2d:null 2e:["$","title",null,{"children":"The xxx^xxx-spindle (just dom) | Andreas Plesch | Observable"}] 33:Tc2b,// Generates the spindle with branches -n through n function* spindle(n, step=0.001) { let height = 0.8 * Math.min(width, window.screen.height); let container = html`

`; let x3d = container.appendChild(html``); let scene = x3d.appendChild(html``); scene.appendChild( html` `); scene.appendChild( html` `); scene.appendChild( html` `); scene.appendChild( range( -n, n+1 ) .map( k => { let this_coord_string = spindle_string(k, step); return html` `; }) .reduce( (b, spindle) => {b.appendChild(spindle); return b}, html` `) ) // for (let k = -n; k <= n; k++) { // let this_coord_string = spindle_string(k); // let bundle_shape = bundle.appendChild( html` // // // // // // // // // `); // }; let principle_points = range(-4, 2, 0.02).map(function(x) { let value = x2x(x, 0); // let vre = value.re; // if (math.abs(vre) < 0.001) { // vre = 0.0; // } // let vim = value.im; // if (math.abs(vim) < 0.001) { // vim = 0.0; // } return [2 * x, value.re, value.im]; }); scene.appendChild(create_tube( principle_points, 0.025, { diffuseColor: '0 0 0' } ).node() ); yield container; x3dom.reload(); }34:[] 31:{"id":"4b04e7cfc8538ecd","slug":"the-xxx-xxx-spindle-just-dom","title":"The xxx^xxx-spindle (just dom)","thumbnail":"fd9e39300b581a8c14e47c7f25938d1d1a6c3c5a194ff018b393ee571a954fcf","access_level":"public","create_time":"$D2019-11-30T23:00:53.694Z","update_time":"$D2019-12-02T18:02:00.748Z","view_time":null,"first_public_time":"$D2019-12-01T15:36:26.737Z","has_unpublished_edits":null,"fork":{"id":"cd120cd5f5048982","slug":"the-xxx-xxx-spindle","title":"The xxx^xxx-spindle","owner":{"id":"3a7167e5e638bcd0","login":"andreasplesch","name":"Andreas Plesch"}},"stars":0,"starred":false,"owner":{"type":"team","id":"3a7167e5e638bcd0","login":"andreasplesch","name":"Andreas Plesch","avatar_url":"https://avatars-next.observableusercontent.com/4da1ba746a4b25e755d1c9b71ca1c72165a9c40e02aee1f3fcae880584d70c9c","tier":"starter_2024"},"version":1034,"publish_version":1034,"role":null,"authored":false,"authors":[{"type":"individual","id":"171053d51d09c7fc","login":"andreasplesch","name":"Andreas Plesch","avatar_url":"https://avatars-next.observableusercontent.com/4da1ba746a4b25e755d1c9b71ca1c72165a9c40e02aee1f3fcae880584d70c9c","tier":null}],"members":[{"type":"individual","id":"171053d51d09c7fc","login":"andreasplesch","name":"Andreas Plesch","avatar_url":"https://avatars-next.observableusercontent.com/4da1ba746a4b25e755d1c9b71ca1c72165a9c40e02aee1f3fcae880584d70c9c","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"The xxx^xxx-spindle (just dom)","cells":[{"id":0,"value":"md`# The ${tex`x^x`}-spindle (just dom)\n\nThe 3D graph of real ${tex`x`} vs the real and imaginary parts of ${tex`x^x = e^{x\\log(x)}`} for various branches of the complex logarithm.\n\nBased on the 1996 paper \"[The ${tex`x^x`}-Spindle](https://www.jstor.org/stable/2691469)\". \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1009,"value":"xx_spindle = spindle(N)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":731,"value":"viewof n = slider({\n min: 0,\n max: N,\n step: 1,\n value: N,\n title: \"Number of threads\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":408,"value":"md`## Code`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":421,"value":"$33","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":456,"value":"// Defining the branches of x^x\nfunction x2x(x, k) {\n if (math.abs(x) < 0.000001) {\n return math.complex(1, 0);\n } else {\n var z = math.complex(x);\n var twoPiI = math.complex(0, 1).mul(2 * math.pi);\n return math.exp(z.mul(z.log().add(twoPiI.mul(k))));\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":460,"value":"// The X3Dom string defining the kth spindle.\nfunction spindle_string(k, step=0.01) {\n const precision = 2;\n return range(-4, 2, step).map( x => {\n const value = x2x(x, k);\n return [2 * x, value.re, value.im]\n .map( n => {\n let scientific = n.toExponential(precision);\n let fixed = Number.parseFloat(scientific).toString();\n return fixed.length <= scientific.length \n ? fixed\n : scientific\n })\n .join(' ');\n }).join(',');\n}\n// var result = '';\n// range(-4, 2, 0.001).map(function(x) {\n// result = result + (2 * x).toString() + ' ';\n// var value = x2x(x, k);\n// var vre = value.re;\n// if (math.abs(vre) < 0.001) {\n// vre = 0.0;\n// }\n// var vim = value.im;\n// if (math.abs(vim) < 0.001) {\n// vim = 0.0;\n// }\n// result = result + vre.toString() + ' ' + vim.toString() + ', ';\n// });\n// result = result.slice(0, -2);\n// return result;\n// }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":943,"value":"spindle_string(0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":433,"value":"md`We never actually remove or add threads, we just set their transparency as follows.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":804,"value":"n_spindles = {\n const spindles = xx_spindle.querySelector('#the_bundle').querySelectorAll('shape');\n spindles.forEach( shape => {\n const thread = shape.getAttribute('thread') * 1.0;\n // const transparency = Math.abs(thread) > n ?\n // 1 :\n // 1 - math.pow(T, -math.abs(3 * thread));\n // //if (thread > n || thread < -n) { transparency = 1; }\n // shape.querySelector('material').setAttribute('transparency', transparency);\n const render = Math.abs(thread) <= n;\n shape.setAttribute('render', render);\n })\n yield spindles\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":491,"value":"md`## A couple of globals`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":495,"value":"// There will be 2*N+1 of branches or threads\nN = 25","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":500,"value":"// Multiplicative factor by which the transparency of higher order branches are dimmed\nT = 1.06","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":449,"value":"md`## Imports`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"math = require('mathjs')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"// x3dom is tricky. The require debugger suggests the following:\n// https://observablehq.com/@tmcw/module-require-debugger\nx3dom = require('x3dom').catch(() => window['x3dom'])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1021,"value":"stylesheet = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":95,"value":"function range (start=0, stop=1, step=1) {\n return Array(Math.round((stop-start) / step)).fill(0).map((v,i)=>start+i*step)\n}\n ","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":729,"value":"import { slider } from \"@jashkenas/inputs\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":744,"value":"import { create_tube } from '@mcmcclur/space-curves-and-tubes'","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":757,"value":"// Supress the annoying dashed box that appears around X3Dom display.\nhtml``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 32:"$31:body"