# Architecture ## Microsim ### Live player <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/HvwKHDtIy" width="100%" height="620" frameborder="0" sandbox="allow-scripts allow-same-origin"></iframe> </div> <div class="microsim-fallback"> <img src="Microsims/thumbs/Architecture.png" alt="Architecture microsim poster" style="width:100%;border:1px solid #4445;border-radius:6px;"> <p><em>Live microsim (desktop) · <a href="https://editor.p5js.org/sciencenibber/sketches/HvwKHDtIy">open sketch in the p5.js editor</a></em></p> </div> **Editor URL:** https://editor.p5js.org/sciencenibber/sketches/HvwKHDtIy **Description (100 words):** This microsim turns the central problem of architecture — making loads stand up — into one picture: the arch. Over a single opening it draws three curves at the same span and crown height: an inverted catenary (blue), a parabola (orange), and a semicircle (red). The catenary is the shape a hanging chain takes under its own weight; flip it and you get the one arch that carries its weight in pure compression, with no bending — the masonry ideal Gaudi and Wren both pursued. Slide the curvature `a` and the span `S` to watch the three forms diverge. Equation: y = a*cosh(x/a). ```js // ===================================================================== // Article : Architecture // Slug : Architecture // Wikitube : en.wikitube.io/wiki/Architecture // Room : Electronics // // Idea : Architecture is, at its structural core, the art of making // loads stand up. The single most important curve in that art // is the ARCH. This microsim draws three arches spanning the // same opening at the same height — an inverted CATENARY, a // PARABOLA, and a SEMICIRCLE — so the reader can see how the // "ideal" arch (the inverted hanging chain) differs from the // two shapes builders have reached for over the centuries. // A hanging chain settles into the one curve that carries its // own weight in pure tension; flip it over and you get the one // arch that carries its weight in pure compression — no // bending, the masonry ideal Gaudi and Wren both chased. // // Equation : y = a·cosh(x/a) (the catenary) // rise = a·cosh(S/2a) − a (arch height for span S) // ASCII form in the footer: "y = a*cosh(x/a)". // ===================================================================== // Rule §3 — single source of truth. HUD URL line + save name derive here. const ARTICLE = "Architecture"; // Rule §4 — disable the Friendly Error System for ship. p5.disableFriendlyErrors = true; // ---------- runtime state ---------- let aSlider; // catenary parameter a (curvature of the chain) let sSlider; // span S of the opening, in pixels // layout constants (computed in setup from width/height) let baseY; // springline / ground line (y where arches spring) let cx; // horizontal centre of the opening // accent palette (rule §8 — at most three accents) const C_CAT = [40, 90, 200]; // catenary — blue (the ideal) const C_PAR = [220, 130, 40]; // parabola — orange const C_CIRC = [200, 60, 60]; // semicircle — red function setup() { // Rule §5 — canvas inside setup, standard size, 2x density. createCanvas(720, 520); pixelDensity(2); // Layout from width/height so the sketch survives a resize. cx = width / 2; baseY = height - 110; // leave a band at the bottom for controls // Rule §6 — controls in setup, positioned explicitly, labelled in draw. // a in [30, 400]: small a = a deeply sagging chain (pointed arch), // large a = a nearly straight chain (very flat arch). 140 is a pleasant // round-arch default for the default span. aSlider = createSlider(30, 400, 140, 1); aSlider.position(150, height - 56); aSlider.style("width", "200px"); // S in [160, 560]: the clear span of the opening, in pixels. sSlider = createSlider(160, 560, 380, 5); sSlider.position(150, height - 30); sSlider.style("width", "200px"); } function draw() { background(248); // ---------- read controls ---------- const a = aSlider.value(); const S = sSlider.value(); const half = S / 2; // ---------- math (rule §10) ---------- // Catenary arch height: peak rise at centre for this a and span S. const yEdge = a * Math.cosh(half / a); // chain height at the ends const rise = yEdge - a; // arch rise = ends - centre dip // All three curves are normalised to the SAME rise and span so the // reader compares SHAPE, not size. riseSpan is the classic rise/span // ratio ("ratio" alone is a reserved p5 name, so we qualify it). const riseSpan = rise / S; // ---------- reference geometry (rule §8 layer 1) ---------- // Ground / springline and the two spring points, in neutral grey. stroke(170); strokeWeight(1); line(40, baseY, width - 40, baseY); // ground line noStroke(); fill(120); circle(cx - half, baseY, 7); // left spring point circle(cx + half, baseY, 7); // right spring point // Crown reference (peak height) as a faint dashed marker. stroke(210); strokeWeight(1); line(cx, baseY, cx, baseY - rise); // rise indicator // ---------- active geometry (rule §8 layer 2) ---------- // Each arch is sampled across the span and drawn as a polyline. drawArch(catenaryHeight, a, half, rise, S, C_CAT); drawArch(parabolaHeight, a, half, rise, S, C_PAR); drawArch(semicircleHeight,a, half, rise, S, C_CIRC); // ---------- HUD watermark (rule §2) ---------- noStroke(); textFont("system-ui"); // §2a — top-left title block. fill(20); textSize(20); textAlign(LEFT, TOP); text("Architecture", 16, 14); textSize(12); fill(110); text("Wikitube microsim - en.wikitube.io/wiki/" + ARTICLE, 16, 40); // §2b — top-right control hints. textAlign(RIGHT, TOP); textSize(11); fill(110); text("sliders: a (catenary curvature), S (span)", width - 16, 