28:null 29:["$","title",null,{"children":"neĝero : SnowFlake generator | Aliaksei Chapyzhenka | Observable"}] 2e:T486,dt2cr = (dt, numLayers) => { const w = Math.sqrt(dt.length); const res = []; for (let l = 1; l <= numLayers; l += 2) { // trace only odd layers const d = []; res.push(d); // find starting point let x = 0; let y = 0; for (let i = 0; i < w; i++) { if (dt[i] === l) { x = i; break; } } d.push([x, y]); // start point dt[x + y * w] = 255; let dir = 1; loop1: for (let i = 0; i < 200000; i++) { // max number of points for (const j of [0, 4, 5, 1, 2, 3]) { // delta directions to try let dir1 = (dir + j) % 6; // direction to try const c = dirLut[dir1]; const xm = x + c[0]; const ym = y + c[1]; if ((x > 0) && (ym > 0) && (dt[xm + ym * w] === l)) { // found a way x = xm; y = ym; if (j === 0) { // straight line d[d.length - 1] = [x, y]; } else { // new point for turn d.push([x, y]); } dt[xm + ym * w] = 255; if (x === y) { break loop1; } dir = dir1; break; } } } } return res; }2f:T5b6,tr2dt = (tr, layers) => { const w = 1024; const mat = new Uint8Array(w * w); mat.fill(255); const nut = (x, y, r) => { mat[x + w * y] = 0; // center for (let i = 1; i <= r; i++) { // layers for (let j = 0; j < 6; j++) { // 6 edges const jlut = [ [ 1, -1, 0, 1], // 0 [ 0, -1, 1, 0], // 1 [-1, 0, 1, -1], // 2 [-1, 1, 0, -1], // 3 [ 0, 1, -1, 0], // 4 [ 1, 0, -1, 1] // 5 ]; const jc = jlut[j]; for (let k = 0; k < i; k++) { const x1 = x + jc[0] * i + jc[1] * k; const y1 = y + jc[2] * i + jc[3] * k; const xy1 = x1 + w * y1; if (mat[xy1] > i) { mat[xy1] = i; } } } } } const line = (x1, y1, dir, len) => { const c = dirLut[(dir + 600) % 6]; const xm = x1 + c[0] * len; const ym = y1 + c[1] * len; for (let i = 0; i <= len; i++) { const x = x1 + c[0] * i; const y = y1 + c[1] * i; if ((x >= 0) && (y >= 0)) { nut(x, y, layers); } } return [xm, ym]; }; const rec = (node, x, y, dir) => { const len = Array.isArray(node) ? node[0] : node; const [xm, ym] = line(x, y, dir, len); if (Array.isArray(node)) { const [s, l, r] = node; rec(l, xm, ym, dir); rec(r, xm, ym, dir + 1); rec(r, xm, ym, dir - 1); } }; rec(tr, 0, 0, 0); return mat; }30:[] 2c:{"id":"8b92a6dad95bd907","slug":"neghero","title":"neĝero : SnowFlake generator","thumbnail":"da370f17d838678e0f66d301f31e63a7e7c4fec8518a804c90480d8d43a323f0","access_level":"public","create_time":"$D2025-11-30T01:51:11.598Z","update_time":"$D2026-08-20T21:48:17.769Z","view_time":null,"first_public_time":"$D2025-11-30T06:49:09.389Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"7b1c5b66fd9285b7","login":"drom","name":"Aliaksei Chapyzhenka","avatar_url":"https://avatars-next.observableusercontent.com/f76b026367381023f99af919f112679e18ac3edad1d4905354ca8bf207f0f651","tier":"starter_2024"},"version":2019,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"feb36c5199c05e3b","login":"drom","name":"Aliaksei Chapyzhenka","avatar_url":"https://avatars-next.observableusercontent.com/f76b026367381023f99af919f112679e18ac3edad1d4905354ca8bf207f0f651","tier":null}],"members":[{"type":"team","id":"7b1c5b66fd9285b7","login":"drom","name":"Aliaksei Chapyzhenka","avatar_url":"https://avatars-next.observableusercontent.com/f76b026367381023f99af919f112679e18ac3edad1d4905354ca8bf207f0f651","tier":"starter_2024","role":"editor"},{"type":"individual","id":"feb36c5199c05e3b","login":"drom","name":"Aliaksei Chapyzhenka","avatar_url":"https://avatars-next.observableusercontent.com/f76b026367381023f99af919f112679e18ac3edad1d4905354ca8bf207f0f651","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"neĝero : SnowFlake generator","cells":[{"id":0,"value":"# neĝero : SnowFlake generator\n\nhttps://github.com/drom/neghero\n\nRenders Snowflake from simple set of parameters:\n\n* **tree** - a structure, defining topology of snowflake arms. it is natural number or array of natural numbers or arrays.