MIP-0047: Equation-drawn art — Desmos as the sketchpad, the equation as the source, static SVG as the only thing shipped¶


Status	Draft
Author	Claude Opus 5, for M. Hoffmann (request of 2026-09-07, verbatim: "create a new MIP with opus to generate desmos images (draw by equation). get some desmos already made drawings related to the sea, create new ones and add this as a stylistic philosophy")
Created	2026-09-07
Phase	3 — `ARCHITECTURE.md` §11 puts the static site under Phase 3 ("the first deploy artefact is already here and free: `site.yml` … publishes the static map"). Nothing from Phase 1 or 2 gates a presentation change. Same honest caveat MIP-0046 records: MIP-0009 and MIP-0037 label this same surface "Phase 1" — a pre-existing docs inconsistency, not resolved here
Related	MIP-0046 (the sprite mechanism this reuses verbatim — `<symbol>` in `index.html` + `<use href="#…">`; this MIP adds symbols to that block and does not invent a second one), MIP-0009 (`WAVE_PATH`, the marker glyph and the legend key — deliberately not replaced here, §5.5), MIP-0044 (its `/about/`, `/news/`, `/dev/` sections are where a large motif has room to be more than an icon; its §4 also found the generated scaladoc pages loading four third-party scripts, which is the same "nothing loads from a third party" claim this MIP's §9.1 refuses to break), MIP-0005 (the site's "plain files, no build step" constraint, which §5.4 keeps), `knowledge/waves-tides-glossary.md` and `knowledge/safety/rip-currents.md` (the domain the motifs draw), `PHILOSOPHY.md` (§11's follow-up)
Effort	S — one ~200-line stdlib Python script with a `--self-test` (the shape `scripts/.py` already has), one equations file, a generated `<symbol>` block inside the sprite MIP-0046 introduces, and one `site_check.js` assertion. No new dependency, no CI workflow, no `site.yml` change, nothing added to `site/dist`. The authoring* (tuning five drawings in Desmos until they look right) is hours of human eye-work, but it is not build effort and it produces no reviewable artefact except numbers
Gain	`user value` — the site gets a visual identity that is about the sea rather than about the framework, at the one moment a first-time visitor decides whether to trust its numbers; `infra/dev-loop` — an illustration whose source is a formula is reviewable in a diff and reproducible by re-running a script, which no hand-drawn or generated image is
Effort vs Gain	`do when MIP-0046 lands` — the mechanism is MIP-0046's sprite block. It is buildable first (this MIP would then introduce the block itself) but that duplicates ~25 lines of CSS and creates a mechanical conflict for whoever lands second, for no gain. MIP-0046 is the smaller, more urgent change; this one waits one merge
Depends on	MIP-0046 for the delivery mechanism (`<symbol>`/`<use>`, `.sprite`/`.ic` CSS) — coordination, not a hard gate: if this landed first it would have to create that block, and MIP-0046 would then extend it. MIP-0044 (Draft) is where the large motifs get room; without it, only the map page exists and §5.6 limits the rollout to two placements. No Phase-1 gate, no cloud resource, no paid tier, no API key — §4.1 verifies the free path and §4.2 verifies exactly where the paid/keyed one starts
Blocked by	none
Risk	Five equation-drawn illustrations are five chances to ship something that looks like a maths homework screenshot rather than a considered drawing. The mechanism is cheap and verifiable; the taste is not, and nothing in `just quality` can tell the difference. If the first motif does not survive a look at 1280 px, the honest outcome is to ship one motif, not five
Cost so far	—

1. Summary¶

marola's visual vocabulary becomes equation-drawn: a small set of illustrative motifs, a trochoidal swell, a right-whale silhouette, a jellyfish, a two-constituent tide curve, a rip-current streamline pair, designed by tuning real equations in Desmos's free graphing calculator, then brought home as the equations, not as the picture, and rendered by a small in-repo script into the same inline SVG <symbol> sprite MIP-0046 introduces. Nothing from Desmos is fetched at runtime and no Desmos-exported file is committed; the shipped asset is marola's own rendering of marola's own formulae, MIT like the rest of the repo. §11 proposes one paragraph in PHILOSOPHY.md, with a real call on what that paragraph may and may not claim.

