Laws of nature

We take real stars from the catalogue. Temperature comes from the star's colour, luminosity from its brightness and distance, radius from the Stefan–Boltzmann law.

• A typical catalogue star is 25 times brighter than the Sun. Only 8 % are dimmer than the Sun.
• Orange dwarfs are the most common at 31 thousand; red dwarfs number only 4.7 thousand.
• At least one catalogue star in four is a giant or a supergiant.

The density of stars at any point is the sum of the thin and thick discs, nine spiral arms, a barred bulge and a halo. Space is split into cubes, and the number of stars in a cube is drawn from a Poisson distribution. A star's mass, age and fate are restored from its number — identically on the server and in the client.

• The Galaxy holds 94.9 million stars. Only 868 thousand bright and unusual ones are stored; the rest are computed from their number when needed.
• 68 million stars live in the thin disc, 17.6 million in the bulge, 8.8 million in the thick disc and half a million in the halo.
• The Sun sits between arms: 1.26 kiloparsecs from the crest of the nearest.

A star gets its population from where it stands. The thin disc gives an age from 0 to 10 billion years, the thick disc 8–12, the bulge 9–13.4, the halo 12–13.4. A star cannot be older than its lifetime, and a giant cannot be younger than it. Nothing is older than the Galaxy itself — 13.4 billion years.

• Almost one star in five lives in the bulge. Everything there is at least 9 billion years old — twice the age of the Sun.
• Real stars almost all belong to the thin disc: 103.8 thousand of 115 thousand. 237 come from the halo, 7 from the bulge.
• Not one star in its prime is older than its lifetime: 0 of 70,505.

From a star's mass we build its whole path. First a long slow brightening, then the subgiant, the red giant, helium burning and the shedding of the envelope. The formulas come from the paper by Hurley and colleagues and are checked line by line against their code. A giant ends when its core grows to the mass of the future white dwarf.

• The model Sun was born 27 % dimmer than today. It will spend 11 billion years in its prime.
• At the end it swells into a red giant of 174 solar radii and 2,750 solar luminosities.
• A star of 5 solar masses stays in its prime for 104 million years, one of 2 masses for 1.2 billion.
• The yellow dwarfs of our world have brightened by about a third since birth; red ones have barely changed.

Every star in the Galaxy has a mass and an age. Younger than its lifetime, it is in its prime. Lighter than 8 solar masses and older — a giant, then a white dwarf. Between 8 and 25 solar masses — a neutron star; heavier — a black hole. A neutron star younger than 100 million years is a pulsar.

• The Galaxy holds 79 million stars in their prime, 14.1 million white dwarfs, 1.12 million giants, 553 thousand neutron stars and 91 thousand black holes.
• There are 1,935 pulsars.
• Giants make up 1.2 % of stars. Around the real Sun it is also about one per cent.

A white dwarf's mass follows from the star's initial mass. After that it only cools: luminosity falls as t to the power −7/5, which is Mestel's law. The normalisation comes from a real dwarf, Procyon B. The radius comes from the equation of degenerate gas.

• A star like the Sun leaves a dwarf of 0.57 solar masses. After a million years it shines at 94,000 K, after a billion at 8,300 K, after 12 billion at 3,500 K.
• A star of 5 solar masses leaves a heavier dwarf, 1.01 solar masses, and a hotter one: 139,000 K in its first million years.
• Check: Sirius B comes out at 27,000 K in the model; 25,000 K is observed.

Stars with a boiling outer envelope are braked by their own magnetic wind: the older, the slower they spin. We take the period from mass and age. Hot stars without such an envelope spin as they were born. A swollen giant slows down like a figure skater opening their arms.

• Without being tuned to the answer, the model hits real stars. Proxima Centauri — 88.5 days (observed 83–90), Barnard's Star — 152 (145–149), α Centauri B — 36.2 (36.2).
• Class A stars turn faster than Earth: 0.55 days on average. Giants take 151 days.
• Red dwarfs vary the most: from 14 to 126 days.

From the rotation period we compute how active the star is and how much it shines in X-rays. X-rays set the strength of its wind, normalised to the Sun. The wind pressure at a planet decides where its magnetosphere ends. You can see it in a body's inspection window.

• The wind reaches planets in 41 thousand real systems.
• In a third of real systems the star is a giant, in another 38 % a hot star. They have no such wind.
• Procedural stars around the Sun are almost all red and orange dwarfs, and 98 % of them blow a wind.

