feat(editor): browse samples in a categorized modal gallery

Replace the cramped Samples dropdown with a modal that lays the gallery
out as a card grid, sectioned by tier, so the growing set stays scannable
and the learning order is visible at once.

docs/adr/0004-rate-rules-not-formulas.md

@@ -21,21 +21,34 @@ loops you _run_. They can never disagree.
 typed-in formula.** Each instantaneous element picks one rule and a plain number
 or two — never an expression:
 
-| Rule             | Value                       | Reads (via Information Links)             | Emergent behaviour         |
+| Rule             | Value                                  | Reads (via Information Links)                | Emergent behaviour         |
-| ---------------- | --------------------------- | ----------------------------------------- | -------------------------- |
+| ---------------- | -------------------------------------- | -------------------------------------------- | -------------------------- |
-| **Constant**     | a fixed number              | nothing                                   | linear Stock change        |
+| **Constant**     | a fixed number                         | nothing                                      | linear Stock change        |
-| **Proportional** | `factor × (its `+` inputs)` | the `+`-polarity inputs                   | exponential growth / decay |
+| **Proportional** | `factor × (its `+` inputs)`            | the `+`-polarity inputs                      | exponential growth / decay |
-| **Gap**          | `factor × (level − target)` | the `+` input is _level_, `−` is _target_ | goal-seeking / asymptotic  |
+| **Gap**          | `factor × (level − target)`            | the `+` input is _level_, `−` is _target_    | goal-seeking / asymptotic  |
+| **Overflow**     | `max(0, factor × (level − threshold))` | the `+` input is _level_, `−` is _threshold_ | a spillway / hard ceiling  |
 
 The famous curves are _compositions_ of these over the structure — a logistic
 S-curve is Proportional growth meeting a Gap-driven ceiling (limits-to-growth);
 goal-seeking decay is a lone Gap (coffee cooling). The user sets up a local rule;
 the global shape **emerges**. That emergence _is_ the lesson.
 
+**Overflow is the one _declared_ limit.** Constant/Proportional/Gap are smooth and
+their ceilings _emerge_ (the S-curve is two of them meeting); Overflow instead is a
+threshold — `max(0, …)` that stays shut until a level crosses it, then spills the
+excess down an outflow (a bathtub brimming onto the floor). It earns a rule of its
+own because Gap _cannot_ stand in: Gap is signed and bidirectional (coffee re-warms
+if it drops below the room), so a Gap outflow runs _backwards_ below its target, and
+that clamp can't be applied to Gap globally without breaking the goal-seekers. So
+Overflow is a deliberate exception to "the shape emerges" — a hard ceiling you
+_declare_, for the real limit that is a wall, not a slope (and the rate-side sibling
+of the non-negative-Stock floor the integrator already enforces).
+
 **Polarity does double duty.** The `+`/`−` already captured for loop
 classification (ADR-0001) also selects each operand's role: Proportional reads
 its `+` inputs; Gap reads its `+` input as the level and its `−` input as the
-target. One gesture, two payoffs — no new per-link data.
+target, and Overflow the same with its `−` input as the threshold. One gesture,
+two payoffs — no new per-link data.
 
 ## Considered Options
 
@@ -70,5 +83,7 @@ target. One gesture, two payoffs — no new per-link data.
 - The vocabulary starts deliberately small (Constant / Proportional / Gap —
   enough for linear, exponential, and goal-seeking, and for the coffee and
   savings samples). Growing it is additive: a new `kind` in the union plus a case
-  in the evaluator. Multi-input products (e.g. `Population × fertility`) are a
+  in the evaluator — as **Overflow** later bore out (one union member, one
-  later increment, not a phase-2 blocker.
+  evaluator case, plus matching touch-ups to the rule validator and the
+  inspector). Multi-input products (e.g. `Population × fertility`) are a later
+  increment, not a phase-2 blocker.

src/components/Editor.vue

@@ -29,7 +29,7 @@ import { useAutosave } from "@/composables/useAutosave"
 import { usePlayback } from "@/composables/usePlayback"
 import { parseModel, serializeModel } from "@/model/io"
 import { project } from "@/model/projection"
-import { type Sample, SAMPLES } from "@/model/samples"
+import type { Sample } from "@/model/samples"
 import { canConnect } from "@/model/validation"
 import { useModelStore } from "@/store/model"
 import { NODE_DND_MIME, type PlaceableKind } from "./palette-dnd"
@@ -38,6 +38,7 @@ import Inspector from "./Inspector.vue"
 import LoopOverlay from "./LoopOverlay.vue"
 import Palette from "./Palette.vue"
 import ResultsPanel from "./ResultsPanel.vue"
+import SampleBrowser from "./SampleBrowser.vue"
 import InfoLinkEdge from "./edges/InfoLinkEdge.vue"
 import PipeEdge from "./edges/PipeEdge.vue"
 import CloudNode from "./nodes/CloudNode.vue"
@@ -55,6 +56,9 @@ const edges = computed(() => graph.value.edges)
 // the Model and recomputes reactively while open.
 const showResults = ref(false)
 