2. Motivation¶

The site has exactly one piece of artwork: the two-stroke wave in index.html's <h1> and the filled WAVE_PATH marker it echoes (app.js:172). Everything else a visitor sees is data, chrome, or (until MIP-0046 lands) a system emoji. There is no illustration, and there is no rule about what an illustration here may be: a grep of AGENTS.md, PHILOSOPHY.md, docs/*.md and the site-frontend skill for AI-generated|generated image|stock photo|illustration returns exactly one hit, and it is the skill's own trigger phrase, not a policy (checked 2026-09-07).

So the first illustration this repo commits also decides the category. Three options were actually open: a stock/AI-generated image, a hand-drawn vector, or a drawing that is a formula. The repo already has a strong opinion about the analogous question for text: "no unsourced text reaches a user", the mip skill's shortest rule, and no opinion at all about pictures. An equation-drawn motif is the only one of the three whose review surface is a diff: h_w = 0.42 changing to 0.31 is a reviewable line, and a re-run of the generator reproduces the artwork byte-for-byte. That is the infra argument, and it is the one that holds; §8 says plainly which stronger argument does not.

The aesthetic argument is separate and also real: marola is about the sea, and the shapes the sea actually makes are the ones its physics writes down. A trochoid is not a decorative wave: it is the wave (§5.1.1). Drawing the site's furniture from the same families the pipeline reasons about is the visual version of what scoring/ already is.

3. User-visible change¶

No text, no number, no colour, no threshold changes. What changes is that the page has drawings.

Today, site/static/index.html, the whole of the site's artwork:

<h1><svg …><path d="M2 9c2.5 0 2.5-2.5 5-2.5S9.5 9 12 9…"/>…</svg>marola</h1>

After (the sprite MIP-0046 §5.1 introduces, extended, ids namespaced art- so the two sets never collide with its 14 px functional marks):

<svg class="sprite" aria-hidden="true">
  <!-- MIP-0046's functional marks: i-wind-0 … i-lifeguard -->
  <!-- equation-art:start  generated by scripts/equation_art.py — edit site/equations.json -->
  <symbol id="art-swell"  viewBox="0 0 240 60">…</symbol>
  <symbol id="art-whale"  viewBox="0 0 120 80">…</symbol>
  <symbol id="art-jelly"  viewBox="0 0 80 120">…</symbol>
  <symbol id="art-tide"   viewBox="0 0 240 60">…</symbol>
  <symbol id="art-rip"    viewBox="0 0 120 120">…</symbol>
  <!-- equation-art:end -->
</svg>

Placements in v1 (two, deliberately few, §5.6): the swell as a full-width rule under the header, replacing nothing; the whale, jellyfish or rip as the illustration of the empty/loading state the map shows before a board arrives, where there is currently blank panel. Everything else waits for MIP-0044's sections to exist.

4. Data sources and dependencies reviewed¶

4.1 Desmos's free graphing calculator, as an authoring tool — the pick¶

https://www.desmos.com/calculator is free and needs no account to graph (an account is needed only to save a graph; not verified independently, see "Not checked"). Its Export Image dialog offers both PNG and SVG: the live app bundle (/assets/build/shared_calculator_desktop-bc7c26f4….js, fetched 2026-09-07, 5.2 MB) contains the localization strings account-shell-button-download-png = Download PNG, account-shell-button-download-svg = Download SVG, account-shell-heading-file-format = File Format. So a keyless, free SVG export genuinely exists.

It is still not what gets committed, and the reason is licensing, not convenience. Desmos's Terms of Service (fetched 2026-09-07, the page is a JS shell, so the text was read out of /assets/build/frontpage/terms-967a1656….js) says two things that matter, and they point in opposite directions:

§6 User Submissions and General Materials: "Desmos does not claim ownership of any materials … lessons, formulae, information, data, text or other materials you submit and create … As between Desmos and you, you own all rights to your User Submissions and Generated Materials."
§5 Personal, Non-Commercial Use Only for Desmos Tools: "you are authorized to distribute that Content generated using the Desmos Tools from your User Submissions and Generated Content under a Creative Commons 'Attribution-ShareAlike' License (CC-BY-SA-4.0), with attribution to include reference to 'Desmos', 'Desmos Studio PBC' or the Desmos logo."

