2d:null 2e:["$","title",null,{"children":"A model for generating multiscale mobility traces | Ulf Aslak | Observable"}] 33:Tb0b,md `The concept of *scale* is very central to the field of geography, referring to the levels (such as buildings, cities, etc.) at which to describe geographical phenomena [[1](https://journals.sagepub.com/doi/10.1191/030913200674086272), [2](https://journals.sagepub.com/doi/pdf/10.1191/0309132504ph502pr), [3](https://rsaiconnect.onlinelibrary.wiley.com/doi/abs/10.1111/j.1435-5597.1958.tb01625.x)]. We should, therefore, expect that human mobility is constrained by geographical scales, and intuitively that seems to be the case. When getting out of the office chair to grab a cup of coffee you move at the scale of the building that your office is in. When leaving work around noon to grab lunch at the nearby sandwich place you move at the scale of the neighborhood. Driving home at the end of the day constitutes a journey at the scale of the city, or the region of the country where one lives and works. Back home, movements in space are again characterized by the typical scale of an indoor space that doesn't require putting on shoes. Large (and larger) scale trips are finally those made between regions of a country, or between countries of a continent, between continents of the globe, and soon, maybe, between planets of our solar system. Yet, most state of the art models for simulating agent mobility is highly influenced by a line of empirical research that finds human mobility to be scale-free [[4](https://www.nature.com/articles/nature04292), [5](https://www.nature.com/articles/nature06958), [6](https://www.pnas.org/content/113/26/7047)]. For example, the "exploration and preferential return" (EPR) model [[7](https://www.nature.com/articles/nphys1760)], which leverages the sensible notion that humans travel either to explore new places or return preferentially to frequently visited locations, draws step length from a power law distribution. In such a framework, scales cannot be captured and so in case the geographers are right we need to imagine other ways to simulate human mobility. In this notebook I introduce and visualize a simple model that simulates mobility on a hierarchy of containers, organized as nested 2d grids. The model assumes a power law distribution over subcontainer *attractivess* within each container and then simulates mobility as a two-stage process: first deciding which scale—i.e. *level* in the hierarchy of containers—to travel at; second selecting a container at that level, then a container within the chosen container and so on down to the lowest level. By simulating mobility on a substrate of nested mobility containers we essentially hard-code scalefullness into the resulting generated trajectory. Interestingly, we can still produce power-law-like displacement distributions when we aggregate distributions of displacement lengths at different scales. `34:T4fd,md ` We model transitions as a two-stage decision process, that entails first choosing a level to travel at, ${tex`l^*`}, and second choosing a destination location *k*. We simulate the mobility of an agent by the following algorithm: 1. Initialize the agent in a random location, ${tex`j`}. 2. Select a level-distance ${tex`l^*`} that the agent should travel at, by drawing from the multinomial distribution, ${tex`p`}. 3. To select a location, ${tex`k`}: At level ${tex`l^*`}, select a sibling container of ${tex`j_{l^*}`}, ${tex`k_{l^*} \neq j_{l^*}`}, by drawing from the attractiveness distribution over all sibling containers within the parent container. At level ${tex`l^*-1`}, select a child container ${tex`k_{l^*-1}`} within ${tex`k_{l^*}`}, by drawing from the attractiveness distribution over child containers. Continue this process until level 1 is reached. 4. Repeat steps 2 and 3 for any desired number of iterations. At each step the agent moves from a location *j* to a new location *k*. The step is stored as a vector ${tex`k=[k_1, ..., k_l, ..., k_L, d(j, k), d_{cart}(j, k)]`}, where ${tex`d(j, k)`} is the level-distance traveled (i.e. at which scale the transition took place), and ${tex`d_{cart}(j, k)`} is the cartesian distance between *j* and *k*. `35:T5e3,{ var dim = 650 var buf = dim / T**S / 2; const { canvas, context } = createCanvas(); context.canvas.width = dim context.canvas.height = dim const pixelRatio = resize(canvas, dim, dim); context.scale(pixelRatio, pixelRatio); if (options.includes('showGrid')) { for (let s = 1; s <= S; ++s) { if (T**s < 1000) { context.globalAlpha = 1/s**2 for (let t=1; t < T**s; ++t) { context.beginPath(); //Horizontal