Real supergiants from the catalogue and the brightest blue stars of the Galaxy become supernovae. The moment of the explosion falls in the star's late phase. Everyone sees the flash: a new star in the sky following a supernova light curve — ten days of rise, a plateau of about a hundred days, then a decline. A nearby supernova destroys ozone — almost half of it at 8 parsecs — and it takes years to recover.

• Somewhere in the Galaxy a supernova flares up about once every 3.4 real years.
• A supernova dangerous to an inhabited world will not happen: once in ten million years or less often.
• At night the flash gives light and casts shadows; by day it is visible if it outshines Venus.

From the star's luminosity we derive three boundaries: the edges of the habitable zone and the snow line. There are 3 to 9 planets. They stand on a ladder: each orbit is 1.35–2.2 times farther out than the previous one. Beyond the snow line, solid bodies collect ice. The ladder itself is a rule: we do not yet derive it from the protoplanetary disc.

• 6 planets per system on average; 13 % of them in the habitable zone.
• There are no Mercuries: the first planet gets no more than 4.5 times Earth's dose of light.
• Every star has the same architecture. The habitable zone lies at 0.35–0.51 of the distance to the snow line — for a red dwarf and a blue star alike.

We draw the mass of a planet's core: inside the snow line from 0.02 to 6 Earth masses, outside up to 30. The share of ice grows with distance from the snow line. The radius follows from mass and composition: volumes of the materials add up, then the body is squeezed by its own weight. Layers settle by density: iron inside, ice outside.

• Half of the inner planets are lighter than 0.06 Earth masses. Only 11 % are heavier than half an Earth.
• In the habitable zone only 4.8 % of planets are heavier than Earth. Earth would be a large world here.
• Gravity on a typical player home world is 0.37 of Earth's.
• Check: the model gets Earth's radius within 3 %, Mars within 5 %, Jupiter within 8 %.

For every gas we compare the body's pull with the thermal speed of its molecules. If the ratio exceeds 40, the gas stays. If it is smaller and the substance evaporates at that temperature, it escapes. Only a body with a core heavier than 1.5 Earth masses gets a hydrogen envelope.

• One planet in five loses its water. In the habitable zone, more than a third do: it is warm there and the planets are small.
• The smallest habitable-zone planets, lighter than 0.03 Earth masses, lose their water 86 % of the time.
• Check: Titan and Pluto keep their nitrogen, the Moon does not.

First we compute how much light the star delivers and how much the body reflects. Heat from the interior and tides is added. Then we look at which gases are in the air: each one traps part of the heat. The coefficients are fitted so that Earth, Venus, Mars and Titan all come out right.

• Check: Earth comes out at 287 K (really 288), Venus 738 K (737), Mars 216 K (about 215).
• A typical player home world is hotter than Earth: 527 K at 4 bar. More than half of home worlds are above 100 °C.
• Earth twins by mass and starlight are almost always Venuses here: only 3 % of them have water.
• The reason is that our world has no thermostat yet. On Earth, rain moves CO₂ from the air into rock over millions of years. Here all the CO₂ stays in the atmosphere.

For each substance we know the triple point, the critical point and the saturation curve. A liquid is possible if the temperature lies between them and the air pressure is above the vapour pressure. The mass of a sea is the supply of the substance minus what went into vapour. If the liquid layer is thicker than the crust can bear, the body becomes an ocean world.

• 42.5 % of systems have at least one body with a sea. But only 7.8 % of planets are wet.
• 85 % of the world's liquid water lies outside the habitable zone: on cold planets, the greenhouse keeps it liquid.
• About 2 % of seas are not water but methane and ammonia.
• Ocean worlds with no land are 1.2 % of planets.

A star may have companions: ordinary stars and, rarely, white dwarfs, neutron stars and black holes. A companion stands far enough away not to destroy the planets' orbits, and it has planets of its own. The odds of companions are a game rule: stellar remnants nearby are more common here than in nature.

• 45 % of systems around real stars are double or triple.
• About 10 % of systems have a stellar remnant nearby: a white dwarf, a neutron star or a black hole.
• One body with weather in six lives around a second sun. The year there is short: 28 days on average.
• A neutron star does not shine, so its planets are icy. So were the very first exoplanets ever found — around a pulsar.

Every body moves on an ellipse around its host — a star or a planet. The position at any moment comes from Kepler's equation; the server and the client compute it independently and identically. The elongation of an orbit is drawn at random, and close to the star the tide damps it.