Read together: the equations come home under the author's own copyright; the exported picture comes home under CC-BY-SA-4.0 with a Desmos attribution. This repo is MIT (LICENSE, "MIT License, Copyright (c) 2026 Matheus Hoffmann"). Committing a Desmos-exported SVG would put a share-alike, attribution-bearing asset inside an MIT tree, a real obligation, not a formality, and one that would have to be tracked in a NOTICE for the life of the file. Re-rendering the author's own equations in-repo avoids it entirely and costs one small script (§5.4). §5 of the same terms also restricts the Desmos Tools to "personal, non-commercial use"; marola is a free personal project with no paid tier, so authoring there is inside that limit today, worth re-reading if that ever changes.

4.2 The Desmos JS API (`calculator.js`) and `asyncScreenshot` — reviewed, rejected (§9.1)¶

It needs a key. The docs (https://www.desmos.com/api/v1.11/docs/index.html, fetched 2026-09-07) give the load URL as https://www.desmos.com/api/v1.11/calculator.js?apiKey=[YOUR_API_KEY_HERE], "To obtain your own API key, visit desmos.com/my-api". Fetching that script without a key returns HTTP 403 (checked 2026-09-07, 52 bytes of body).
asyncScreenshot really can emit SVG. Same docs, verbatim: "callback will be called with the either a URI string or SVG string as its argument … the ability to output SVG in addition to PNG images. … opts.format String that determines the format of the generated image. May be either 'png' or 'svg'. Defaults to 'png'." It operates on a live calculator instance in a page, so any programmatic use means a headless browser, a dependency this repo does not have and this MIP does not add.
The API's own terms are stricter than the calculator's. https://www.desmos.com/api-terms (same JS-shell trick, fetched 2026-09-07): a free "Trial Tier" whose limit is "solely for (a) personal, non-commercial use or (b) a 90 day trial for internal testing", a paid "Commercial Tier" otherwise, and §5.b forbidding "(ii) use, reproduce, distribute or publicly display any Content other than through the Applications; (iii) remove, alter, or obscure any branding (including copyright and trademark notices) of Desmos Studio".

4.3 Existing public Desmos sea graphs, as prior art — cited, not copied¶

Four were verified by fetching each graph's thumbnail (/calc_thumbs/production/<id>.png) and looking at it, and by fetching its saved state (https://saved-work.desmos.com/calc-states/production/<id>, an undocumented endpoint found by request, not from Desmos's docs) and reading the actual LaTeX:

Graph	What it actually renders	Why it matters here
Troichoidal Ocean Waves	A trochoid construction: rolling circle, generating point, the traced curve	Its state contains `p_x(t)=\frac{L_w}{2\pi}t-h_w\sin t`, `p_y(t)=h_w\cos t` with wavelength `L_w` and height `h_w` as sliders — the exact family §5.1.1 uses, and proof it reads as a sea surface
The Ocean	A full scene: layered wave bands, a boat, and a jellyfish — all equations, with an animation parameter `v`	The best evidence that a scene, not just a curve, is achievable this way
Whale	A whale under a wavy sea line, a sun, an octopus	Its state is ~40 domain-restricted conics and sinusoids (`9=(x+2)^2+(y+7)^2\{-9.2<y<1\}\{-5.1\le x\le0\}`) — an honest look at how much fiddling a recognisable animal costs
Jellyfish	A bell with oscillating tentacles streaming from it	Its tentacles are phase-shifted restricted sinusoids (`\frac{\sin(3x)}{2}\{-2<x<8.5\}`, `\\|\sin(x+1)\\|+1`), not polar roses — which is why §5.1.3 proposes damped sinusoids

Two candidates from the same searches were checked and failed: Jellyfish Graph (2yttmwvhzv) renders only a short line of red dots, and Trig project- whale (omhbfyzodp) renders an empty grid. Both are named plausibly and neither draws anything; they are recorded here because the failure mode of this section is citing a title.

Licensing of the above: the finding that decides §9.3. Desmos's ToS §6 assigns ownership of a user's submissions to that user. The CC-BY-SA carve-out in §5 authorizes you to distribute Content generated from your submissions; nothing in the terms grants one user a licence to another user's graph, and "public" on Desmos means visible, not licensed. So these five graphs are cited as prior art and inspection material only. The one thing taken from them is a fact about mathematics, the trochoid parametrization, published by Gerstner in 1802 and in every coastal- engineering text, which is not anyone's expression to license.

4.4 The renderer: Python 3 stdlib, already in the shell¶

flake.nix provides python3; just quality-other already runs ruff check ., ruff format --check . and a --self-test on each of six scripts/*.py (justfile:75-90, read 2026-09-07). A sixth-of-a-page sampler that turns x(t), y(t) into an SVG path needs math and json and nothing else. No new dependency, no flake.nix change.