lines context.moveTo(0, dim * t / T**s) context.lineTo(dim, dim * t / T**s) context.stroke() context.beginPath(); // Vertical lines context.moveTo(dim * t / T**s, 0) context.lineTo(dim * t / T**s, dim) context.stroke() } } } } context.globalAlpha = 0.5; context.lineWidth = 2; // context.globalCompositeOperation='destination-over' for (let time = 1; time < walk.length; ++time) { let x0 = walk[time-1][0] let y0 = walk[time-1][1] let x1 = walk[time][0] let y1 = walk[time][1] let s = walk[time][2] context.beginPath(); context.moveTo(dim * x0 / T**S + buf, dim * y0 / T**S + buf); context.lineTo(dim * x1 / T**S + buf, dim * y1 / T**S + buf); context.strokeStyle = colors[s-1] context.stroke(); if (options.includes('animated')) { yield context.canvas } } if (!options.includes('animated')) { yield context.canvas } }36:Tc97,{ // Layout var width = 650 var height = 300 var margin = ({top: 20, right: 20, bottom: 30, left: 40}) var barMargin = -0.5 // Histogramming var xMax = d3.max(walk.map(d => d[3])) var xTicks = linspace(0, Math.log(xMax+1), nticks+1).map(d => Math.exp(d)) var histogram_model = d3.histogram() .domain([0, xTicks[xTicks.length-1]]) .thresholds(xTicks) var allData = walk.map(d => d[3]) var histogramAll = histogram_model(allData) histogramAll = histogramAll.slice(1, histogramAll.length-1) // .slice(1, -1) because first and alst bin are zero histogramAll = histStyle == "density" ? normalizeHistogram(histogramAll) : histogramAll.map(bin => bin.length) var histograms = d3.range(1, d3.max(walk.map(d => d[2]))+1).map(s => { let data_s = walk.filter(d => d[2] == s).map(d => d[3]) let histogram_s = histogram_model(data_s) return histogram_s.slice(1, histogram_s.length-1) }) // Scaling var x = d3.scaleLog() .domain([1, xTicks[xTicks.length-1]]) .range([margin.left, width - margin.right]) var yMin = histStyle == "density" ? d3.min(histogramAll.filter(v => v > 0)) / 2 : 0.5 var yMax = d3.max(histogramAll) var y = d3.scaleLog() .domain([yMin, yMax]) .range([height - margin.bottom, margin.top]) // Drawing const { canvas, context } = createCanvas(); context.canvas.width = width context.canvas.height = height const pixelRatio = resize(canvas, width, height); context.scale(pixelRatio, pixelRatio); context.lineWidth = 2 // Draw histogram histogramAll.forEach((bin, i) => { let scaleCols = flattenArray( histograms.map((bins, s) => Array(bins[i].length).fill(s+1)) // [[1, 1, ..., 1], [2, 2, ..., 2], ...] ).map(s => {return colors[s-1]}) context.fillStyle = scaleCols.length == 0 ? "#000000" : colormixer(scaleCols) context.fillRect(x(xTicks[i])+barMargin, y(bin), x(xTicks[i+1]) - x(xTicks[i])-barMargin, y(yMin)-y(bin)) }) // Axes context.fillStyle = "black" context.beginPath() context.moveTo(margin.left, margin.top) context.lineTo(margin.left, height - margin.bottom) context.lineTo(width - margin.right, y(yMin)) context.stroke() // Ticks for (let power in d3.range(Math.floor(Math.log10(xMax))+1)) { let val = parseFloat("1e" + power) if (x(val) >= margin.left){ context.beginPath() context.moveTo(x(val), y(yMin)) context.lineTo(x(val), y(yMin)+5) context.stroke() context.font = "15px Helvetica Neue"; context.fillText("10", x(val)-12, y(yMin)+29) context.font = "12px Helvetica Neue"; context.fillText(power, x(val)+5, y(yMin)+22) } } for (let power of d3.range(Math.floor(Math.log10(yMin)), Math.ceil(Math.log10(yMax)))) { let val = parseFloat("1e" + power) if (y(val) <= height - margin.bottom){ context.beginPath() context.moveTo(margin.left, y(val)) context.lineTo(margin.left-5, y(val)) context.stroke() context.font = "15px Helvetica Neue"; context.fillText("10", margin.left-40, y(val)+7) context.font = "12px Helvetica Neue"; context.fillText(power, margin.left-23, y(val)-2) } } return context.canvas }37:T8d3,function model(n_samples) { // Instantiate cell indices initial location var box_indices = d3.range(1, T**2+1) // Draw the first location. Note that location vector is reversed in the code , i.e. c = [c_S, ..., c_0] var prev_loc = d3.range(S).map(s => { //return sample_power_law((S-s-1)*c1_beta+c0_beta, T**2) return sample_power_law(beta, T**2) }) // Shuffle cell indices in each subcell. Shuffling uses the concatenation of the subcell index // `loc.slice(0, s)` as the seed to the random number generator that determines the order indices, // such that when shuffling subcell cell indices is consistent for each subcell across shuffles. // If you don't make this shuffling of subcell cell indices, because the cell index ordering is // from top left to bottom right, visiting probabilities are always highest in cells' top left // corner. Try it. var prev_loc_ = shuffleCellIds(prev_loc, box_indices) // Record first step in the list of `trips` var trips = [[...convert_to_cartesian(prev_loc_), null, null]] var trips_vec = [prev_loc_] // Start walk let iter = 0; while (iter < n_samples-1) { // Choose a location. Example outcome: [1, 1, 2, 4] (if `prev_loc == [1, 1, 1, 1]`, scale == 2) let complete_rest = false let loc = prev_loc.map((l, s) => { let scale = S - s if (Math.random() > Math.exp(-exponent_p*scale) && !complete_rest) { // Not passing bernoulli trial return l } else { // Pass bernoulli trial complete_rest = true //return sample_power_law((scale-1)*c1_beta+c0_beta, T**2, l) return sample_power_law(beta, T**2) } }) // If it is a new location, infer scale and store datapoint if (!_.isEqual(loc, prev_loc)) { let scale = compute_scale(loc, prev_loc) // Convert the locations such that each subcell has its own random map of subsubcell ids let loc_ = shuffleCellIds(loc, box_indices) let loc_cartesian = convert_to_cartesian(loc_) trips.push([loc_cartesian[0], loc_cartesian[1], scale, dist(trips[trips.length-1].slice(0, 2), loc_cartesian)]) trips_vec.push(loc) iter += 1; } prev_loc = loc } return trips }38:Ta7c,colors = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd', '#8c564b', 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31:{"id":"5e31ece5b03e78a6","slug":"a-model-for-generating-multiscale-mobility-traces","title":"A model for generating multiscale mobility traces","thumbnail":"cf30dae41eccde71c528e845f6ec727b97c234a2cff3ec7efe83091beadee373","access_level":"public","create_time":"$D2018-12-12T10:09:22.969Z","update_time":"$D2020-09-12T04:46:44.048Z","view_time":null,"first_public_time":"$D2020-01-09T13:14:11.090Z","has_unpublished_edits":null,"fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"6e39539fdcd54038","login":"ulfaslak","name":"Ulf Aslak","avatar_url":"https://avatars-next.observableusercontent.com/49dd6371d9660f6642b5c92221ac7c785d45e5d7cd9b302104e634188d045adc","tier":"starter_2024","bio":""},"version":2695,"publish_version":2695,"role":null,"authored":false,"authors":[{"type":"individual","id":"2d5d2f67a6aa1cf7","login":"ulfaslak","name":"Ulf 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traces`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"md `### Framework and model dynamics\n\nThe model generates stochastic location sequences, constructed from a multiscale view of human mobility. It imagines space as a square, that containes ${tex`T^2`} subsquares. Each subsquare containes again ${tex`T^2`} subsubsquares, and so on, *L* times. As such, *L* is the number of *levels* and *T* is the granularity of space at each level, represented as the number of *ticks* per square. We refer to these squares, at any level, as *containers* of mobility. In an abstract sense they represent different geographical entities at various scales, such as buildings, neighborhoods, cities, and so on.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"{\n var dim = 300\n \n const { canvas, context } = createCanvas();\n context.canvas.width = dim\n context.canvas.height = dim\n \n const pixelRatio = resize(canvas, dim, dim);\n context.scale(pixelRatio, pixelRatio);\n \n for (let s = 1; s <= S_; ++s) {\n if (T_**s < 500) {\n context.globalAlpha = 1/s**2\n for (let t=1; t < T_**s; ++t) {\n context.beginPath(); //Horizontal lines\n context.moveTo(0, dim * t / T_**s)\n context.lineTo(dim, dim * t / T_**s)\n context.stroke()\n context.beginPath(); // Vertical lines\n context.moveTo(dim * t / T_**s, 0)\n context.lineTo(dim * t / T_**s, dim)\n context.stroke()\n }\n }\n }\n \n return context.canvas\n\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2636,"value":"viewof S_ = slider({\n min: 0, \n max: 5, \n step: 1, \n value: 2, \n title: \"L\",\n description: \"Number of levels\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2641,"value":"viewof T_ = slider({\n min: 2, \n max: 20, \n step: 1, \n value: 3,\n title: \"T\",\n description: \"Number of ticks per square\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"md `Each of the finest containers constitutes a location that a movement can either start or end in. It can be represented as a vector ${tex`k=[k_1, ..., k_l, ..., k_L]`}, where ${tex`k_l\\in\\{1, 2, ..., T^2\\}`}, intuitively denoting that the location is container ${tex`k_1`} in container ${tex`k_2`} in container ${tex`k_3`} and so on.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2451,"value":"md`\nAt each level, we assign each container an *attractiveness* distribution, which gives the probabilities of child-containers being visited when the agent is in the parent-container. This distribution follows a power law with exponent ${tex`\\beta`}.