• Orbits are more elongated than Earth's: 39 % of planets have an eccentricity above 0.1.
• An elongated orbit warms a planet: on dry bodies the mean temperature rises, in places by 17 K.
• Years are long: 8.6 Earth years on average. Catalogue stars are bright and their zones lie far out.

We draw the length of day from 4 to 400 hours and an axial tilt of about 20° with some spread. One planet in fifteen lies on its side or spins backwards. Seasons follow by themselves: the weather takes the direction to the star from the orbit and the tilt, including the changing distance. A moon's seasons follow its planet's orbit.

• Days are almost twice as long as Earth's: 44 hours on average. A third of planets have days longer than 100 hours.
• The average axial tilt is 20°.

A planet closer than 0.1 astronomical units to its star always faces it with one side: its day equals its year. The star stands still in the sky — eternal day on one side, eternal night on the other. All moons face their planet with one side.

• Locked bodies are few: 3.8 % of bodies with weather.
• Almost all of them orbit a second sun: 154 of 177. A player's home world is locked in only seven cases.
• The year of a locked planet lasts from 1.7 to 23 days.

A body on an elongated orbit is kneaded by the tide, and friction heats its interior. The power grows with the fifth power of the radius, the fifth power of the orbital frequency and the square of the orbit's elongation. The body's pliability is two numbers: rock and ice behave like Io, giants like Jupiter.

• Check: Io — 2.24 W/m² (about 2 observed), Europa — 0.23, Enceladus — 0.028.
• In a test sample, 4.5 % of moons are heated by tides above 0.2 W/m².
• The hottest moon of the sample gets 142 W/m², sixty times more than Io.

The number of moons grows with the planet's mass: a giant has 2–8, a body heavier than Earth 0–4, small ones 0–1. A moon lives between 4 planetary radii and half of the Hill sphere — farther out the star would take it. A giant's moons are born in its disc: the inner ones rocky, the outer ones icy. A rocky planet's moon comes from an impact, and the tide pushes it outwards. One moon in eight orbits backwards — these are captured guests.

• The formula reproduces Jupiter: Io comes out rocky, Ganymede and Callisto half ice.
• For our Moon the recession formula gives 45 Earth radii; the real value is 60.
• Captured moons are made differently: they hold 25 times more carbon than the planet's native moons.
• Planets close to their star have no moons: the Hill sphere is too small.

The impact rate comes from the layout of the system: asteroid belts, a giant next to them, outer comets and the size of the body itself. Everyone shares one schedule: the host and guests see the same events, and impacts are announced in advance. An impact puts new causes into the body — a crater in the relief, dust and soot in the sky, lost ozone. From there, light, cold, hunger and extinction are computed by the same laws of weather and life.

• Earth around the Sun would be among the most bombarded worlds. A typical habitable world is 25–80 times calmer: home worlds are small, a giant by the belt is rare, and a third of systems have no belts at all.
• For a typical world around a real star, a regional impact comes once in 5 real years, a global one once in 45, an extinction impact once in over five hundred.
• An extinction impact darkens the sky for a year and a half to two years: land cools by 28 K, the sea by 12 K.

A game day lasts 20 real minutes and always equals one rotation of the body. So time runs at its own speed on each planet: the longer the day, the faster the world goes. Orbits, seasons and weather take their time from here.

• A world with Earth-length days runs 72 times faster than real time and lives through a year in about 5 real days.
• A typical player home world runs 127 times faster. Its year — 7.4 Earth years — passes in about 20 real days.
• On a locked planet the day equals the year, and a year passes in 20 minutes.

The inputs are the body's mass, radius, layers and age. The decay of uranium, thorium and potassium heats the mantle, and convection carries the heat out. We run the body's whole life and keep 16 epochs: mantle temperature, heat flow, thickness of the cold lithosphere.

• Young worlds are hotter inside. A kilogram of rock on Litha c, which is 294 million years old, holds four times as much radioactive heat as Earth today. On Drador f, 9.6 billion years old, almost half as much.
• The lithosphere of the prologue worlds is thicker than Earth's: 102–253 km against 66 km for Earth in the same model.
• Check: Earth's heat flow in the model is 0.081 W/m², the Moon's 0.014, Mars's 0.028.

The cooling mantle pulls the cold crust down. The crust's strength is Byerlee friction: it grows with gravity and thickness. If the convective stress is larger, the crust breaks into plates; if not, it stays whole as a "stagnant lid". Wet rock slides twelve times more easily than dry, and only open water at the surface wets it — a sea from 10 m to 1 km deep over the whole globe. An episodic lid stands still most of the time and breaks in windows of 150 million years. Small bodies do not stir at all.