\n* **s** - tree scale. natural number to scale tree numbers. (optional, default: 4)\n* **l** - layers count. natural number defining number of layers lines around the skeleton of the tree. (optional, default: 4)\n* **p** - display grid pitch. (optional, default: 2)\n\nCan generate SVG line path or G-code for 3D printer.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1781,"value":"heghero0014 = flake({tree: [5, [5, [4, [4, [9, [18, [4, [10, [6, [6, 4, 3], 6], 1], [10, [4, 3, 1], 4]], 3], [8, [5, 3, 1], [4, 1, 1]]], 5], 4], 3], 4], p:6, s:1, l:7})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1743,"value":"flake({tree:[13,[8,[5,[3,[2,1,1],[2,1,1]],2],[3,[2,1,1],1]],5,[3,[2,[1,1,1],1],[2,1,1]],[2,[1,1,1],[1,1,1]],[1,[1,1,1],1]],s:4,l:13,p:2.8})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1778,"value":"flake({tree:[12,[8,[5,[3,[2,1,1],[2,1,1]],2],[4,[2,1,1],2]],4,[3,[2,[1,1,1],1],[2,1,1]],[2,[1,1,1],[1,1,1]],[1,[1,1,1],1]],s:5,l:15,p:2.8})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1667,"value":"nghero0011 = flake({tree:[16,[2,[2,[8,[8,[16,3,1],[16,3,1]],6],6],4],2],l:27})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1612,"value":"nghero0010 = flake({tree:[6,[3,[7,[9,[6,4,1],[6,4,1]],[5,2,[2,2,[2,2,1]]]],5],3],s:8,l:11,p:2})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1537,"value":"neghero009 = flake({tree:[6,[3,[3,[3,[3,[4,[3,[3,[3,[3,[3,[3,[3,[3,[3,[6,[5,3,1],4],6],3],7],9],7],5],1],[16,[1,[1,3,2],2],1]],1],4],10],6],4],3],1],s:4,l:9})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1434,"value":"neghero008 = flake({tree:[5,[4,[4,[2,[6,[5,[3,[1,[6,[2,[2,3,3],1],1],[6,[2,[2,3,3],1],1]],2],3],3],[5,[6,1,6],1]],1],4],3],s:5,l:9})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1312,"value":"heghero0007 = flake({tree:[7,[5,[11,[11,[10,[9,[7,2,1],5],[5,4,1]],[6,[5,5,1],1]],[7,[7,4,2],3]],8],4],l:9}) // snow crystals cover RT","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1230,"value":"heghero0006 = flake({tree:[7,[5,[11,[12,[4,[6,[9,4,4],10],15],13],16],5],3],l:15}) // snow crystals cover LT","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1025,"value":"heghero0005 = flake({tree:[7,[4,[5,[7,[5,[2,[5,[6,[6,[7,5,1],7],3],15],2],1],[9,[4,4,2],3]],5],5],3],s:4,l:11})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":783,"value":"nghero0004 = flake({tree:[4,[3,[10,[8,[2,1,1],[3,1,1]],[5,5,[3,2,[2,1,1]]]],3],3],s:8,l:7,p:2})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":843,"value":"nrghero0003 = flake({tree:[8,[3,7,8],5],s:10,l:11})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1411,"value":"neghero0002 = flake({tree:[10,[5,4,3],[3,2,1]],s:8,l:11})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":817,"value":"neghero0001 = flake({tree:[2,1,1],s:64,l:19,p:2})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1425,"value":"neghero0000 = flake({tree: 32, l:29})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"### Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":212,"value":"tr1 = [17,[8,[2,1,1],[3,1,1]],[5,5,[3,2,[2,1,1]]]]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":781,"value":"flake = (cfg) => {\n let {tree, s, l, p} = cfg;\n s = s || 4;\n l = l || 4;\n p = p || 2;\n const tree1 = treeScale(tree, s);\n const dt = tr2dt(tree1, l);\n const cr = dt2cr(dt, l);\n const hex1 = cr2hex(cr);\n const path = cr2path(hex1, p);\n return render6(path); \n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":327,"value":"//render(['g', tr2path(tr1s, 4), dtRender(dt1s, 4), cr2path(cr1s, 4)], 