+// The sample-browser modal (opened from the header "Samples" button).
+const browserOpen = ref(false)
+
 // The playback clock that advances the playhead while a run is playing (mounted
 // once here; the simulation store holds the state it drives).
 usePlayback()
@@ -270,12 +274,12 @@ function onDragOver(event: DragEvent): void {
  */
 function loadSample(sample: Sample): void {
   if (store.nodeCount > 0 && !window.confirm(`Replace the current model with “${sample.title}”?`)) {
+    // Cancelled: leave the model untouched and the browser open to pick again.
     return
   }
   fitAfterInit = true
   store.setModel(sample.build())
-  // Close the DaisyUI dropdown (it stays open while the trigger keeps focus).
+  browserOpen.value = false
-  ;(document.activeElement as HTMLElement | null)?.blur()
 }
 
 const fileInput = useTemplateRef<HTMLInputElement>("fileInput")
@@ -397,20 +401,7 @@ onBeforeUnmount(() => {
         {{ store.nodeCount }} {{ store.nodeCount === 1 ? "element" : "elements" }}
       </span>
       <div class="ml-auto flex items-center gap-1">
-        <div class="dropdown dropdown-end">
+        <button class="btn btn-ghost btn-sm" @click="browserOpen = true">Samples</button>
-          <button tabindex="0" class="btn btn-ghost btn-sm">Samples</button>
-          <ul
-            tabindex="0"
-            class="dropdown-content menu z-40 mt-1 max-h-80 w-72 flex-nowrap gap-1 overflow-y-auto rounded-box border border-base-300 bg-base-100 p-2 shadow-lg"
-          >
-            <li v-for="sample in SAMPLES" :key="sample.title">
-              <button class="flex flex-col items-start gap-0.5" @click="loadSample(sample)">
-                <span class="font-medium">{{ sample.title }}</span>
-                <span class="text-xs text-base-content/60">{{ sample.blurb }}</span>
-              </button>
-            </li>
-          </ul>
-        </div>
         <button
           class="btn btn-primary btn-sm"
           :class="{ 'btn-active': showResults }"
@@ -504,5 +495,7 @@ onBeforeUnmount(() => {
          the canvas to the space above, where the diagram re-fits (see the
          `dimensions` watcher in <script>). -->
     <ResultsPanel v-if="showResults" @close="showResults = false" />
+
+    <SampleBrowser v-model:open="browserOpen" @select="loadSample" />
   </div>
 </template>

src/components/Inspector.vue

@@ -115,6 +115,8 @@ const RULE_HINT: Record<Rule["kind"], string> = {
   constant: "A fixed number — no inputs.",
   proportional: "rate = factor × its “+” inputs.",
   gap: "rate = factor × (level − target): the “+” input is the level, the “−” the target.",
+  overflow:
+    "rate = max(0, factor × (level − threshold)): spills only once the “+” level passes the “−” threshold.",
 }
 </script>
 
@@ -167,6 +169,7 @@ const RULE_HINT: Record<Rule["kind"], string> = {
             <option value="constant">Constant</option>
             <option value="proportional">Proportional</option>
             <option value="gap">Gap</option>
+            <option value="overflow">Overflow</option>
           </select>
         </label>
 
@@ -204,7 +207,7 @@ const RULE_HINT: Record<Rule["kind"], string> = {
     <label class="mt-2 block">
       <span class="text-xs text-base-content/60">Description</span>
       <textarea
-        rows="3"
+        rows="6"
         class="textarea textarea-bordered textarea-sm mt-1 w-full leading-snug"
         :value="(element ?? link)?.description ?? ''"
         placeholder="Why this element is here…"