• Plates are rare: 0.4 % of bodies have a mobile lid and another 0.1 % an episodic one. All of them have a sea.
• Two thirds of bodies live under a stagnant lid. A third do not stir inside at all — all of them lighter than 0.1 Earth masses.
• A heavy body with a sea breaks its lid more often than a light one. Above 0.7 of Earth's gravity one in five has plates; below 0.3, one in eighteen.
• The prologue worlds — Litha c, Sarion d, Sarion e — have lived under a stagnant lid all their history: their seas are shallow, 50–240 m.
• Drador f has a sea and plates: 9 plates, 21 seams.
• Plates and their boundaries show on the "Lithosphere" map layer.

The crust floats on the mantle like ice on water. Thick light continental crust stands high, thin heavy crust stands low. The ocean floor cools and sinks with age, and the water presses on it from above. The crust's history is run over the body's whole age: for Earth that is 17,871 steps.

• Continents are rare: on bodies with a crustal history they cover 4.6 % of the surface on average.
• Under a stagnant lid, light crust spreads into a thin layer over billions of years: the prologue worlds have almost no continents.
• The Earth model reproduces the essentials: two levels of elevation, continents and seafloor, more than 3 km apart, and land on 27.7 % of the surface.

A mountain cannot be taller than the rock at its foot can bear: strength divided by weight. On a light body mountains are taller, on a heavy one lower. The strength is fitted to Everest. An ice crust has its own strength, and it depends on temperature.

• Earth's ceiling in the model is 7.6 km.
• Drador f has 0.6 of Earth's gravity, and its ceiling is about 12.6 km.
• Volcanoes grow to between half and three quarters of the ceiling. On Litha c the three main shields are 9.5, 12.1 and 12.6 km high and up to 177 km in radius.

The higher the land above the sea, the deeper rivers cut into it. Valleys branch from 16 km down to 256 m. When the mountain relief exceeds a kilometre, slopes reach their limit of 30–40° and ridges turn sharp. A wall cannot be steeper than the rock can bear: a low wall stands steeper than a tall one. Above the glacier line, ice carves the valleys. We compute the outcome of erosion, not its course in time.

• On a light body walls are steeper: on Drador f a two-kilometre wall stands at up to 56°, on Earth up to 52°.
• Glaciers on Drador f come down to 3.3 km at the equator and 0.7 km at the pole. Under weak gravity the air cools more slowly with height, and the ice line drops twice as far as on Earth.
• A dry body has no rivers — and its mountains stay uncarved.

Glaciers cut mountains down faster than they rise. So ridges settle to the glacier line plus one and a half kilometres, and only then do valleys cut into them. Fast uplift breaks through the saw. Under a cold polar ice sheet there is no saw: the ice is frozen to the rock and does not cut.

• The belts of Drador f rise slowly, and the saw has brought them down to the glacier line: 99 % of the land is now below 3.3 km rather than 7.5 km, and the mean slope is 16° instead of 32°.
• The most common land elevation on Drador f now sits at the glacier line — as on Earth's ranges.
• On Litha c, mountains above the glacier line stand at high latitudes under a cold ice sheet, and the saw leaves them alone.

The lithosphere is an elastic plate on the mantle. A heavy volcano bends it: a moat forms around it and a low bulge farther out. At a trench the plate is broken and arched into a bulge; in front of a mountain belt it sags. When rivers cut mountains down, the crust is unloaded and floats up: the mean height drops by only a sixth of what was removed, and the peaks grow.

• The lithosphere of Drador f is 248 km thick. The moat around the main shield is 1.4 km deep at the centre and stretches 970 km, while the bulge beyond it is only 18 m. Wide and shallow, like on Mars.
• In the Earth model the bend is three and a half times narrower: the elastic part of the plate is 29 km.

A high plateau spreads under its own weight, and the elastic part of the plate holds it up. That sets a height limit: higher on a light body with a thick lid, lower on a heavy one. The slopes of mountain belts are a critical taper: their steepness is set by friction at the base and water in the pores.

• The Earth model gives a plateau of 4.8 km — like Tibet.
• A belt slope is 3.7° on Earth and 6.6° on a dry body: without water in the pores the wedge is steeper.

A hot jet in the mantle brings up melt, and the interior's history computes its volume. A quarter spreads into a trap plateau with steps along its edge. The rest gathers into a main shield with a caldera, satellite shields and a field of cinder cones. Every edifice remembers its last eruption. Local runoff erodes it: in wet belts cirques bite into edifices, in dry belts they stand.