5. Design¶

5.1 The five motifs, and the actual mathematics behind each¶

Each is a real family a human can build in Desmos in an evening: parameters below are starting points to tune, not results.

5.1.1 art-swell: a trochoidal wave train. Parametric, one curve: x(t) = (L/2π)·t − h·sin t, y(t) = h·cos t, t ∈ [0, 2πn] for n crests. This is the trochoid (Gerstner) surface: sharp crests, broad flat troughs, visibly not a sine, which is the whole point, because a sine is what a generic wave graphic is. Two or three trains superposed at different (L, h) and offset vertically give the layered-swell band; the sea is a spectrum, not one wave, so the superposition is the honest drawing. Verified prior art: rqvqvf6uy8 (§4.3). Deep water relates L to period by L = gT²/2π, and the board already carries sea.period_s and wave_m per beach, see §11 for why v1 does not make the drawing data-driven.

5.1.2 art-whale: a southern right whale silhouette (the species knowledge/whales-santa- catarina.md is about). Body: a superellipse |x/a|^n + |y/b|^n = 1 with n ≈ 2.6, blunter than an ellipse, which is exactly the right whale's shape, and the one parameter that separates it from a dolphin. Fluke: two lobes of the rose r(θ) = c·sin 2θ rotated onto the tail root. Head callosity: a small circle differenced out of the outline near x = −a. Drawn as one closed parametric outline so it fills as a silhouette. Honest: the fluke-as-rose-lobe is a design bet, and gaeav8oi2q (§4.3) is evidence that whales cost more expressions than one expects.

5.1.3 art-jelly: a jellyfish. Bell: the upper half of a lobe-modulated circle, r(θ) = a(1 − ε·cos 4θ), θ ∈ [0, π], ε ≈ 0.12, a dome with four soft scallops, not a rose; a true rose (r = a sin kθ) makes a flower, which is the mistake this note exists to avoid. Tentacles: k damped, phase-shifted sinusoids hanging from the rim, y_j(s) = −s, x_j(s) = x_j0 + A·e^(−λs)·sin(ω s + jφ), s ∈ [0, S], with A and S varying per strand so they do not read as a comb. Evidence: a83ylfdj0s uses restricted phase-shifted sinusoids for exactly this and it works.

5.1.4 art-tide: a real tide curve, not a sine. h(t) = A_M2·cos(2πt/T_M2 + φ₁) + A_S2·cos(2πt/T_S2 + φ₂) over t ∈ [0, 30] h, with T_M2 ≈ 12.42 h (principal lunar semidiurnal) and T_S2 = 12.00 h (principal solar semidiurnal). NOAA's own page (fetched 2026-09-07) states M2 "has 2 peaks every 24-hours and 50 minutes" and S2 "2 peaks every 24-hours", which is where those two periods come from. With A_M2 ≈ 2·A_S2 the sum gives the unequal successive highs a real tide has and a single sinusoid cannot: the drawing is the same harmonic model tide prediction uses, at two terms.

5.1.5 art-rip: a rip current, as streamlines. Level curves of a stream function for uniform onshore flow plus a sink at the rip neck: ψ(x, y) = U·y − (m/2π)·arctan(y/x); plot two or three level sets ψ = c_k. They converge into a narrow seaward jet and spread into the head: the shape knowledge/safety/rip-currents.md describes in words. This is the one motif that could later carry meaning rather than mood, and the one to draw most carefully, because a decorative safety diagram that misleads is worse than none (§8).

5.2 What comes back from Desmos¶

Only numbers and formulae, in one checked-in file, site/equations.json:

{ "art-swell": { "viewBox": [240, 60], "curves": [
    { "kind": "parametric", "x": "(L/(2*pi))*t - h*sin(t)", "y": "h*cos(t)",
      "t": [0, 12.566], "samples": 240, "params": { "L": 60, "h": 9 },
      "stroke": 2, "fill": null } ] } }

The expression strings are evaluated by the generator against a whitelisted math-only namespace: no eval of arbitrary Python, which is the one security note this file carries (a site/ data file is not attacker-controlled here, but a generator that evals is a bad habit to install).