src/components/SampleBrowser.vue

@@ -0,0 +1,85 @@
+<script setup lang="ts">
+/**
+ * Sample browser — a modal gallery of the curated example models, laid out as a
+ * card grid sectioned by pedagogical tier (Primer → … → Mechanics & capstone).
+ * As the gallery grows this beats the old narrow dropdown: the whole set stays
+ * scannable in one scroll and the tiers show how the samples relate.
+ *
+ * Presentational only — it never touches the Model store. Picking a card emits
+ * `select`; the Editor owns the confirm/replace/fit logic (one place for it).
+ * Built on the native <dialog> so Esc, the backdrop click and focus-trapping come
+ * for free; `open` drives showModal()/close() and the native close event keeps the
+ * parent's state in sync.
+ */
+import { computed, useTemplateRef, watch } from "vue"
+import { type Sample, SAMPLE_CATEGORIES, SAMPLES } from "@/model/samples"
+
+const props = defineProps<{ open: boolean }>()
+const emit = defineEmits<{ "update:open": [boolean]; select: [Sample] }>()
+
+const dialog = useTemplateRef<HTMLDialogElement>("dialog")
+
+// Mirror the `open` prop onto the native dialog (showModal gives us the focus trap
+// and inert backdrop a plain div can't).
+watch(
+  () => props.open,
+  (open) => {
+    const el = dialog.value
+    if (!el) return
+    if (open && !el.open) el.showModal()
+    else if (!open && el.open) el.close()
+  },
+)
+
+// Fired by Esc, the backdrop form, the ✕, or our own close() — fold them all into
+// one update:open so the parent's state can't drift from the dialog's.
+function onClose(): void {
+  if (props.open) emit("update:open", false)
+}
+
+// The categories in display order, each with its samples (SAMPLES is already in
+// pedagogical order, so first-appearance order is preserved). Empty tiers drop out.
+const sections = computed(() =>
+  SAMPLE_CATEGORIES.map((category) => ({
+    category,
+    samples: SAMPLES.filter((sample) => sample.category === category),
+  })).filter((section) => section.samples.length > 0),
+)
+</script>
+
+<template>
+  <dialog ref="dialog" class="modal" @close="onClose">
+    <div class="modal-box w-11/12 max-w-3xl">
+      <div class="mb-4 flex items-center gap-2">
+        <h3 class="text-base font-semibold">Browse samples</h3>
+        <span class="text-xs text-base-content/50">{{ SAMPLES.length }} models</span>
+        <form method="dialog" class="ml-auto">
+          <button class="btn btn-circle btn-ghost btn-sm" aria-label="Close">✕</button>
+        </form>
+      </div>
+
+      <section v-for="section in sections" :key="section.category" class="mb-5 last:mb-0">
+        <h4 class="mb-2 text-xs font-semibold tracking-wide text-base-content/50 uppercase">
+          {{ section.category }}
+        </h4>
+        <div class="grid grid-cols-1 gap-3 sm:grid-cols-2 lg:grid-cols-3">
+          <button
+            v-for="sample in section.samples"
+            :key="sample.title"
+            type="button"
+            class="flex flex-col gap-1 rounded-box border border-base-300 bg-base-100 p-3 text-left transition hover:border-primary hover:shadow-md"
+            @click="emit('select', sample)"
+          >
+            <span class="font-medium">{{ sample.title }}</span>
+            <span class="text-xs text-base-content/60">{{ sample.blurb }}</span>
+          </button>
+        </div>
+      </section>
+    </div>
+
+    <!-- Click outside the box to dismiss (submits the dialog → fires @close). -->
+    <form method="dialog" class="modal-backdrop">
+      <button aria-label="Close">close</button>
+    </form>
+  </dialog>
+</template>

src/model/io.ts

@@ -55,7 +55,8 @@ function isPolarity(value: unknown): value is Polarity {
 function isRule(value: unknown): value is Rule {
   if (!isObject(value)) return false
   if (value.kind === "constant") return isFiniteNumber(value.value)
-  if (value.kind === "proportional" || value.kind === "gap") return isFiniteNumber(value.factor)
+  if (value.kind === "proportional" || value.kind === "gap" || value.kind === "overflow")
+    return isFiniteNumber(value.factor)
   return false
 }
 

src/model/samples.ts

@@ -21,27 +21,31 @@
  *   6. Predator and prey — two coupled Stocks whose interlocking loops oscillate.
  *   7. Epidemic          — a chain of Stocks joined by Stock→Stock Flows: no clouds.
  *
- * Last, four of Donella Meadows' system *traps* — structures that reliably misbehave
+ * Last, five of Donella Meadows' system *traps* — structures that reliably misbehave
  * (Thinking in Systems, ch. 5), to contrast the healthy dynamics above — and, paired
  * with the first, the cure that escapes it:
  *
- *   8. Tragedy of the commons   — two Reinforcing herds overgraze a *renewable* shared
+ *   8. Tragedy of the commons    — two Reinforcing herds overgraze a *renewable* shared
- *                                 Stock to bare dirt, then starve with it: all ruined.
+ *                                  Stock to bare dirt, then starve with it: all ruined.
- *   9. …commons, fixed          — the same renewable commons, but stocking is regulated
+ *   9. …commons, fixed           — the same renewable commons, but stocking is regulated
- *                                 against an agreed reserve: it holds, and the herds end
+ *                                  against an agreed reserve: it holds, and the herds end
- *                                 *larger* than the trap's boom leaves alive.
+ *                                  *larger* than the trap's boom leaves alive.
- *  10. Escalation               — a single Reinforcing loop spanning two Stocks, with
+ *  10. Escalation                — a single Reinforcing loop spanning two Stocks, with
- *                                 no brake in the structure: an arms race.
+ *                                  no brake in the structure: an arms race.
- *  11. Fixes that fail          — a fix drains the symptom Stock (B) while its side
+ *  11. Success to the successful — two equal rivals split one conserved prize (the field's
- *                                 effect refills it (R): the cure feeds the disease.
+ *                                  attention); a gap-driven Flow tilts it to whoever leads,
- *  12. Drift to low performance — a goal that erodes toward actual performance, so the
+ *                                  so a 51–49 near-tie locks in to ~100–0. Escalation's
- *                                 effort it drives never overcomes a steady decay: a
+ *                                  zero-sum twin — it concentrates instead of exploding.
- *                                 Reinforcing loop ratchets both downward.
+ *  12. Fixes that fail           — a fix drains the symptom Stock (B) while its side
+ *                                  effect refills it (R): the cure feeds the disease.
+ *  13. Drift to low performance  — a goal that erodes toward actual performance, so the
+ *                                  effort it drives never overcomes a steady decay: a
+ *                                  Reinforcing loop ratchets both downward.
  *
  * Next, the dynamic the book is named for, and the one the gallery has saved until a
  * reader knows every piece it needs:
  *
- *  13. Overshoot and collapse   — a Reinforcing harvester on a *renewable* Resource with
+ *  14. Overshoot and collapse   — a Reinforcing harvester on a *renewable* Resource with
  *                                 an extinction threshold (an Allee floor): a fleet
  *                                 overshoots the renewal rate and pushes the fishery past
  *                                 the point of no return. The dark twin of "Limits to
@@ -50,10 +54,46 @@
  * Last, the language pointed at a live debate — a classic trap (Shifting the burden to
  * the intervenor, ch. 5) wearing today's clothes:
  *
- *  14. AI deskilling spiral     — handing the burden of code quality to AI atrophies the
+ *  15. AI deskilling spiral     — handing the burden of code quality to AI atrophies the
  *                                 Expertise that holds quality up, so the team leans on AI
  *                                 harder and Technical debt spirals: addiction, not a fix.
  *
+ * And a mechanical coda — the gallery's one *hard* ceiling, to contrast the emergent
+ * ones (above all "Limits to growth"):
+ *
+ *  16. Bathtub with an overflow — the tap runs flat out (a Constant inflow that never
+ *                                 reads the level) and a spillway carries whatever rises
+ *                                 past the brim into a second Stock, the floor. The only
+ *                                 model on the `overflow` rule — a one-sided Gap, the
+ *                                 threshold the smooth rules can't draw — so here the
+ *                                 ceiling is *declared*, not emergent.
+ *
+ * Then one last trap, held back until the overflow rule existed to carry it — the
+ * language pointed at the most-told cautionary tale in systems thinking:
+ *
+ *  17. The cobra effect         — a bounty on dead cobras (a Balancing fix) quietly funds a
+ *                                 cobra *farm* (a Reinforcing engine); breeding outruns what
+ *                                 the bounty can absorb, the farm gluts, and its now-worthless
+ *                                 surplus spills through an `overflow` gate into the wild —
+ *                                 leaving four times the snakes there were to begin with. The
+ *                                 perverse incentive: rewarding the proxy (dead cobras) over
+ *                                 the goal (fewer cobras), and the overflow rule's dark payoff.
+ *
+ * And the capstone — every piece at once, at the scale the whole gallery points toward:
+ *
+ *  18. 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.
@@ -68,10 +108,31 @@ import {
   type SimSpec,
 } from "./types"
 
