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feat(samples): add "World on a warming planet" capstone

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A miniature of the Club of Rome's World3 with its pollution sector
reframed as a climate channel: four coupled Stocks where Reinforcing
capital and population overshoot a finite Resource and the carbon they
burn locks in the warming that finishes them. A qualitative tribute to
the overshoot-and-collapse shape on the existing four rules, not a port
of the equations.
This commit is contained in:
Julien Calixte
2026-06-21 20:06:35 +02:00
parent 9ddff65072
commit 62f6c5cda1
1 changed files with 273 additions and 1 deletions
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src/model/samples.ts
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@@ -64,6 +64,21 @@
* threshold the smooth rules can't draw — so here the
* ceiling is *declared*, not emergent.
*
* And the capstone — every piece at once, at the scale the whole gallery points toward:
*
* 16. World on a warming planet — the Club of Rome's World3 (Meadows et al., *The Limits
* to Growth*) in miniature, its pollution sector reframed
* as a climate channel: four coupled Stocks where two
* Reinforcing engines (capital, population) overshoot a
* finite Resource and the carbon they burn locks in the
* warming that finishes them. The gallery's largest model,
* it composes the whole vocabulary — a Stock→Stock bridge
* ("Epidemic"), logistic-style limits ("Limits to growth"),
* a renewable-resource overshoot ("Overshoot and collapse"),
* and the bathtub's slow sink ("Bathtub with an overflow")
* — into one system. A qualitative tribute to the shape, not
* a port of the equations.
*
* These are plain data built from the same tested constructors the store uses
* (factory.ts), so every sample is a valid Model by construction. `build()`
* mints fresh ids on each call, so loading a sample twice never collides.
@@ -1425,6 +1440,256 @@ function bathtubOverflow(): Model {
)
}
/**
* World on a warming planet — the gallery's capstone: the Club of Rome's World3
* (Donella Meadows et al., *The Limits to Growth*, 1972) in miniature, with its
* persistent-pollution sector reframed as the climate channel. It is a *qualitative
* tribute*, not a port: World3 runs on hundreds of equations, table-function
* nonlinearities, and delays; here four Stocks on the gallery's four rules
* reproduce the famous *shape* — overshoot and collapse — without the apparatus.
*
* The four sectors and how they couple:
* - **Capital** is the growth engine. output = factor × Capital × availability;
* a slice is reinvested (investment, an inflow) so Capital → output → investment
* → Capital is **Reinforcing** — the economy compounds. depreciation drains it
* (**Balancing**).
* - **Resources** is the finite planet: a nonrenewable Stock with *no* inflow.
* `availability` ∝ Resources scales output, so as the reserve runs down the
* economy is choked: Resources → availability → output → combustion → Resources,
* one `−` → **Balancing**. This is the World3 limit.
* - **Atmospheric carbon** is the climate channel. The same act that runs the
* economy loads the sky: `combustion` is a single Stock→Stock Flow that drains
* Resources straight *into* carbon — burning the reserve *is* the emission. A
* slow `removal` (a Gap toward preindustrial) is the sink; tuned slow, so the
* carbon **stays** — the bathtub, the lesson that stabilising emissions ≠
* stabilising concentration.
* - **Population** grows on births (**Reinforcing**) against baseline deaths
* (**Balancing**). `warming` (a Gap reading carbon above the same preindustrial
* baseline — the constant does double duty) drives `heat deaths`, the climate's
* bite on people, and `climate damage`, its bite on Capital. That damage closes
* the long cross-sector loop output → combustion → carbon → warming → climate
* damage → Capital — so the climate is genuine *feedback*, not one-way forcing.
*
* Note what is *absent*: there is no Reinforcing tipping loop. The climate here is
* slow accumulation braked by its sink, not a runaway — faithful to World3's
* pollution sector, and a different model from a carbon-cycle one built to tip.