5.3 What is not supported, stated before anyone assumes it¶

The generator handles explicit parametric curves x(t), y(t) and closed outlines built from them. It does not handle Desmos's implicit/inequality forms (4 ≥ (x−4)² + (y−2)², −y² + 2x ≥ −8 {x < −2}), which is how much of the prior art in §4.3 is actually written, nor Desmos's automatic domain restrictions. There is no lossless equation-to-SVG-path pipeline: any claim of one would be wrong. A drawing sketched with inequalities in Desmos has to be re-expressed parametrically by its author before it can come home. That is real authoring friction and it is the reason §5.1 chose five motifs that are naturally parametric.

5.4 The generator: `scripts/equation_art.py`¶

Stdlib only, ~200 lines, three jobs: sample each curve at samples points; emit a <path d="M…L…"> (or Q smoothing) fitted into the viewBox with a stated margin; splice the resulting <symbol> block into site/static/index.html between  and . That splice-between-markers pattern is not new here: just mip-graph already regenerates a block inside docs/MIPs/README.md between markers, and quality-other fails when it is stale (AGENTS.md, scripts/mip_graph.py). This follows it exactly:

just equation-art regenerates the block.
python3 scripts/equation_art.py --check fails if the committed block does not match what site/equations.json produces, added to quality-other beside the other six self-tests.
python3 scripts/equation_art.py --self-test covers the sampler (a circle's path closes, a known trochoid's crest lands where the closed form says), the --self-test convention quality-other already enforces on every other scripts/*.py.

No CI change and no build step. The generated markup is committed inside index.html, which is already on site.yml's publish allowlist (site.yml:162-170: index.html app.js style.css chat.js chatbot-config.js CNAME plus vendor/ data/ smoke/ coverage/, exit 1 on anything else). Nothing new lands in site/dist, so the allowlist is untouched: the same reason MIP-0046 §4.1 picked an inline sprite over a separate icons.svg. The generator runs on a human's machine, like just mip-graph, and --check is what keeps it honest.

5.5 What this does not touch¶

WAVE_PATH (app.js:172) and the legend key it is asserted equal to (site_check.js:213-216) stay exactly as they are. MIP-0009 tuned that shape for legibility at 24 px over map tiles across eighty overlapping markers, and MIP-0046 §5.2 already deliberately leaves the markers on inline paths. A sampled trochoid is a worse 24 px marker than a hand-tuned filled path, and pretending otherwise would trade a working glyph for a principle. MIP-0046's twelve 14 px functional marks are likewise out of scope: at that size a hand-drawn stroke beats a sampled curve, and this MIP is about illustration, not pictograms. The two sets share one sprite block and one CSS class family, and nothing else.

5.6 Placement, v1¶

Two placements only, both on the existing page: the swell band under the header, and one motif in the map's empty/loading state. MIP-0044's /about/, /news/ and /dev/ sections are the natural home for the rest, a section header per motif, and that is where the remaining three go once it lands. Shipping five illustrations onto a one-page map would be exactly the "decorated" look MIP-0046 is removing.

6. Scoring / safety impact¶

None. No board field, no threshold, no note text, no Swimability call, no LLM. One caveat that is about safety even though the code is not: art-rip (§5.1.5) draws a hazard. It must never sit next to a beach's own numbers where it could read as "the rip is here": it is a motif for a knowledge or about section, never a map overlay. Stated here so a later PR cannot quietly promote it.

7. Verification plan¶

python3 scripts/equation_art.py --self-test and --check, both wired into quality-other.
node --check site/static/app.js; node scripts/site_check.js green, plus one new assertion: every art-* id referenced by a <use> resolves to a <symbol id> present in index.html (the generalized form of the assertion MIP-0046 §7 adds for i-*).
ruff check . / ruff format --check . on the new script.
just site-build floripa && just site-serve, then screenshots at 390 px and 1280 px: the site-frontend step-6 rule and the only check that can see whether a motif is any good.
Reproducibility check, which is the whole claim: just equation-art twice from a clean tree produces a byte-identical index.html.
Done = the harness green, --check clean, two screenshots in the PR, and no Desmos-exported file anywhere in the tree (git ls-files | grep -i desmos empty).