-/** A loadable example: a title and one-line blurb for the menu, plus a builder. */
+/**
+ * The pedagogical tier a sample belongs to. Tiers run simplest-first and double as
+ * the section order in the sample browser (see SAMPLE_CATEGORIES).
+ */
+export type SampleCategory =
+  | "Primer"
+  | "Classics"
+  | "System traps"
+  | "Dynamic edge"
+  | "Mechanics & capstone"
+
+/** The categories in display order, simplest tier first. */
+export const SAMPLE_CATEGORIES: SampleCategory[] = [
+  "Primer",
+  "Classics",
+  "System traps",
+  "Dynamic edge",
+  "Mechanics & capstone",
+]
+
+/** A loadable example: a title, one-line blurb and tier for the browser, plus a builder. */
 export interface Sample {
   title: string
   blurb: string
+  category: SampleCategory
   build: () => Model
 }
 
@@ -907,6 +968,82 @@ function escalation(): Model {
   )
 }
 
+/**
+ * Success to the successful — Donella Meadows' competitive-exclusion trap (Thinking
+ * in Systems, ch. 5), known in the sociology of science as the *Matthew effect*
+ * (Robert Merton, after Matthew 25:29: "unto every one that hath shall be given").
+ * Two researchers of equal ability compete for one finite thing — the field's
+ * attention — and the only difference between them is that A begins a single point
+ * ahead (Renown 51 vs 49 of a fixed 100).
+ *
+ * The community's attention is a *conserved* budget: a citation, an invitation, a
+ * grant that goes to one does not go to the other, so Renown A + Renown B never
+ * leaves 100. The marginal piece of it drifts to whoever is already better known —
+ * `attention = factor × (Renown A − Renown B)`, a single Stock→Stock Flow draining
+ * the lesser name into the greater. There are no clouds: nothing enters or leaves
+ * the system, it only *redistributes*. That one valve carries *two* Reinforcing
+ * loops — Renown A → [+] → attention → (fills A) → Renown A (more renown wins more
+ * attention), and Renown B → [−] → attention → (drains B) → Renown B (the falling
+ * name is forgotten ever faster). Neither loop has a surviving `−`, so both are
+ * Reinforcing: nothing brakes the gap, and it can only widen.
+ *
+ * A tie is therefore an *unstable* equilibrium — the knife-edge this trap balances
+ * on. A's one-point lead is enough: attention tilts to A, the gap grows, attention
+ * tilts harder, and the field locks in. Renown A climbs 51 → 100 and Renown B fades
+ * 49 → 0 by t≈42 — a near-total monopoly of acclaim, though the two were equally
+ * able. The cruel lesson Meadows draws: where the prize for winning is more power to
+ * win, it is *initial conditions*, not merit, that decide the outcome.
+ *
+ * Contrast "Escalation", the gallery's other two-Stock all-Reinforcing trap: there
+ * the cross-loop has no minus and *both* arsenals blow up together (positive-sum,
+ * unbounded); here the single loop is zero-sum — A rises only as fast as B is drained
+ * — so the same Reinforcing structure *concentrates* instead of exploding. (The cure
+ * Meadows prescribes is to break the coupling — level the field, diversify the prize,
+ * or handicap the leader — none of which the structure here contains: that is the trap.)
+ */
+function successToTheSuccessful(): Model {
+  // Two Stocks on one line, the lone attention valve nudged above their midpoint so
+  // the pipe (Renown B → attention → Renown A) and the two info links (each Stock
+  // into the valve) read apart instead of overlapping. Hand-placed, not at midpoint.
+  const renownB = makeStock({ x: -260, y: 80 }, "Renown B")
+  renownB.initialValue = 49
+  renownB.description =
+    "Researcher B's standing — equal in ability to A, and a single point behind at the start. The lesser name the attention drains away from, fading to nothing though B never did anything wrong."
+  const renownA = makeStock({ x: 260, y: 80 }, "Renown A")
+  renownA.initialValue = 51
+  renownA.description =
+    "Researcher A's standing — one point ahead at the start, and that hair's lead is all it takes. Attention concentrates here until A holds nearly the whole field's acclaim."
+  // attention = factor × (Renown A − Renown B): a Gap whose `+` level is A and `−`
+  // target is B. Source B, target A, so a positive rate drains the lesser name into
+  // the greater — and since draining B only widens the gap, the rate never reverses.
+  const attention = makeFlow({ x: 0, y: -120 }, "attention", renownB.id, renownA.id)
+  attention.rule = { kind: "gap", factor: 0.05 }
+  attention.description =
+    "The field's finite attention drifting to the better-known name, ∝ the lead (Renown A − Renown B). A conserved transfer: what A gains, B loses — the one valve through which both Reinforcing loops run."
+  return model(
+    "Success to the successful",
+    [renownB, renownA, attention],
+    [
+      link(
+        renownA,
+        attention,
+        "+",
+        "Renown A is the level in the gap: the further ahead A is, the faster attention flows its way. With the inflow it fills, this closes A's Reinforcing loop — the rich getting richer.",
+      ),
+      link(
+        renownB,
+        attention,
+        "-",
+        "Renown B is the target the gap is measured against (the − input). As B fades the gap only widens, so it is drained faster still — a second Reinforcing loop, the same minus on both the link and the outflow.",
+      ),
+    ],
+    // From a 51–49 near-tie the gap runs away: Renown A climbs 51 → ~100 and Renown B
+    // fades 49 → ~0 by t≈42, then both hold — a near-total monopoly of acclaim won on a
+    // one-point head start. The unstable 50–50 knife-edge a hair's difference tips.
+    { start: 0, stop: 50, dt: 1 },
+  )
+}
+
 /**
  * Fixes that fail — the archetype where a quick fix relieves a symptom but feeds it
  * through a side effect, so the symptom returns and the fix is reapplied for ever.
@@ -1343,72 +1480,599 @@ function aiDeskillingSpiral(): Model {
   )
 }
 
