2e:null 2f:["$","title",null,{"children":"Poisson, KPZ and Quenched KPZ | Bryan Gin-ge Chen | Observable"}] 34:[{"id":"496aa34d00b91c96cd341a19aa836b4c5381c4e8ced843ec0ddf7be368e56bc6b88a42b67853b604af0e80b94f576af1e0693ba8ef14ca6116a9eed7c2eb1d91","href":"https://static.observableusercontent.com/files/496aa34d00b91c96cd341a19aa836b4c5381c4e8ced843ec0ddf7be368e56bc6b88a42b67853b604af0e80b94f576af1e0693ba8ef14ca6116a9eed7c2eb1d91","name":"hsl-rgb-1.0.0.js","type":"application/javascript","lastModified":1588416998500.326,"size":1130}] 32:{"id":"aaae0b87eec786c0","slug":"poisson-kpz-and-quenched-kpz","title":"Poisson, KPZ and Quenched KPZ","thumbnail":"1a214f24782317e54d210aafda7b8f1643c53cc0d6af51c68d385239f86c4d16","access_level":"public","create_time":"$D2019-02-09T01:56:21.902Z","update_time":"$D2020-05-02T10:56:52.764Z","view_time":null,"first_public_time":"$D2019-02-09T04:08:33.062Z","has_unpublished_edits":null,"fork":false,"stars":10,"starred":false,"owner":{"type":"team","id":"d2fd23101beb2a61","login":"bryangingechen","name":"Bryan Gin-ge Chen","avatar_url":"https://avatars-next.observableusercontent.com/73f0dccc0b7fc5c845e6a52a58e01a2ae432cc529aaada0d10ab602137e603c0","tier":"starter_2024"},"version":273,"publish_version":273,"role":null,"authored":false,"authors":[{"type":"individual","id":"5c13a1a27cf52564","login":"bryangingechen","name":"Bryan Gin-ge Chen","avatar_url":"https://avatars-next.observableusercontent.com/73f0dccc0b7fc5c845e6a52a58e01a2ae432cc529aaada0d10ab602137e603c0","tier":null}],"members":[{"type":"individual","id":"5c13a1a27cf52564","login":"bryangingechen","name":"Bryan Gin-ge Chen","avatar_url":"https://avatars-next.observableusercontent.com/73f0dccc0b7fc5c845e6a52a58e01a2ae432cc529aaada0d10ab602137e603c0","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":2,"collection":{"id":"1bd9754ae5c8b895","slug":"morsels","title":"Morsels","owner":{"id":"d2fd23101beb2a61","login":"bryangingechen","name":"Bryan Gin-ge Chen"}},"type":"notebook","body":{"title":"Poisson, KPZ and Quenched KPZ","cells":[{"id":0,"value":"md`# Poisson, KPZ and Quenched KPZ`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":152,"value":"{ \n if (navigator.userAgent.match('HeadlessChrome'))\n return html``;\n return md`See Kim Krieger's article [\"Coffee Stains Test Universal Equation\"](https://physics.aps.org/articles/v6/7), which describes the paper:\n\n* Peter J. Yunker, Matthew A. Lohr, Tim Still, Alexei Borodin, D. J. Durian, and A. G. Yodh, [\"Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Drops of Colloidal Suspensions\"](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.035501#supplemental), Phys. Rev. Lett. 110, 035501 (2013), [arXiv:1209.4137](https://arxiv.org/abs/1209.4137).\n\nSee also [these tweets of mine](https://twitter.com/blockspins/status/1094086525351088128).`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":190,"value":"{\n if (navigator.userAgent.match('HeadlessChrome'))\n return html``;\n return md`## Poisson growth\n\nIn this model, particles fall from the top to the bottom and settle when they either hit the bottom or land on top of another settled particle. This and the following two models are what're known as \"ballistic deposition\" models of random surface growth.`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":96,"value":"poisson = {\n if (navigator.userAgent.match('HeadlessChrome'))\n // show the more exciting KPZQ in the thumbnail\n return show(particlesPoisson, fieldPoisson, updateParticleKPZQ(0.03), 5000);\n const ctx = DOM.context2d(width, height, 1);\n ctx.canvas.style.width = \"100%\";\n ctx.fillStyle = 'black';\n ctx.fillRect(0, 0, width, height);\n yield ctx.canvas;\n await visibility();\n yield* show(particlesPoisson, fieldPoisson, updateParticlePoisson, 5000);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":69,"value":"viewof resetPoisson = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":194,"value":"md`## KPZ growth\n\nIn this model, particles fall from the top to the bottom and settle when they either hit the bottom or land either on top of or next to another settled particle. Much more can be said about this fascinating model...