16)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":448,"value":"dirLut = [[1, 0], [0, 1], [-1, 1], [-1, 0], [0, -1], [1, -1]]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":274,"value":"tr2path = (tr, scale) => {\n scale = scale || 8;\n const d = [];\n const line = (x1, y1, dir, len) => {\n const c = dirLut[(dir + 600) % 6];\n const xm = x1 + c[0] * len;\n const ym = y1 + c[1] * len;\n if ((y1 < 0) || (ym < 0)) {\n return [xm, ym];\n }\n d.push('M', x1, y1, 'L', xm, ym);\n return [xm, ym];\n };\n const rec = (node, x, y, dir) => {\n const len = Array.isArray(node) ? node[0] : node;\n const [xm, ym] = line(x, y, dir, len);\n if (Array.isArray(node)) {\n const [s, l, r] = node;\n rec(l, xm, ym, dir);\n rec(r, xm, ym, dir + 1);\n rec(r, xm, ym, dir - 1);\n }\n };\n rec(tr, 0, 0, 0);\n return ['path', {d: scaled(d, scale, scale).join(' ')}];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":325,"value":"tr2 = [5,1,1] // key","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":751,"value":"tr1s = treeScale(tr1, 8)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":756,"value":"dt1s = tr2dt(tr1s, 5)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":758,"value":"cr1s = dt2cr(dt1s, 5)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":663,"value":"$2e","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":359,"value":"$2f","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":366,"value":"dtRender = (dt, scale) => {\n scale = scale || 8;\n const colorLut = ['#ccc','#f00', '#ccc', '#0a0', '#ccc', '#00f', '#ccc', '#f0f', '#ccc', '#aa0', '#ccc']\n const res = ['g'];\n const w = Math.sqrt(dt.length);\n for (let i = 0; i < dt.length; i++) {\n if (dt[i] !== 255) {\n res.push(['circle', {r: 1, cx: scale * (i % w), cy: scale * ((i / w)|0), fill: colorLut[dt[i]]}])\n }\n } \n return res; \n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":317,"value":"//render(tr2path(tr1s))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":312,"value":"treeScale = (root, scale) => {\n const rec = (node) => {\n if (typeof node === 'number') {\n return node * scale;\n }\n return node.map(rec);\n }\n return rec(root);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":214,"value":"spktr2cr = (spktr, dist) => {\n // trace around spectral lines at specific distance\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"cr1 = [\n [[40,0],[39,1],[27,1],[27,13],[26,14],[25,14],[25,1],[1,1]],\n [[42,0],[39,3],[29,3],[29,5],[33,5],[33,8],[30,11],[29,11],[29,13],[26,16],[23,16],[23,14],[22,15],[19,15],[19,12],[23,8],[23,3],[3,3]],\n]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"//render(cr2path(cr1, 8))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":72,"value":"cr2hex = (segments) => {\n const tx = 0.5; // Math.sin(Math.PI / 6);\n const ty = Math.cos(Math.PI / 6); // 0.866\n const res = [];\n segments.map((points) => {\n const $ = points.map((point) => [point[0] + tx * point[1], point[1] * ty]);\n\n for (let q = 0; q < 6; q++) {\n for (let i = 0; i < $.length; i++) {\n const a = (q / 3) * Math.PI;\n const ca = Math.cos(a);\n const sa = Math.sin(a);\n const [x, y] = $[i];\n res.push([\n ca * x - sa * y,\n sa * x + ca * y\n ]);\n }\n for (let i = ($.length - 1); i >= 0; i--) {\n const a = ((q + 1) / 3) * Math.PI;\n const ca = Math.cos(a);\n const sa = Math.sin(a);\n const [x, y] = $[i];\n res.push([\n ca * x - sa * -y,\n sa * x + ca * -y\n ]);\n }\n }\n });\n return [res];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":29,"value":"hex1 = (scale, desc) => {\n \n \n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"cr2path = (segments, scale) => {\n const d = segments.flatMap((points) =>\n points.flatMap((point, i) =>\n [((i === 0) ? 