+/**
+ * Bathtub with an overflow — the bathtub given a hard ceiling the honest way. The tap
+ * keeps running flat out (filling stays a Constant; it never reads the level), and a
+ * spillway carries off whatever rises past the brim: overflow = max(0, factor ×
+ * (Water − capacity)). That `overflow` rule is a one-sided Gap — shut until Water passes
+ * the `−` threshold (capacity), then draining the excess into a second Stock, the Floor.
+ * The loop Water → overflow → Water carries one `−` (the outflow) → Balancing, so Water
+ * climbs in a straight line, then plateaus just above the brim — a weir needs a little
+ * head of water to discharge — while the Floor goes on filling. The equilibrium comes
+ * from the *spill*, not from the inflow easing off: the counterpoint to a float valve,
+ * which throttles the inflow instead, and to "Limits to growth", whose ceiling emerges.
+ */
+function bathtubOverflow(): Model {
+  const source = makeCloud({ x: -280, y: 0 })
+  const water = makeStock({ x: 0, y: 0 }, "Water")
+  water.initialValue = 20
+  water.unit = "L"
+  water.description =
+    "The water level — the tap fills it in a straight line, then it holds just above the brim as the overflow carries off everything extra."
+  const filling = makeFlow(
+    midpoint(source.position, water.position),
+    "filling",
+    source.id,
+    water.id,
+  )
+  // A constant tap — it never reads the level, so it keeps pouring even at the brim.
+  // The ceiling comes from the overflow below, not from the inflow easing off.
+  filling.rule = { kind: "constant", value: 5 }
+  filling.description =
+    "A constant 5 L/step from the tap (the Source cloud), running flat out. It never throttles — the ceiling is the overflow's doing, not the tap's."
+  const floor = makeStock({ x: 0, y: 240 }, "Floor")
+  floor.initialValue = 0
+  floor.unit = "L"
+  floor.description =
+    "Water spilled onto the floor — the second Stock the overflow collects in. Empty until the tub brims, then it fills at the spill rate."
+  const overflow = makeFlow(
+    midpoint(water.position, floor.position),
+    "overflow",
+    water.id,
+    floor.id,
+  )
+  // overflow = max(0, 1 × (Water − capacity)): shut below the brim, spilling the excess
+  // above it. factor 1 at dt 1 settles in a step without oscillating; the level rides a
+  // touch over capacity — the head a spillway needs to discharge its inflow.
+  overflow.rule = { kind: "overflow", factor: 1 }
+  overflow.description =
+    "The spillway, max(0, Water − capacity): nothing while the tub is below the brim, then it carries off the excess — the Balancing drain that holds the level."
+  const capacity = makeConverter({ x: 240, y: 120 }, "capacity")
+  capacity.rule = { kind: "constant", value: 100 }
+  capacity.description =
+    "The tub's brim (a fixed 100 L) — the threshold the overflow opens above; the level holds just over it."
+  return model(
+    "Bathtub with an overflow",
+    [source, water, filling, floor, overflow, capacity],
+    [
+      link(
+        water,
+        overflow,
+        "+",
+        "Water is the level in the overflow rule: the higher it rises past the brim, the harder it spills. With the outflow, this closes the Balancing loop that holds the level.",
+      ),
+      link(
+        capacity,
+        overflow,
+        "-",
+        "Capacity is the threshold the spill opens above (the − input): a higher brim → less spill at the same level.",
+      ),
+    ],
+    { start: 0, stop: 40, dt: 1 },
+  )
+}
+
+/**
+ * The cobra effect — the perverse-incentive trap, and Meadows' "rule beating"
+ * (Thinking in Systems, ch. 5) in its most-told form. Colonial Delhi has too many
+ * cobras, so the British put a bounty on them: cash for every dead snake. The intent
+ * is a Balancing fix — more cobras → more killed for the reward → fewer cobras (Wild
+ * cobras → [+] → culling, an outflow draining the Stock). And at first it works: the
+ * streets empty of snakes.
+ *
+ * But the bounty pays for *dead cobras delivered*, not for *fewer wild cobras* — it
+ * rewards the proxy, not the goal. So the same reward funds a second thing the policy
+ * never intended: people breed cobras to cash in. That farm is a Reinforcing engine
+ * (Farmed cobras → [+] → breeding → Farmed cobras: more breeding stock, more bred), and
+ * the snakes raised on it are killed and turned in for the bounty too (Farmed cobras →
+ * [+] → harvest — the rule beating: producing dead cobras to the letter of the policy
+ * while making its goal worse). One lever, the bounty, wired into all three flows.
+ *
+ * The engine has no scripted policy reversal — no "the bounty is cancelled at year X" —
+ * so the famous release is *emergent*. Breeding (Reinforcing) outruns what the bounty
+ * can absorb; the farm gluts, and a glutted farm crashes the cobra's worth. Past that
+ * glut threshold the now-worthless surplus is dumped into the wild: releases =
+ * max(0, factor × (Farmed cobras − glut)), the `overflow` rule from "Bathtub with an
+ * overflow", here a one-sided gate shut until the farm overflows. Wild cobras have *no
+ * inflow of their own* (no natural breeding is modelled), so the only thing that can
+ * refill the wild is the farm — which leaves no doubt what brings the snakes roaring back.