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2414,"value":"md `\nWe define a multinomial probability distribution *p* that here follows an exponential distribution ${tex`p = e^{-\\alpha l^*}`}, where ${tex`l^*`} is the level that the agent travels at and ${tex`\\alpha`} is a tunable parameter.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2411,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2404,"value":"md `#### Simulation`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":999,"value":"md `Let's run the model for ${tex`\\texttt{numIter}=5000`} iterations (you can change this parameter below, in the 'Global parameters' section).`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":132,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2480,"value":"viewof options = checkbox({\n //title: 'Options',\n// description: '',\n options: [\n { value: 'animated', label: 'Animated' },\n { value: 'showGrid', label: 'Show grid' },\n { value: 'randomSeed', label: 'Random seed' }\n ],\n value: []\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2439,"value":"viewof S = slider({\n min: 0, \n max: 5, \n step: 1, \n value: 3, \n title: \"L\",\n description: \"Number of levels\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2442,"value":"viewof T = slider({\n min: 2, \n max: 20, \n step: 1, \n value: 5,\n title: \"T\",\n description: \"Number of ticks per square\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2590,"value":"viewof exponent_p = slider({\n min: 0, \n max: 3,\n step: 0.1,\n value: 1, \n title: \"α\",\n description: \"Exponent of multinomial distribution, p\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2599,"value":"viewof beta = slider({\n min: -5, \n max: -0.1,\n step: 0.1,\n value: -2, \n title: \"β\",\n description: \"Exponent of attractiveness distributions, a\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":949,"value":"md `Try adjusting *L* and *T* in the sliders above, until you get something that looks realistic. Trips are colored by scale. Play with the parameters below to manipulate the results, and see if you create some displacements that collectively looks like something you might see in real life.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1045,"value":"md `\n
\n#### Distribution of distances`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1051,"value":"md `Having generated the data ourselves, we know to which scale each displacement belongs. This presents an important opportunity: to visualize the distribution of distances for each scale. Why is this important? In the literature where human mobility is described as being scale-free, the main argument presented is that the distribution of trip distances resembles a power law. What if this is simply a phenomenon that occurs when you [aggregate](https://observablehq.com/@ulfaslak/a-visual-exploration-of-how-a-power-law-can-emerge-from-aggre) distances of trips at different scales?`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2018,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1872,"value":"viewof histStyle = radio({\n description: 'Toggle bin-normalization',\n options: [\n { label: 'Density', value: 'density' },\n { label: 'Counts', value: 'counts' },\n ],\n value: 'density'\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1317,"value":"viewof nticks = slider({\n min: 5, \n max: 50, \n step: 1, \n value: 20, \n description: \"Number of bins\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2126,"value":"md `Here, I have colored each bin according to the displacement scales it contains. For example, if a bin contains 80% scale 1 displacements and 20% scale 2 displacements the color of that bin is the corresponding linear interpolation between scale 1 and 2's respective colors.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":166,"value":"md `### Functions, utilities and global parameters`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":382,"value":"md `#### Model`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":509,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":228,"value":"function convert_to_cartesian(loc) {\n var num_ticks = T**S\n var x = _.sum(loc.map((c, s) => {\n return Math.floor(num_ticks / T**(1 + s)) * ((c-1) % T)\n }))\n var y = _.sum(loc.map((c, s) => {\n return Math.floor(num_ticks / T**(1 + s)) * Math.floor((c-1) / T)\n }))\n return [x, y]\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":227,"value":"function sample_power_law(beta, x_max, invalidSample) {\n var sample = x_max + 1\n while (sample > x_max || sample == invalidSample) {\n let u = Math.random()\n sample = Math.floor(u**(1./beta))\n }\n return sample\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":256,"value":"function compute_scale(loc1, loc2) {\n for (let s = 0; s < loc1.length; ++s) {\n if (loc1[s] != loc2[s]) return S - s;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":706,"value":"function shuffleCellIds(loc, box_indices){\n return loc.map((l, s) => {\n let seed = arrayToInt(loc.slice(0, s)) + globalSeed\n let new_box_indices = shuffle(box_indices, seed)\n return new_box_indices[l-1]\n })\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1063,"value":"function dist(a, b) {\n return Math.sqrt((a[0] - b[0])**2 + (a[1] - b[1])**2)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2512,"value":"walk = model(numIter)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2517,"value":"md`#### Global parameters`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":884,"value":"globalSeed = options.includes('randomSeed') ? Math.random()*1000 : 0","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2508,"value":"numIter = 5e3","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":385,"value":"md `#### Utilities`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":389,"value":"function createCanvas() {\n const canvas = document.createElement('canvas');\n const context = canvas.getContext('2d');\n return { canvas, context };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":387,"value":"function resize(canvas, width, height) {\n \n // Device screen density, e.g. MacBook Pro is @2x\n const pixelRatio = window.devicePixelRatio;\n \n // Scale it up by pixel ratio for higher density screens\n canvas.width = width * pixelRatio;\n canvas.height = height * pixelRatio;\n \n // Set the style to the desired size so that it scales back down\n canvas.style.width = `${width}px`;\n canvas.style.height = `${height}px`;\n\n return pixelRatio;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":430,"value":"function seedRandom(seed) {\n var x = Math.sin(seed++) * 10000; \n return x - Math.floor(x);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":463,"value":"function shuffle(array, seed) {\n // Fisher-Yates shuffle (source: https://bost.ocks.org/mike/shuffle/)\n // Modified with seed\n var array = array.slice()\n var m = array.length, t, i;\n while (m) {\n i = Math.floor(seedRandom(seed) * m--);\n t = array[m];\n array[m] = array[i];\n array[i] = t;\n ++seed\n }\n return array;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":482,"value":"function arrayToInt(array) {\n if (array.length == 0) return 0;\n return parseInt(array.join(\"\"))\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1152,"value":"linspace = function(start, stop, nsteps){\n var delta = (stop-start)/(nsteps-1)\n return d3.range(nsteps).map(function(i){return start+i*delta;}) ;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1897,"value":"function flattenArray(array) {\n return [].concat.apply([], array)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1955,"value":"function normalizeHistogram(histogram, totalMass) {\n var massHistogram = histogram.map(bin => bin.length)\n var totalMass = totalMass || d3.sum(massHistogram)\n var densityHistogram = massHistogram.map((binMass, i) => binMass / totalMass / (histogram[i].x1 - histogram[i].x0))\n return densityHistogram\n} ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2007,"value":"function log(literallyAnything) {\n console.log(literallyAnything)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2046,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2558,"value":"function colormixer(colList) {\n return chroma.average(colList, 'lch').hex()\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2686,"value":"colormixer([\"#000000\", \"#ffffff\"])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2121,"value":"c = d3.scaleLinear().domain([1, S]).range([0, colors.length-1])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"md `### Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"d3 = require(\"d3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":153,"value":"_ = require(\"lodash\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"import {slider} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":342,"value":"import {checkbox} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1876,"value":"import {radio} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2540,"value":"chroma = require('chroma-js@1.3.7')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W39","stdlib":"1"}} 32:"$31:body"