8. Risks, limitations, and honest caveats¶

Taste is not a gate. Everything in §7 verifies that the drawing is reproducible, not that it is good. Five motifs is an ambitious v1; the fallback is to ship art-swell alone and let the rest wait for a second look.
Nothing here is rendered yet. Every claim about how these look is written, not run. The mechanism is verified against MDN via MIP-0046 §4.1 and against this repo's own workflow file; no curve has been sampled and no browser opened.
The philosophy claim has a ceiling, and here it is. It is true that an equation-drawn asset is deterministic and reproducible, and true that its source is inspectable in a way a raster is not. It is not true that this makes it "sourced, never invented" in the sense PHILOSOPHY.md and the mip skill use those words. That rule is about facts shown to a user, a wave height, a water-quality verdict, a line of lore, and an illustration asserts no fact. Stretching Pillar 2 ("the deterministic parts kept deterministic", which is about the scoring path) to cover a decorative whale would be the kind of inflation PHILOSOPHY.md's own "What this is not" section exists to prevent. §11's proposed paragraph therefore claims the narrow thing: the source of a picture can be a formula, and then review is a diff, and not the wide one.
Authoring is manual and unattributed. Desmos is a sketchpad, so the record of how a curve was tuned is the parameters in site/equations.json and nothing else; there is no saved graph the repo can point at unless the author chooses to publish one (and publishing it makes it a User Submission under §4.1's terms, which is fine, but it is a choice, not a requirement).
art-rip can mislead, §6.
Sampling artefacts. 240 points on a trochoid is smooth at 240 px and visibly polygonal at 1200 px. The samples figure is per-motif and per-placement, and the swell band is the one most likely to be scaled up by MIP-0044.
One file, two generators. After MIP-0046, index.html holds a hand-written sprite block; after this, a generated one too, inside the same <svg class="sprite">. Whoever edits by hand inside the equation-art markers will have it silently overwritten: the --check gate catches it in quality-other, before push, which is why it is a gate rather than a comment.

9. Alternatives considered¶

9.1 Embed the live Desmos calculator (calculator.js) in the page: rejected, firmly. It is a third-party runtime script on a page whose CSP is default-src 'self' with no script-src opening and whose own source comment says "script-src/object-src stay locked to same-origin: this page loads no third-party script" (index.html:13-14, read 2026-09-07). It would need an API key in the page (§4.2: 403 without one), it would put a personal-non-commercial Trial Tier term on a public site, it forbids obscuring Desmos branding, and it would make every visitor download a calculator engine to look at a picture, against a vendored Leaflet of 147,552 bytes for the entire map. MIP-0044 §4 found the generated scaladoc pages already breaking the "no third-party script" claim and treats that as a bug to fix; adding a second violation on purpose, in the same session, would be incoherent.

9.2 Vendor Desmos's own SVG export (asyncScreenshot, or the UI's Download SVG): rejected. It works and it is free (§4.1, §4.2), but distributing that output is licensed to the author under CC-BY-SA-4.0 with a Desmos attribution, inside an MIT repo. A share-alike asset with a permanent NOTICE obligation, to avoid writing 200 lines of Python, is a bad trade. The programmatic path additionally needs a headless browser and an API key.

9.3 Adapt the equations from an existing public graph (e.g. gaeav8oi2q's whale): rejected. Desmos's ToS §6 gives ownership of a submission to the user who made it, and grants no user-to-user licence; public means visible, not reusable. The graphs in §4.3 are cited as prior art and as evidence that the technique works. The trochoid parametrization is taken as mathematics, not as anyone's artwork.

9.4 Hand-draw the motifs in a vector editor: the real alternative, rejected on review surface. It is faster and probably prettier. It gives up the property this MIP is actually for: a change is a number in a diff, and the artwork is reproducible from the repo. Note this is not a rejection of hand-drawing in general: MIP-0046's twelve 14 px marks stay hand-drawn, and §5.5 says why.

9.5 An AI-generated illustration: rejected. It is the fastest option and it is the one thing this repo's entire culture argues against for text: an artefact nobody can check, whose provenance is a prompt, which cannot be reproduced or reviewed. The site-frontend skill exists because a page "looks AI-generated" is already treated here as a defect.

9.6 Do nothing: a serious option. The page is disciplined and MIP-0046 makes it more so; a site with no illustrations is not broken. Rejected because the request is explicit, and because §5.6's v1 is two placements, which is close enough to "nearly nothing" that the do-nothing case is mostly answered by scope.