• The prologue worlds are volcanically alive: 69, 90 and 99 edifices. Half of them last erupted less than half a million years ago.
• On Drador f, in the dry belt between 15° and 45°, only one edifice of 98 keeps its cirques; near the equator, under tropical rain, all 11 do.
• A dry world keeps its volcanoes, like Mars.
• A main shield carries 16 to 31 cinder cones up to 400 m tall.

A dome over a hot jet stretches the crust, and it splits into troughs — grabens. Under a large dome the lithosphere cracks into a canyon. A body without plates cools as a whole and shrinks, and its crust breaks into scarps with steep fronts.

• On Litha c a dome has 24–27 radial grabens up to 1.3 km deep.
• The canyons of Sarion d are 39–47 km wide and up to 4.3 km deep. The thicker the lithosphere, the wider the canyon: on Sarion e, 102–135 km.
• Canyons only form on bodies without plates. The Earth model has none: the dome rides away with its plate before it can split.
• Compression scarps on Sarion d reach 1.3 km. Young Litha c has shrunk nine times less.

Each pair of neighbouring plates has its own seam: convergence, divergence or transform. The plate with less continental crust sinks. Ocean under ocean gives a trench and an island arc. Under a continent — a cordillera with a fold belt. Continent into continent — a collision plateau. Divergence on a continent makes a rift, in the ocean a mid-ocean ridge.

• 350 stratovolcanoes have risen over the sinking plates of Drador f.
• On light bodies trenches are deeper and arcs taller, but no more than 1.6 times Earth's.
• Folds rise in arches every 12–24 km, and rivers run between them in a trellis, like in the Zagros.

A hot jet stays put in the mantle, a plate rides over it, and volcanoes line up in a chain: the farther, the older. Leaving the swell, an island sinks. Waves shave its top at sea level, making a guyot, a flat-topped seamount. If the sea is warm and alive, a coral reef grows as the island sinks, making an atoll.

• An atoll needs a sea warmer than 23 °C with life in it: a reef grows up to 5 mm a year and has to keep up with the sinking island.
• Slow plates make short chains. When the plates of Drador f slowed down under the new lid law, its chains dropped from seven groups to two.
• A chain ends at the plate’s edge: mountains that reach the seam disappear into the trench.

A volcano that grows under ice cannot spread: lava freezes against the ice. The part of the edifice inside the ice becomes a table with a flat top at the ice surface and a steep flank, while the summit above the ice stays as it was. At the foot lie plains of meltwater floods.

• On Drador f, 184 of the 350 arc stratovolcanoes have become tuyas: their bases stand at the glacier line.
• On Sarion e, table shields reach 126 km across: a table 2.6 km high with a summit at 8.2 km above it.

The melt's composition depends on the setting: a hot jet gives basalt, an arc andesite, a continental rift rhyolite. Viscosity comes from composition and temperature. A flow runs downhill and cools by radiation. It stops when it has frozen or thickened. A lava lake in a caldera keeps the size at which the magma's heat equals the radiation from its crust.

• Basalt runs for tens of kilometres, andesite for a kilometre or two, rhyolite for a few hundred metres in a thick tongue. On Drador f the averages are 19.5 km, 1.3 km and 200 m.
• The lava lakes of Drador f have radii of 625–800 m, like the Halemaʻumaʻu lake at Kīlauea in 2018–2023.
• Water does not stand on fresh lava: basalt drains thousands of times more water than the rain brings, and the caldera stays dry.
• The glow follows Planck's law: cracks in the lake's crust shine at 1,400 K, the crust itself at 900 K.

Every young edifice smokes. The column height comes from buoyant plume laws: Morton, Taylor and Turner in calm air, Briggs in wind. Dense air presses the column down. A lava fountain is gas expanding from the pressure in the magma to the pressure of the air. The gas of all edifices — CO₂, steam and SO₂ — adds up to the body's output.

• Under the six bar of Drador f a lava fountain reaches 330 m. On Earth the same law gives 550 m.
• Above a lava lake the column rises to 4.9 km in calm air and 3.2 km in a 3 m/s wind.
• Check against Kīlauea: the law gives about 9 thousand tonnes of CO₂ a day; 8.5 thousand are observed.

Impacts hit every body, but the marks do not survive everywhere. Dense air burns up small impactors and smooths the scars. Interior heat floods them with lava. Water washes and buries them. A body shows as many craters as the time it has been collecting them.