+ *
+ * The shape (start 0, stop 70, dt 1): Wild cobras crash 100 → ~3 by t≈20 — the bounty
+ * looks like a triumph — while the unseen farm booms 5 → past the glut (200). Then the
+ * overflow opens, the wild population climbs back above its start by t≈24 and overshoots
+ * to ~404 — four times where it began — settling there for good as the farm levels at
+ * ~308. The fix didn't fail quietly; it left the System far worse than it found it. Kin
+ * to "Fixes that fail" (a fix whose own side effect defeats it), but here the side effect
+ * is a Stock the reward built, the brake is the overflow gate, and the damage is permanent.
+ */
+function cobraEffect(): Model {
+  // Laid out left→right: the farm engine on the left (a Source breeds Farmed cobras,
+  // harvest draining up to a Sink), the release bridge in the centre spilling the glut
+  // rightward into Wild cobras, and the bounty-driven cull running off to the right. The
+  // policy lever (bounty) sits up top, wired down into all three flows — cull, breeding,
+  // cash-out — with glut beneath the bridge it gates. Hand-placed valves keep links clear.
+  const bounty = makeConverter({ x: -80, y: -340 }, "bounty")
+  bounty.rule = { kind: "constant", value: 1 }
+  bounty.description =
+    "The reward paid per dead cobra — held at 1, a normalised policy lever, so every rate here scales with it (a bigger bounty would only run the whole story faster). One lever wired into three flows: the cull, the breeding, and the cash-out."
+
+  // The intended fix: a bounty-driven cull empties the streets of wild cobras.
+  const wild = makeStock({ x: 380, y: -40 }, "Wild cobras")
+  wild.initialValue = 100
+  wild.description =
+    "The actual problem the bounty targets — hunted down at first, then overrun once the farm's surplus is loosed on it. It has no inflow of its own, so any rebound can only be the farm's doing."
+  const cullSink = makeCloud({ x: 920, y: -40 })
+  const culling = makeFlow({ x: 660, y: -40 }, "culling", wild.id, cullSink.id)
+  // culling = 0.16 × Wild × bounty: the Balancing drain, ∝ the stock. Fast enough to
+  // crash the wild population by t≈20 — the policy's whole visible success.
+  culling.rule = { kind: "proportional", factor: 0.16 }
+  culling.description =
+    "Wild cobras killed for the bounty, ∝ Wild cobras × bounty — the intended Balancing fix that empties the streets at first."
+
+  // The perverse stock: a farm bred to cash in on the bounty.
+  const farm = makeStock({ x: -520, y: -40 }, "Farmed cobras")
+  farm.initialValue = 5
+  farm.description =
+    "Cobras bred to cash in on the bounty — the Stock the reward calls into being. It compounds unseen while the streets look clear, then spills its surplus into the wild."
+  const breedSrc = makeCloud({ x: -980, y: -200 })
+  const breeding = makeFlow({ x: -760, y: -200 }, "breeding", breedSrc.id, farm.id)
+  // breeding = 0.31 × Farm × bounty: Farm → breeding → Farm, no `−` → the Reinforcing
+  // engine the bounty funds without meaning to.
+  breeding.rule = { kind: "proportional", factor: 0.31 }
+  breeding.description =
+    "The farm breeding more cobras, ∝ Farmed cobras × bounty — the Reinforcing engine the bounty funds without intending to: more breeding stock, more bred."
+  const harvestSink = makeCloud({ x: 600, y: -220 })
+  const harvest = makeFlow({ x: 400, y: -220 }, "harvest", farm.id, harvestSink.id)
+  // harvest = 0.10 × Farm × bounty: farmed cobras killed and turned in — the rule beating,
+  // and a Balancing drain on the farm.
+  harvest.rule = { kind: "proportional", factor: 0.1 }
+  harvest.description =
+    "Farmed cobras killed and turned in for the bounty, ∝ Farmed cobras × bounty — the rule beating: dead cobras to the letter of the policy, while its goal slips away."
+
+  // The backfire bridge: once the farm gluts, its worthless surplus is dumped into the
+  // wild. A one-sided overflow gate (shut below the glut) — no scripted policy reversal
+  // needed; the release falls out of the farm outgrowing its own worth.
+  const glut = makeConverter({ x: -260, y: 260 }, "glut")
+  glut.rule = { kind: "constant", value: 200 }
+  glut.description =
+    "The farm size past which cobras lose their worth (a fixed 200) — the threshold the spill opens above. A structural stand-in for the day the bounty was scrapped and the snakes became worthless."
+  const releases = makeFlow({ x: -40, y: 60 }, "releases", farm.id, wild.id)
+  // releases = max(0, 0.6 × (Farm − glut)): shut while the farm is worth keeping, then it
+  // carries off the surplus. The overflow that overruns the wild — and, draining the farm
+  // above the glut, the Balancing brake that caps it.
+  releases.rule = { kind: "overflow", factor: 0.6 }
+  releases.description =
+    "The farm's glut spilling into the wild, max(0, 60% of the excess above the glut each step): nothing while the farm stays under it, then the worthless surplus is dumped — the overflow that overruns the wild, and the Balancing drain that caps the farm."
+  return model(
+    "The cobra effect",
+    [
+      bounty,
+      wild,
+      cullSink,
+      culling,
+      farm,
+      breedSrc,
+      breeding,
+      harvestSink,
+      harvest,
+      glut,
+      releases,
+    ],