'M' : 'L'), point[0] * scale, point[1] * scale])\n ).join(' ')\n return ['path', {d}];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"onml = require('onml')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"tt = onml.tt","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"defs = ['defs',\n ['radialGradient', {id: \"Gradient\", cx: 0.5, cy: 0.5, r: 1, fx: 0.25, fy: 0.25},\n ['stop', {offset: \"0%\", 'stop-color': \"yellow\"}],\n ['stop', {offset: \"100%\", 'stop-color': \"red\"}]\n ]\n]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"style = ['style', {}, `\n.box { stroke: #000; fill: none; }\n.grid { stroke: #eee; fill: none; stroke-width: 1px; }\n.axis { stroke: #f00; fill: none; stroke-width: 1px; }\nrect { fill: none; stroke: #000; }\n/* circle { fill: none; stroke: #000; } */\nellipse { fill: none; stroke: #000; }\nline { stroke: #000; }\ntext { font-size: 32px; font-family: 'sans'}\npath { fill: none; stroke: #000; }\n\n`];","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"grid = (w, h, step) => {\n let res = ['g', {}];\n for (let x = 0; x <= width; x+= step) {\n res.push(['line', {class: 'grid', x1: x, x2: x, y1: 0, y2: h}]);\n }\n for (let y = 0; y <= h; y+= step) {\n res.push(['line', {class: 'grid', x1: 0, x2: w, y1: y, y2: y}]);\n }\n res.push(['line', {class: 'axis', x1: 0, x2: h, y1: 0, y2: h}]);\n res.push(['line', {class: 'axis', x1: 0, x2: w, y1: step, y2: step}]);\n return res;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"grid6 = (w, h, step) => {\n let res = ['g', {}];\n const dx = h * Math.tan(Math.PI / 6) / 2;\n const dy = Math.cos(Math.PI / 6); // 0.866\n for (let x = -w; x <= w; x += step) {\n res.push(['line', {class: 'grid', x1: x + dx + w/2, x2: x - dx + w/2, y1: 0, y2: h}]);\n }\n for (let x = -w; x <= w; x += step) {\n res.push(['line', {class: 'grid', x1: x - dx + w/2, x2: x + dx + w/2, y1: 0, y2: h}]);\n }\n for (let y = -h; y <= h; y += step) {\n res.push(['line', {class: 'grid', x1: 0, x2: w, y1: y * dy + h/2, y2: y * dy + h/2}]);\n }\n res.push(['line', {class: 'axis', x1: w/2, x2: w/2, y1: 0, y2: h}]);\n res.push(['line', {class: 'axis', x1: 0, x2: w, y1: h/2, y2: h/2}]);\n return res;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"getSvg = cfg => {\n cfg = cfg || {};\n cfg.w = cfg.w || 880;\n cfg.h = cfg.h || 256;\n return ['svg', {\n xmlns: 'http://www.w3.org/2000/svg',\n width: cfg.w + 1,\n height: cfg.h + 1,\n viewBox: [0, 0, cfg.w + 1, cfg.h + 1].join(' ')\n }];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"render6 = arr => {\n if (typeof arr === 'function') {\n arr = arr();\n }\n return html`${onml.stringify(\n getSvg({w:1024, h:1024})\n .concat([defs, style, grid6(1024, 1024, 8), ['g', tt(512, 512)].concat([arr])])\n)}`\n};","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"render = (arr, scale) => {\n if (typeof arr === 'function') {\n arr = arr();\n }\n scale = scale || 8;\n return html`${onml.stringify(\n getSvg({w:1024, h:512})\n .concat([defs, style, grid(1024, 512, scale), ['g', tt(scale, scale)].concat([arr])])\n)}`\n};","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"scaled = (d, sx, sy) => {\n if (sy === undefined) { sy = sx; }\n let i = 0;\n while (i < d.length) {\n switch (d[i]) {\n case 'h':\n case 'H':\n d[i + 1] *= sx; i++; break;\n case 'v':\n case 'V':\n d[i + 1] *= sy; i++; break;\n case 'm':\n case 'l':\n case 'M':\n case 'L':\n d[i + 1] *= sx; d[i + 2] *= sy; i += 2; break;\n case 'a':\n d[i + 1] *= sx; d[i + 2] *= sy; d[i + 6] *= sx; d[i + 7] *= sy; i += 7; break;\n }\n i++;\n }\n return d;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W30","stdlib":"1","titling":"auto"}} 2d:"$2c:body"