• Under air denser than a quarter of Earth's there are no craters at all.
• A water layer of a few metres over the whole globe is enough to erase them.
• A simple bowl turns into a complex crater with a central peak at 15 km on the Moon and at 2.5 km on Earth: the threshold goes inversely with gravity.

We cut the planet into 90 latitude bands, each with its own column of land and sea. The star heats a band, the band cools by radiation, and the air carries heat to the poles. The strength of that transport depends on the mass of air and on rotation: fast spin breaks the flow into small eddies, and the poles stay cold. Over water seas, vapour itself traps heat. A planet's mean temperature is not an input but the result.

• On fast planets the equator–pole difference averages 36 K, on slow ones 13 K.
• Rimar d turns in 5 hours: 320 K at the equator, 246 K at the pole. Almost twice Earth's difference.
• On 40 % of bodies atmospheric eddies are wider than the planet itself — their weather is closer to Venus than to Earth.

Ice and snow reflect light better than water and ground. Where it is cold, ice forms, reflects more and makes it colder still. Clouds reflect too. The freezing point is taken from whatever the planet's seas are made of: water, methane, ammonia.

• About 30 bodies freeze over completely even though without ice they would be warm. Taratha d is 276 K without ice and 237 K with it, and the ice covers the whole planet.
• 20 bodies have two stable climates. Hatasa e can be a warm ocean at 292 K or a snowball at 253 K. For now the world always picks the warm one.
• Nine player home worlds also have a second, frozen climate.

On a locked planet, latitude is measured from the point under the star. Waves in the air carry heat to the night side, but the night surface lies under an inversion and warms little. The denser the air, the smaller the day–night difference. Such planets have no seasons and no hurricanes.

• The day–night difference is 333 K under air thinner than 0.1 bar, 50 K at 1–10 bar, and only 7 K above 10 bar.
• Drarion C b: a water sea under 1.4 bar. 324 K under the star, 311 K in the eternal night.

From the temperature contrast, gravity and rotation we find the width of the tropical cell. If it is wider than 60°, the planet has one cell from equator to pole. Otherwise there are three, as on Earth. Rotation deflects the wind, and fronts run through mid-latitudes. The wind pushes the player.

• A player stays on their feet up to 12 m/s. A 32 m/s hurricane shoves them at 8 m/s, and against such a wind you cannot walk.

A hurricane is a heat engine: warm sea below, cold outflow above. It is fed by the imbalance between air and sea, and that imbalance can never exceed what the star's energy at the surface allows. Wind shear tilts the vortex and dry air blows into its core — ventilation kills weak vortices. It needs open water, and the wind cannot exceed the limit at which the eye would become a vacuum. Where and when a storm is born is left to chance, but the odds follow from its strength and the planet's spin.

• Only one wet body in five has hurricanes, and most of those see a few a year.
• Hot oceans under thick air give birth to no hurricanes: there is too little energy at the surface to run the engine.
• The strongest hurricane is 175 m/s on Manoria c: the air there is 0.14 bar, the day 128 hours long, and there are only two storms a year. The strongest hurricanes overall happen on slow planets.
• The stormiest world is Serrion e: a 4.5-hour day and 28 storms a year.
• No hurricane is born over methane, ammonia or ice anywhere.

A thunderstorm needs daytime heating, air warmer than the daily mean and a lot of vapour: a storm's energy is latent heat. A cell lives 3–8 hours and drifts with the wind. Lightning strikes at the same instant for every player, and thunder arrives late by the speed of sound in the local air.

• On the 4,177 dry bodies of the census there is not a single thunderstorm.
• Slow planets, with days longer than ten Earth days, have more storms.
• On Mars thunder would travel slower: sound there is about 240 m/s.

The wind carries a column of vapour over sea and land. The sea gives up vapour no faster than the star's energy allows. On a slope the air cools and the excess falls out: the windward slope is wet, beyond the ridge it is dry. Moisture neither appears from nowhere nor vanishes. Rain, snow or graupel depend on the melting and triple points of the planet's liquid.

• Nine bodies out of ten have no seas — no rain, no rivers, no storms.
• Methane and ammonia worlds get methane and ammonia rain.
• Weak gravity lifts clouds higher. Without this correction, vapour on light bodies would never condense at all.

Runoff from land follows precipitation and evaporation. Water flows over the relief of the whole planet in 5 km nodes. A depression becomes a lake, either through-flowing or a salty closed basin. Channel width and depth grow with discharge. On a light planet channels are wider and shallower.