+    [
+      link(
+        wild,
+        culling,
+        "+",
+        "More wild cobras → more killed for the bounty: the + that makes the cull a Balancing fix.",
+      ),
+      link(
+        bounty,
+        culling,
+        "+",
+        "A bigger bounty → harder hunting: the policy driving its intended effect.",
+      ),
+      link(
+        farm,
+        breeding,
+        "+",
+        "More farmed cobras → more breeding stock → more bred: the Reinforcing engine.",
+      ),
+      link(
+        bounty,
+        breeding,
+        "+",
+        "A bigger bounty → more worth breeding for: the reward funding the farm it never intended.",
+      ),
+      link(farm, harvest, "+", "More farmed cobras → more turned in for cash."),
+      link(
+        bounty,
+        harvest,
+        "+",
+        "A bigger bounty → more worth cashing in: the reward the rule beating chases.",
+      ),
+      link(
+        farm,
+        releases,
+        "+",
+        "Farmed cobras is the level in the overflow rule: only the surplus past the glut spills. With the outflow, this closes the Balancing loop that caps the farm.",
+      ),
+      link(
+        glut,
+        releases,
+        "-",
+        "The glut is the threshold the spill opens above (the − input): below it the farm is worth keeping, and nothing is released.",
+      ),
+    ],
+    // The bounty crashes Wild cobras 100 → ~3 by t≈20 (it looks like a triumph) while the
+    // unseen farm booms 5 → past the glut (200). Then the overflow opens: the wild climbs
+    // back above its start by t≈24 and overshoots to ~404 — four times where it began —
+    // settling there as the farm levels at ~308. The fix left the System far worse, for good.
+    { start: 0, stop: 70, dt: 1 },
+  )
+}
+
+/**
+ * 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 },
+  {
+    title: "Bathtub",
+    blurb: "A stock filled and drained — no feedback yet.",
+    category: "Primer",
+    build: bathtub,
+  },
   {
     title: "Savings account",
     blurb: "Interest on a balance: a Reinforcing loop.",
+    category: "Primer",
     build: savings,
   },
   {
     title: "Coffee cooling",
     blurb: "Settling toward room temperature: a Balancing loop.",
+    category: "Primer",
     build: coffee,
   },
   {
     title: "Population",
     blurb: "Births and deaths: Reinforcing and Balancing together.",
+    category: "Primer",
     build: population,
   },
   {
     title: "Limits to growth",
     blurb: "Growth into a ceiling: a Reinforcing and a Balancing loop on one Flow.",
+    category: "Classics",
     build: limitsToGrowth,
   },
   {
     title: "Predator and prey",
     blurb: "Two coupled Stocks whose loops make them oscillate.",
+    category: "Classics",
     build: predatorPrey,
   },
   {
     title: "Epidemic",
     blurb: "Susceptible → Infected → Recovered: a chain of Stocks, no clouds.",
+    category: "Classics",
     build: epidemic,
   },
   {
     title: "Tragedy of the commons",
     blurb: "Two Reinforcing herds overgraze a renewable Stock, then starve with it: a system trap.",
+    category: "System traps",
     build: tragedyOfTheCommons,
   },
   {
     title: "Tragedy of the commons, fixed",
     blurb: "Regulate the same renewable commons with a reserve: it holds, and the herds last.",
+    category: "System traps",
     build: tragedyOfTheCommonsFixed,
   },
   {
     title: "Escalation",
     blurb: "An arms race: one Reinforcing loop spanning two Stocks.",
+    category: "System traps",
     build: escalation,
   },
+  {
+    title: "Success to the successful",
+    blurb:
+      "Two equal researchers, one a hair ahead: the field's attention locks onto the leader and the rival fades — a winner-take-all trap.",
+    category: "System traps",
+    build: successToTheSuccessful,
+  },
   {
     title: "Fixes that fail",
     blurb: "Road building eases congestion (B) but induces the traffic that refills it (R).",
+    category: "System traps",
     build: fixesThatFail,
   },
   {
     title: "Drift to low performance",
     blurb: "An eroding goal leaves steady decay no floor: both slide downhill.",
+    category: "System traps",
     build: driftToLowPerformance,
   },
   {
     title: "Overshoot and collapse",
     blurb: "A fleet overfishes past the point of no return: the stock collapses for good.",
+    category: "Dynamic edge",
     build: overshootAndCollapse,
   },
   {
     title: "AI deskilling spiral",
     blurb: "Leaning on AI to hold quality erodes the expertise that holds it: shifting the burden.",
+    category: "Dynamic edge",
     build: aiDeskillingSpiral,
   },
+  {
+    title: "Bathtub with an overflow",
+    blurb:
+      "A flat-out tap and a spillway: the excess spills to a second Stock and the level holds.",
+    category: "Mechanics & capstone",
+    build: bathtubOverflow,
+  },
+  {
+    title: "The cobra effect",
+    blurb:
+      "A bounty on dead cobras breeds a cobra farm; its glut spills into the wild, leaving four times the snakes: a perverse incentive.",
+    category: "Mechanics & capstone",
+    build: cobraEffect,
+  },
+  {
+    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.",
+    category: "Mechanics & capstone",
+    build: worldOnAWarmingPlanet,
+  },
 ]