* The Reinforcing engines are growth (Capital) and births (Population); everything
* the planet pushes back with is Balancing. That asymmetry *is* limits-to-growth.
*
* What emerges (start 0, stop 250, dt 1): the economy booms, then overshoots the
* reserve and collapses — output peaks ≈540 at t≈47, Capital ≈1040 at t≈60, both
* falling to near nothing as Resources deplete 1000 → ~120. The carbon they burned
* climbs to ~1085 ppm and *holds* near 1000 (warming locked at ~4 °C) long after
* the emissions stop. That locked-in heat is what finishes Population: it overshoots
* to ~310 at t≈60 — the *last* sector to peak — then collapses to ~30, a third of
* where it began. Growth first, people last; the limit and the heat together.
*/
function worldOnAWarmingPlanet(): Model {
// Economy upper-left (Resources, Capital and their converters/flows); the carbon
// Stock sits centre on the same baseline as Resources, joined by the combustion
// bridge; `warming` hangs below it and radiates harm out to *both* the economy
// (up-left, climate damage) and Population (right, heat deaths). Population runs
// its own birth/death column on the right. Valves are hand-placed, not at
// midpoints, to keep every Information Link in open space.
// Resources sector (far left): a finite reserve that only depletes; its grade
// (availability) is what the economy can actually draw on.
const resources = makeStock({ x: -820, y: 60 }, "Resources")
resources.initialValue = 1000
resources.description =
"The planet's nonrenewable reserve — it has no inflow, so it only ever falls. As it runs down it chokes the economy that lives off it."
const availability = makeConverter({ x: -820, y: -140 }, "availability")
// availability = 0.001 × Resources: a 0…1 grade (starts at 1.0) that scales output.
availability.rule = { kind: "proportional", factor: 0.001 }
availability.description =
"How much of the reserve is still cheap to reach (∝ Resources, ~1.0 at the start, → 0 as it empties). It is the brake the finite planet puts on output."
// Economy: Capital is the hub — investment fills it (Reinforcing), depreciation
// and climate damage drain it (Balancing). output relays Capital × availability.
const capital = makeStock({ x: -420, y: -40 }, "Capital")
capital.initialValue = 50
capital.description =
"Industrial capital — the engine that compounds by reinvesting its own output, until the reserve it burns runs short and the heat it raises bites back."
const output = makeConverter({ x: -600, y: -200 }, "output")
// output = Capital × availability (both `+`): the economy's activity, throttled by
// how much reserve is left. It feeds investment, combustion, and (via carbon) warming.
output.rule = { kind: "proportional", factor: 1 }
output.description =
"Industrial output, Capital × availability: more capital makes more, but a depleting reserve scales it down. The relay that ties the economy to the planet."
const investSrc = makeCloud({ x: -680, y: -40 })
const investment = makeFlow({ x: -550, y: -40 }, "investment", investSrc.id, capital.id)
// investment = 12% of output, reinvested: Capital → output → investment → Capital,
// no `−` → the Reinforcing engine that drives the boom.
investment.rule = { kind: "proportional", factor: 0.12 }
investment.description =
"Output ploughed back into capital, 12% per step. More capital → more output → more investment: the Reinforcing engine of growth."
const deprSink = makeCloud({ x: -240, y: -200 })
const depreciation = makeFlow({ x: -330, y: -120 }, "depreciation", capital.id, deprSink.id)
// depreciation = 4% of Capital: wear. Below investment while the reserve lasts,
// above it once availability collapses — which is what tips Capital into decline.
depreciation.rule = { kind: "proportional", factor: 0.04 }
depreciation.description =
"Capital wearing out, 4% per step — the Balancing drain that overtakes investment once a depleted reserve starves output."
const dmgSink = makeCloud({ x: -640, y: -260 })
const climateDamage = makeFlow({ x: -540, y: -160 }, "climate damage", capital.id, dmgSink.id)
// climate damage = 0.004 × Capital × warming: the heat's bite on the economy. It
// closes the long climate→economy loop, so warming is feedback, not just forcing.
climateDamage.rule = { kind: "proportional", factor: 0.004 }
climateDamage.description =
"Capital lost to a hotter world, ∝ Capital × warming. It closes the loop from output through carbon and warming back onto Capital — the climate biting the economy that warmed it."