• On a test body with 0.39 of Earth's gravity the main river carries 25,700 m³/s. In flood it is 1.7 km wide. On Earth the same river would be about 1.4 km.
• A lake without an outlet gathers salt up to saturation, and where water cannot stay, a salt flat remains.

Over the planet's age a river saws through the pass by which it leaves a depression. Where it does not cut, it drops sediment and fills the depression. On a heavy planet water cuts harder. A young surface is less carved than an old one.

• Sarion d has a giant depression: the water's path across it is about 16,000 km.
• The surface of Litha c is 284 million years old, that of Sarion d and Sarion e 2.6 billion. On the old worlds all runoff reaches the sea.

A river on a gentle floodplain meanders: a loop is about 11 channel widths long. On a steep slope the river runs straight. A stretch four times steeper than the usual profile becomes a waterfall, and the jet falls ballistically under the planet's gravity. Foam appears where the flow is faster than a wave at its depth. Lake waves grow with fetch.

• On a light planet the same river foams more: the Froude number uses the body's gravity.
• A 19,000 km² lake on Litha c holds 84 % of an ocean wave in wind; a one-kilometre lake 15 %.

The wind drags the water, rotation turns the flow sideways. Where the flow diverges, cold water rises from the depths. In each basin the wind spins up a gyre with a fast warm current along the western shore. Ice forms where the water would cool below the freezing point of salt water. Rivers bring salt; gases dissolve by Henry's law.

• Salt builds up slowly: Earth's sea needs 70 million years, the sea of Litha c about a million. Young systems have brackish seas, and methane and ammonia seas have no salt at all.
• In a methane sea nitrogen dissolves by hundreds of moles per cubic metre — by Raoult's law rather than Henry's.

The server knows how much light reaches the surface and whether a place is fit for life: light, liquid, warmth, ground. Plants capture 0.5 % of that light. Animals spend energy by Kleiber's law: the bigger, the more frugal per kilogram. A tenth passes to the next step of the food chain.

• Check: Earth in the model produces 0.55 W/m² of living matter; the real figure is about 0.4.
• Energy only rules out dead and tiny bodies. A moon 100 km in radius would feed a predator thousands of times over. Who ends up at the top of the chain is decided not by energy but by which species exist.

An animal's metabolism depends on its mass and body temperature. Warm-bloodedness is written in a gene: a warm-blooded animal keeps 37 °C regardless of the weather. A cold-blooded one lives on the warmth around it, spends six times less and stops feeding in the frost. Soil also breaks down the dead faster when it is warm and moist.

• An icy planet lives tens of times slower than a warm one. On a test body at 245 K animal metabolism runs at 0.013 of Earth's; at 290–315 K at 0.43–0.76.
• Dead matter on a warm body rots 54 times faster than on an icy one.
• At 20 °C a cold-blooded animal spends 24 times less than a warm-blooded one of the same mass.

How much a predator eats depends on how much prey is around: rare prey is hard to find. The satiation threshold grows with the prey's mass. When prey is scarce, predators share it at the same time, without a queue. Herbivores are satiated by greenery the same way, and herds in the world graze grass by the same response.

• Before this law, predators died out on every test body; with it they survive on almost half. Four times as many species stay alive.
• Without predators, herbivores graze plants down to 5–15 % of the untouched level — the island-without-predators effect.

Herbivores eat the young tissue of plants — leaves, shoots, plankton. It toughens in three months and melts away without light. Animals carry fat: the bigger they are, the longer they last without food. For a warm-blooded animal cold costs food: metabolism rises with frost, and insulation holds it back. A cold-blooded animal kept colder than it is used to for long dies within weeks: the margin is 15 K on land and 5 K in the sea.

• A 600 kg cold-blooded swimmer at 6 °C has fat for 18 years: hunger alone does not kill the large.
• In a test impact winter, 45 % of species and half of the animals drop out beyond the usual.
• A check of the sea's cold margin is the 2010 cold spell off Florida: the law gives 37 % of shallow corals dying; 15–39 % was observed.

Oxygen in the air is carbon that life has buried in sediments. Eroding ancient organic matter and volcanic gases take it back. The balance of these flows sets the oxygen pressure. Above 35 kPa everything burns — that is the ceiling. Oxygen makes ozone, ozone blocks ultraviolet, ultraviolet cuts life down — the loop is closed.

• Check: Earth in the model holds 21 kPa of oxygen.
• Without burial there would be hundreds of times less oxygen: only what is breathing right now.
• A body without mountains and erosion runs into the fire ceiling of 35 kPa.
• Volcanism three times stronger than Earth's eats all the oxygen. A system 100 thousand years old gathers less than 10 % of Earth's.
• Without ozone, ultraviolet at the surface is 1,120 times stronger than on Earth: land is nearly dead, and the sea loses 85 % of its life.

