses
automatically. The proper fix is a co-moving reference frame.
Jets are not lensed geometrically — only by the screen-space pass.
The three diagnostic modes are not decoration; they were written because each one caught a real bug.
python3 main.py --selftest # exercises all 25 controls
python3 main.py --stress 45 # watches memory, threads, frame time
python3 main.py --benchmark 600 --no-vsync--stress found a leak that grew to 17 GB in 30 seconds and took a machine
down with it — Panda3D copy-on-writes an entire vertex buffer if you call
modify_vertex_data() inside the render loop, which does not reproduce outside
one. The memory guard exists so that class of mistake can never again reach the
point of locking up a desktop.
4ec6b82 (add readme and other functions)