11. Open questions¶

Should the swell be data-driven? The board carries sea.period_s and wave_m per beach, and deep water gives L = gT²/2π, so the header band could be drawn from today's actual swell. That is a genuinely good idea and a different MIP: it turns an illustration into a data display, which brings the honesty rules with it (what is drawn when there is no data?). v1 is static. Proposal: static now, revisit after MIP-0042's live-map work has an opinion.
Five motifs or one? §8's fallback. A human should look at the first one before the other four are drawn.
Where does art-rip live: a knowledge/safety page (MIP-0044 §5.5) or nowhere in v1? Proposal: nowhere in v1, per §6.
PHILOSOPHY.md: the call, made. Yes, this earns a paragraph, and no, it does not go in this change. The connection that is real is the one PHILOSOPHY.md already makes about everything else, the gate is there by construction, not by discipline, applied to pictures: an equation-drawn asset carries its own source, so reviewing it is reading a diff and reproducing it is running a script, whereas a raster (drawn, photographed or generated) can only be looked at and believed. The connection that is not real is the Pillar 2 / "sourced, never invented" one, for the reason in §8. Proposed wording, for a separate PR after this MIP is accepted, as a short section after "Why a justfile":

Why the pictures are equations. The site's drawings are generated from formulae checked into the repo, not from a raster someone drew or a model produced. It is the same move as everywhere else here: put the artefact somewhere it can be checked. A wave whose source is x(t) = (L/2π)t − h sin t is reviewed by reading a diff and reproduced by running a script; an image file is reviewed by looking at it and taking someone's word for where it came from. This claims nothing about the facts marola shows — a drawing asserts none — only about where the artwork's source lives.

It is the author's voice and the author's file, so it needs his go-ahead; a separate PR keeps that decision separable from the mechanism, exactly as the mip skill's step 8 keeps design separable from implementation. 5. Reciprocal cross-references. This MIP's "see also" line landed in MIP-0009 on this branch. MIP-0046 is still unmerged on docs/mip-0046-remove-ai-slop-ui, so its pointer back to this MIP has to be added on that branch (or after it merges), noted rather than done, to avoid editing another draft's branch.

Appendix¶

Checked live (all 2026-09-07)¶

https://www.desmos.com/calculator/rqvqvf6uy8 → HTTP 200, <title> "Troichoidal Ocean Waves | Desmos"; body is a JS shell. State via https://saved-work.desmos.com/calc-states/production/rqvqvf6uy8 → 200, JSON containing p_x(t)=\frac{L_w}{2\pi}t-h_w\sin t, p_y(t)=h_w\cos t, plus the rolling-circle construction. Thumbnail https://www.desmos.com/calc_thumbs/production/rqvqvf6uy8.png → 200, 20,680 bytes, viewed: a circle with a generating point and a traced curve. Basis for §4.3, §5.1.1.
https://www.desmos.com/calculator/koa2npwoir ("The Ocean") → thumbnail 200, 20,206 bytes, viewed: layered blue wave bands, a boat with a flag, a jellyfish, a green seabed. State 200, expressions include 4\ge(x-4)^2+(y-2+v)^2\{y\le2-v\} and an animation parameter v=-0.025.
https://www.desmos.com/calculator/gaeav8oi2q ("Whale") → thumbnail 200, 12,399 bytes, viewed: a whale silhouette below a y=\sin(.5x) sea line, a sun, an octopus. State 200, ~40 domain-restricted conics/sinusoids.
https://www.desmos.com/calculator/a83ylfdj0s ("Jellyfish") → thumbnail 200, 18,928 bytes, viewed: a filled bell at left with oscillating strands to the right. State 200, tentacles are \frac{\sin(3x)}{2}\{-2<x<8.5\}, \cos(3x)\{-2<x<8.75\}, \|\sin(x+1)\|+1, etc. Basis for §5.1.3's "damped sinusoids, not polar roses".
https://www.desmos.com/calculator/fhfmlynqtn ("ocean-waves") → 200; thumbnail viewed: a low-amplitude periodic ripple on the axis, y=\exp(\sin(x))-family. Real but trivial; not cited as prior art in §4.3 because it draws a curve, not a scene.
https://www.desmos.com/calculator/2yttmwvhzv ("Jellyfish Graph") → thumbnail 200, 3,731 bytes, viewed: a short line of red dots, no jellyfish. Negative result, recorded in §4.3.
https://www.desmos.com/calculator/omhbfyzodp ("Trig project- whale") → thumbnail 200, 12,035 bytes, viewed: an empty grid. Negative result.
https://www.desmos.com/api/v1.11/docs/index.html → 200, 130,163 bytes. Quotes in §4.2 (the ?apiKey= load URL, asyncScreenshot's SVG output and opts.format) are verbatim from it.
https://www.desmos.com/api/v1.11/calculator.js (no key) → HTTP 403, 52-byte body.
https://www.desmos.com/terms → 200 but a JS shell; the terms text lives in /assets/build/frontpage/terms-967a1656797971392b61a5acb62049b98e6ca524.js (200, 760,940 bytes), from which §4.1's §5 and §6 quotes are taken verbatim.
https://www.desmos.com/api-terms → 200, JS shell; text from /assets/build/frontpage/api-terms-325f708586a27e144921977549c8a0b30512f7b6.js (200, 754,732 bytes). Trial-Tier and §5.b quotes in §4.2 are verbatim.
https://www.desmos.com/assets/build/shared_calculator_desktop-bc7c26f4a69c5a57ad227a86cf55617a542da234.js → 200, 5,210,660 bytes; contains account-shell-button-download-png = Download PNG, account-shell-button-download-svg = Download SVG, account-shell-heading-file-format = File Format. Basis for §4.1's "the free UI exports SVG".
https://tidesandcurrents.noaa.gov/about_harmonic_constituents.html → 200; M2 "the largest lunar constituent", "2 peaks every 24-hours and 50 minutes"; S2 "the largest solar constituent", "2 peaks every 24-hours". Basis for §5.1.4's 12.42 h / 12.00 h.
https://help.desmos.com/hc/en-us/articles/4405901719309 (Export Image help article) → HTTP 403, Cloudflare interstitial ("Enable JavaScript and cookies to continue"). Not readable; the export-format claim in §4.1 rests on the app bundle instead.
https://tidesandcurrents.noaa.gov/harmonic_constituents_defs.html → HTTP 404.