// The combustion bridge: a single Stock→Stock Flow draining Resources *into*
// carbon. Burning the reserve is the emission — no Source, no Sink, both ends Stocks.
const carbon = makeStock({ x: 40, y: 60 }, "Atmospheric carbon")
carbon.initialValue = 280
carbon.unit = "ppm"
carbon.description =
"Carbon in the air (ppm), 280 at the preindustrial start. Combustion fills it fast, the sink empties it slow — so it climbs, then stays. The bathtub."
const combustion = makeFlow({ x: -380, y: 60 }, "combustion", resources.id, carbon.id)
// combustion = 3% of output: the reserve burned each step, drained from Resources
// and added to carbon in one move. Conserved — what leaves the ground enters the sky.
combustion.rule = { kind: "proportional", factor: 0.03 }
combustion.description =
"The reserve burned to run the economy, ∝ output — drained from Resources straight into the air. The same act depletes the planet and loads the sky."
const removalSink = makeCloud({ x: 40, y: -140 })
const removal = makeFlow({ x: 40, y: -40 }, "removal", carbon.id, removalSink.id)
// removal = 0.001 × (carbon − preindustrial): the natural sink, a Gap toward the
// baseline. Deliberately slow, so carbon barely recedes — the locked-in warming.
removal.rule = { kind: "gap", factor: 0.001 }
removal.description =
"Nature drawing carbon back toward the preindustrial baseline — a slow Gap. So slow that once emitted, the carbon stays for the run: warming you cannot take back."
const preindustrial = makeConverter({ x: -180, y: 240 }, "preindustrial")
preindustrial.rule = { kind: "constant", value: 280 }
preindustrial.description =
"The preindustrial carbon baseline (280 ppm), doing double duty: the target the sink draws toward and the zero from which warming is measured."
const warming = makeConverter({ x: 300, y: 200 }, "warming")
// warming = 0.005 × (carbon − preindustrial): °C above preindustrial. A Gap reading
// carbon as the level and the baseline as the target; ~4 °C at the carbon peak.
warming.rule = { kind: "gap", factor: 0.005 }
warming.description =
"Warming in °C above preindustrial, ∝ (carbon − baseline) — about 4 °C at the peak. It feeds both the deaths it causes and the capital it destroys."
// Population: births compound it (Reinforcing), baseline deaths brake it (Balancing),
// and heat deaths add the climate toll that eventually overwhelms the birth engine.
const population = makeStock({ x: 660, y: 60 }, "Population")
population.initialValue = 100
population.unit = "people"
population.description =
"The people — grows on births, thinned by ordinary deaths, and finally overwhelmed by the heat the economy's carbon locked in. The last sector to peak, and to fall."
const birthSrc = makeCloud({ x: 660, y: -140 })
const births = makeFlow({ x: 660, y: -40 }, "births", birthSrc.id, population.id)
// births = 5% of Population: the Reinforcing engine, +3%/step net of baseline deaths.
births.rule = { kind: "proportional", factor: 0.05 }
births.description =
"New people, 5% of the population each step — the Reinforcing engine that grows it while the world stays cool enough to bear it."
const deathSink = makeCloud({ x: 520, y: 240 })
const deaths = makeFlow({ x: 600, y: 160 }, "deaths", population.id, deathSink.id)
// deaths = 2% of Population: ordinary mortality, the Balancing drain births outrun early.
deaths.rule = { kind: "proportional", factor: 0.02 }
deaths.description =
"Ordinary deaths, 2% of the population each step — the Balancing drain the birth engine outpaces, until the heat tips the balance."