src/model/simulation.ts

@@ -107,6 +107,19 @@ function evalRule(rule: Rule, links: InformationLink[], valueOf: (id: string) =>
         rule.factor * ((level ? valueOf(level.source) : 0) - (target ? valueOf(target.source) : 0))
       )
     }
+    case "overflow": {
+      // max(0, factor × (level − threshold)): a one-sided gap. The `+` input is the
+      // level, the `−` the threshold; it stays shut until the level passes it, so an
+      // overflow Flow spills only the excess. Clamping at 0 is what stops it running
+      // backwards below the threshold — gap can't, by design (it's bidirectional).
+      const level = links.find((link) => link.polarity === "+")
+      const threshold = links.find((link) => link.polarity === "-")
+      return Math.max(
+        0,
+        rule.factor *
+          ((level ? valueOf(level.source) : 0) - (threshold ? valueOf(threshold.source) : 0)),
+      )
+    }
   }
 }
 

src/model/types.ts

@@ -42,11 +42,15 @@ export interface Position {
  *                     (→ exponential growth/decay)
  *  - `gap`          — `factor × (level − target)`, where the `+` input is the
  *                     level and the `−` input the target. (→ goal-seeking)
+ *  - `overflow`     — `max(0, factor × (level − threshold))`: a one-sided `gap`
+ *                     that only fires once the `+` level exceeds the `−`
+ *                     threshold. (→ a spillway / hard ceiling)
  */
 export type Rule =
   | { kind: "constant"; value: number }
   | { kind: "proportional"; factor: number }
   | { kind: "gap"; factor: number }
+  | { kind: "overflow"; factor: number }
 
 /**
  * The run parameters for a simulation: integrate from `start` to `stop` in steps