14); text("blue=catenary (ideal) orange=parabola red=semicircle", width - 16, 30); // §2c — bottom-left live readouts (canonical parameter symbols). textAlign(LEFT, BOTTOM); textSize(13); fill(C_CAT[0], C_CAT[1], C_CAT[2]); text("a = " + a, 16, height - 64); fill(20); text("S = " + S + " px", 110, height - 64); text("rise = " + rise.toFixed(0) + " px", 250, height - 64); text("rise/span = " + riseSpan.toFixed(3), 420, height - 64); // Slider labels (rule §7) — to the LEFT of each slider, right-aligned. textAlign(RIGHT, CENTER); textSize(12); fill(60); text("a (curvature)", 142, height - 56 + 8); text("S (span)", 142, height - 30 + 8); // §2d — bottom-right equation footer (ASCII only — see pitfalls.md). textAlign(RIGHT, BOTTOM); textSize(11); fill(80); text("y = a*cosh(x/a) -> inverted catenary = pure-compression arch", width - 16, height - 8); } // ---------- arch height helpers (rule §10) ---------- // Each returns the *un-normalised* height of the curve at horizontal // offset x (measured from the crown) for the given parameters. drawArch // normalises every curve to the common `rise` so shapes are comparable. // Inverted catenary: the hanging-chain curve, flipped. Its own peak is // already `rise`, so it needs no rescaling — it is the literal arch. function catenaryHeight(x, a, half, rise) { const yEdge = a * Math.cosh(half / a); return yEdge - a * Math.cosh(x / a); } // Parabola through the same two spring points; peak at the crown. // Native peak is `rise`, scaled to the common rise (identity here, but // kept explicit so the helper is self-contained). function parabolaHeight(x, a, half, rise) { const t = x / half; // -1 .. 1 across the span return rise * (1 - t * t); } // Semicircle on the same span; native peak is `half`, rescaled to `rise` // so it shares the crown height and only its SHAPE differs. function semicircleHeight(x, a, half, rise) { const native = Math.sqrt(Math.max(0, half * half - x * x)); return native * (rise / half); } // Sample a height-function across the span and stroke it as a polyline. function drawArch(fn, a, half, rise, S, col) { noFill(); stroke(col[0], col[1], col[2]); strokeWeight(2); beginShape(); const STEPS = 160; for (let i = 0; i <= STEPS; i++) { const x = -half + (S * i) / STEPS; // -half .. +half const h = fn(x, a, half, rise); vertex(cx + x, baseY - h); } endShape(); } ``` ## Links (Wikipedia order) <!-- injected from _registry/childlinks/Architecture.json (2026-07-30T02:09:12Z) --> `.design` · `A_Room_of_One's_Own` · `Abhinavagupta` · `Active_design` · `Activity-centered_design` · `Adaptive_reuse` · `Adaptive_web_design` · `Advertising` · `Aesthetic_Realism` · `Aesthetic_emotions` · `Aesthetic_interpretation` · `Aestheticism` · `Aestheticization_of_politics` · `Aesthetics` · `Aesthetics_of_music` · `Aesthetics_of_nature` · `Aesthetics_of_science` · `Affective_design` · `African_aesthetic` · `Afromodernism` · `Against_Interpretation` · `Agile_software_development` · `Alexander_Gottlieb_Baumgarten` · `Alfeld` · `Algorithms-Aided_Design` · `American_Institute_of_Graphic_Arts` · `Ananda_Coomaraswamy` · `Ancient_Egypt` · `Ancient_Greece` · `Ancient_Greek_architecture` · 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`Çatalhöyük` · `Émile_Zola` ## From the Real GENERATIVE library ![Architecture](https://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/View_of_Santa_Maria_del_Fiore_in_Florence.jpg/320px-View_of_Santa_Maria_del_Fiore_in_Florence.jpg) *Architecture — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (STEM and Music room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:View_of_Santa_Maria_del_Fiore_in_Florence.jpg).* > Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction.[3] It is both the process and the product of sketching, conceiving,[4] planning, designing, and constructing buildings or other structures.[5] The term comes from Latin architectura; from Ancient Greek ἀρχιτέκτων (arkhitéktōn) 'arch ([Wikipedia](https://en.wikipedia.org/wiki/Architecture)) <!-- REAL-GENERATIVE-MEDIA:END --> <!-- LOCAL-MEDIA-PASS:START --> ## From the vault media library !Architecture thumb.png *Architecture — from the vault's own media holdings, placed 2026-07-09. MTN / Wikitube.io original · CC BY-SA 4.0.* <!-- LOCAL-MEDIA-PASS:END --> > **Room:** [[Electronics]] · **Status:** ✅ shipped ## Overview Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction.3 It is both the process and the product of sketching, conceiving,4 planning, designing, and constructing buildings or other structures.5 The term comes fromLatin architectura; fromAncient Greek ἀρχιτέκτων (arkhitéktōn)'architect'; from ἀρχι- (arkhi-)'chief'and τέκτων (téktōn)'creator'. Architectural works, in the material form of buildings, are often perceived as cultural symbols and as works of art. Historical civilisations are often identified with their surviving architectural achievements.6 _(Overview is shorter than 200 words; the pipeline should expand it from textbook context before publishing.)_ ## See also - Room hub: [[Electronics]] - p5.js Editor conventions: P5 JS EDITOR - Wiki root: MAIN --- *Scaffolded by `generative-microsim` from row 11 of the Electronics sheet on 2026-06-04T00:18:30Z.* <!-- REAL-GENERATIVE-MEDIA:START --> <!-- CRAFT-LINK:START g12 --> *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].* <!-- CRAFT-LINK:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Architecture) : [Wikitube](https://en.wikitube.io/wiki/Architecture) ## Previous hub tags Tree parents: [[Monte_Carlo_method]] · [[Reliability_engineering]]. Legacy hubs: `GENERATIVE`. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*