A body's carbon lies in three purses: living, dead and available. Their sum never changes, neither in a step nor over years. A species dies out when it has fewer than 50 individuals or no kin left within reach, and moves into the planet's history. A new species splits off only if a mutation visibly changes its look. Each new species gets a Latin name: genus, family, order. Animals evolve in real time: once an hour a planet's fauna lives through a generation.

• Over 10 years matter is conserved to within 4·10⁻¹³.
• Test worlds hold about 50 species; each year about 6 new ones appear and about 2 die out.
• A test fauna gives rise to about 60 new animal species a day, and most of them live longer than three hours.
• Moved into water or changed diet — a new family; took to the air — a new order. Names are the same in every language.

A species' genome is a chain of up to 1,024 bytes; a gene is a four-byte record. Copies of a gene add up: a doubled segment gene lengthens the body, an extra limb gene adds another pair of legs. Between genes lies a silent reserve — a new gene can be born from it. A mutation shifts a value, inserts or deletes a byte, duplicates or inverts genes.

• A new species appears only if the difference is visible: a new body plan, size shifted by more than 10 %, or hue by more than 30°.
• The environment selects by seven rules: fur in the heat, bare skin in the frost, wings without air to hold them, and others.
• The body of an animal from a late world has about 135 parts, assembled by some 346 gene operations in 15 microseconds.
• The server and the client mutate the chain identically, bit for bit.

A gene sets the mass — from a microgram to thousands of tonnes. Then the environment shapes the look. Legs are shorter and thicker on a heavy planet. Flight is possible only if the mass is small enough for the local pressure and gravity. Stems are shorter on a heavy planet. In dim light, plants grow bigger leaves and animals bigger eyes.

• The flight limit on Earth is 20 kg. At 2 bar and half of Earth's gravity it is 80 kg; at 1 bar and double gravity, 10 kg. At 0.1 bar there are no fliers.
• A plant of the same mass is 1.4 times taller at half of Earth's gravity.
• Under light four times weaker than Earth's, leaves are 1.4 times bigger. In total darkness an animal's eyes are 1.5 times larger.

Every new body plan is assembled into a model: bones, muscles, flesh. It is placed on the ground under the planet's gravity, in its air or water. The species' gait is run through physics: does the body stand, how fast does it walk, how much does it spend. The gait is inherited and mutates. When the body plan changes, the gait is retrained.

• In test worlds 84–100 % of species stand up in physics. On land they cover 3–5 body lengths a second, in shallow water 1.5.
• One species learned to walk tail first: movement counts in any direction, and selection found that gait on its own.
• Colonists from another planet relearn their gait for the new gravity.
• One gait trial takes 36 ms. The fauna of a whole planet is 800 generations, 10–13 minutes on graphics cards.

A bone's strength grows with its cross-section, weight with volume. So on land every bone must carry its share of the body, or the species is not viable. A strut that folds under the load breaks — the species crawls. In water, buoyancy carries the weight.

• The largest animals of the test worlds: a 2.7-tonne giant and a 154 kg flying predator 5.3 m long.
• Tall species appear in bursts — up to 3.7 m — and die out by the end of a run.
• Once selection found a loophole: all 40 species of a world became threads up to 16.8 thousand km long. It was closed by a rule: a bone may be no thinner than a hundredth of its length.

A species' head count is its biomass divided by the mass of one animal. Around a player the world is cut into 20 km cells, and each cell gets herds by the species' density. A place is fit while it is warmer than the freezing point of the planet's liquid. When winter comes, a herd moves along the meridian to look for warmth and returns when home is warm again.

• A herd ranges from a single animal to three thousand head, as written in a gene.
• Searching for warmth, a herd travels up to 500 km.
• Winter is set by what the planet's seas are made of: on a methane world, by methane.
• Two players at the same cell see the same herds.

Skin colour comes from genes: dark melanin and yellow-red carotenoid. The background of a place is soil, greenery, snow or the water column. The lower the contrast with the background, the less often predators find the animal. In the look, colour follows the role: a predator wears the colours of the ground, prey under pressure from predators is bright and warning, prey without predators is showy, for courtship.

• In the first runs on Earth the animals came out dark, with almost no red: red on green does not pay.
• Camouflage disappears when the contrast with the background exceeds 0.3.