const heatSink = makeCloud({ x: 820, y: 240 })
const heatDeaths = makeFlow({ x: 740, y: 160 }, "heat deaths", population.id, heatSink.id)
// heat deaths = 0.011 × Population × warming: the climate toll. Once warming passes
// ≈2.7 °C this outflow overtakes net births and Population turns from boom to collapse.
heatDeaths.rule = { kind: "proportional", factor: 0.011 }
heatDeaths.description =
"Deaths from a hotter world, ∝ Population × warming. Once warming passes ≈2.7 °C this overtakes net births, and the population collapses with the heat that never lifts."
return model(
"World on a warming planet",
[
resources,
availability,
capital,
output,
investSrc,
investment,
deprSink,
depreciation,
dmgSink,
climateDamage,
carbon,
combustion,
removalSink,
removal,
preindustrial,
warming,
population,
birthSrc,
births,
deathSink,
deaths,
heatSink,
heatDeaths,
],
[
link(resources, availability, "+", "More reserve left → more of it cheap to reach."),
link(capital, output, "+", "More capital → more output: the level the economy compounds on."),
link(
availability,
output,
"+",
"More availability → more output. With Capital, output = Capital × availability — the planet throttling the economy.",
),
link(
output,
investment,
"+",
"More output → more reinvested: the + that makes the growth loop Reinforcing.",
),
link(capital, depreciation, "+", "More capital → more wearing out each step."),
link(capital, climateDamage, "+", "More capital → more of it exposed to a hotter world."),
link(
warming,
climateDamage,
"+",
"More warming → more capital destroyed. This − outflow closes the climate→economy loop: feedback, not forcing.",
),
link(
output,
combustion,
"+",
"More output → more reserve burned: economic activity is what emits.",
),
link(carbon, removal, "+", "More carbon above the baseline → faster (but slow) removal."),
link(
preindustrial,
removal,
"-",
"The baseline the sink draws toward (the − target): removal stops once carbon is back to it.",
),
link(carbon, warming, "+", "More carbon → more warming: carbon is the level in the gap."),
link(
preindustrial,
warming,
"-",
"The baseline warming is measured from (the − target): no carbon above it, no warming.",
),
link(
population,
births,
"+",
"More people → more births: the + that makes the population loop Reinforcing.",
),
link(population, deaths, "+", "More people → more ordinary deaths."),
link(population, heatDeaths, "+", "More people → more of them exposed to the heat."),
link(
warming,
heatDeaths,
"+",
"More warming → more heat deaths. With Population this is the climate toll that ends the boom.",
),
],
// The economy overshoots the reserve and collapses (output peaks ≈540 @ t≈47,
// Capital ≈1040 @ t≈60 → ~1); Resources deplete 1000 → ~120. The carbon burned
// climbs to ~1085 ppm and holds near 1000 (warming locked at ~4 °C). Population
// overshoots last (~310 @ t≈60) then collapses to ~30 as the locked-in heat bites.
{ start: 0, stop: 250, dt: 1 },
)
}
/** The gallery, ordered simplest first. */
export const SAMPLES: Sample[] = [
{ title: "Bathtub", blurb: "A stock filled and drained — no feedback yet.", build: bathtub },
@@ -1495,7 +1760,14 @@ export const SAMPLES: Sample[] = [
},
{
title: "Bathtub with an overflow",
blurb: "A flat-out tap and a spillway: the excess spills to a second Stock and the level holds.",
blurb:
"A flat-out tap and a spillway: the excess spills to a second Stock and the level holds.",
build: bathtubOverflow,
},
{
title: "World on a warming planet",
blurb:
"The Club of Rome's World3 in miniature, with a climate channel: growth overshoots a finite planet and the carbon it burns locks in the heat that finishes it.",
build: worldOnAWarmingPlanet,
},
]