Checked in this repo (2026-09-07, `origin/main` at `07882ae`)¶

LICENSE → "MIT License / Copyright (c) 2026 Matheus Hoffmann". Basis for §4.1's licence clash.
site/static/index.html:13-14 → the CSP comment "this page loads no third-party script" and default-src 'self'; img-src 'self' https:; connect-src 'self' https:; object-src 'none'. index.html:21 → the <h1> two-path wave. index.html:38 → the legend wave key.
site/static/app.js:172 → WAVE_PATH = 'M3 10c2.6-7 6.4-7 9 0s6.4 5 9 0v10H3z'; §5.5 leaves it.
.github/workflows/site.yml:162-170 → the publish allowlist and its exit 1. Nothing in §5.4 adds a file to site/dist.
justfile:75-90 → quality-other runs ruff check ., ruff format --check . and six python3 scripts/*.py --self-test invocations. Basis for §4.4 and §5.4.
site/static/vendor/leaflet.js → 147,552 bytes. The comparison in §9.1.
grep -rn 'AI-generated|generated image|stock photo|illustration' AGENTS.md PHILOSOPHY.md docs/*.md .claude/skills/site-frontend/SKILL.md → one hit, the skill's own description: line. Basis for §2's "no policy about pictures exists".
knowledge/ → whales-santa-catarina.md, jellyfish-and-man-o-war.md, waves-tides-glossary.md, safety/rip-currents.md. The domain §5.1's motifs draw from.
MIP-0046 read from the unmerged branch origin/docs/mip-0046-remove-ai-slop-ui (commit 2d4114f); MIP-0044 from origin/docs/mip-0044-site-sections (commit 40e9e8a).

Not checked¶

No browser was opened and no curve was sampled. Every visual claim in §3 and §5.1 is written, not run: including whether a 240-point trochoid path looks smooth, and whether a superellipse with n = 2.6 reads as a right whale rather than a blob.
Whether Desmos's own SVG export is true vector paths or an embedded raster: not verified, no file was produced. §9.2 rejects that path on licence, which does not depend on the answer.
Whether graphing on desmos.com without an account is possible (as opposed to saving): assumed from the calculator page loading anonymously, not confirmed against a Desmos statement: the help centre is behind Cloudflare (above).
saved-work.desmos.com/calc-states/production/<id> is undocumented; it returned the states quoted above today, and may change or disappear without notice. Nothing in §5 depends on it.
The five graphs' authors were not contacted, and their expressions are not used (§9.3).
MIP-0046's and MIP-0044's statuses are read from unmerged branches; if either draft changes before merging, this MIP's Depends-on and §5.4 marker placement may need revisiting.