`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"kpz = {\n // poisson; // little hack to prevent everything from running at once\n const ctx = DOM.context2d(width, height, 1);\n ctx.canvas.style.width = \"100%\";\n ctx.fillStyle = 'black';\n ctx.fillRect(0, 0, width, height);\n yield ctx.canvas;\n await visibility();\n yield* show(particlesKPZ, fieldKPZ, updateParticleKPZ, 5000);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"viewof resetKPZ = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":198,"value":"md`## Quenched KPZ growth\n\nIn this model, particles fall from the top to the bottom and settle when they either hit the bottom or land on top of another settled particle. The more particles have settled in a column, the more likely it is for particles to begin falling there; this effect is controlled by the parameter \"\\`strength\\`\" below. When \\`strength\\` is closer to 0, we recover the KPZ growth model, and when \\`strength\\` approaches 1, the model approaches a single growing column.\n\nFor details, see [the code](#updateParticleKPZQ). I'm not sure if the algorithm I used is exactly what Yunker et al did in their paper, since I can't access the Supplementary Info at the moment, but it seems to be in the same spirit.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"kpzq = {\n // kpz;\n const ctx = DOM.context2d(width, height, 1);\n ctx.canvas.style.width = \"100%\";\n ctx.fillStyle = 'black';\n ctx.fillRect(0, 0, width, height);\n yield ctx.canvas;\n await visibility();\n const update = updateParticleKPZQ(strength);\n yield* show(particlesKPZQ, fieldKPZQ, update, 5000);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":126,"value":"viewof resetKPZQ = {\n strength;\n return html``\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"viewof strength = slider({\n min: 0,\n max: 0.999,\n precision: 8,\n scale: input => Math.pow(input,5),\n description: \"Strength\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":216,"value":"md`## Code \n\nQuestions? Comments? Let me know at [@blockspins](https://twitter.com/blockspins).\n\nI copied some code from Tom MacWrights' [Diffusion-limited aggregation](https://beta.observablehq.com/@tmcw/diffusion-limited-aggregation) notebook. To the best of my knowledge, DLA and these KPZ-type models are not directly related (other than being beautiful models of random interfaces / surfaces), in statistical physics jargon, these models lie in distinct universality classes.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"function* show(particles, field, update, num=5000) {\n const ctx = DOM.context2d(width, height, 1);\n ctx.canvas.style.imageRendering = \"pixelated\";\n ctx.canvas.style.width = \"100%\";\n let maxStuck = height;\n let c = 0;\n while (maxStuck > 0 && particles.stuck.reduce((a,b) => a+b, 0) < count) {\n for (let i = 0; i < count; i++) {\n while (!particles.stuck[i]) {\n update(particles, field, i);\n c++;\n if (c % num === 0) {\n c=0;\n render(ctx, particles, i);\n yield ctx.canvas;\n }\n }\n if (particles.y[i] < maxStuck)\n maxStuck = particles.y[i];\n if (maxStuck === 0)\n break;\n }\n }\n render(ctx, particles);\n yield ctx.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"function render(ctx, particles, j=null) {\n ctx.fillStyle = 'black';\n ctx.fillRect(0, 0, width, height);\n const imageData = ctx.getImageData(0, 0, width, height);\n const data = imageData.data;\n\n for (var i = 0; i < count; i++) {\n if (particles.stuck[i] || i === j) {\n const x = particles.x[i];\n const y = particles.y[i];\n const fieldIndex = y * width + x;\n let index = fieldIndex * 4;\n // dumb choice of color; feel free to make suggestions / fork\n const [r, g, b] = hsl2rgb(Math.floor(360*i/count), 1, 0.5);\n data[index] = r; // red\n data[++index] = g; // green\n data[++index] = b; // blue\n data[++index] = 255; // alpha\n }\n }\n ctx.putImageData(imageData, 0, 0);\n\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"startParticle = (particles,i) => {\n particles.x[i] = Math.floor(Math.random()*width);\n particles.y[i] = 0;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"updateParticlePoisson = (particles,field,i) => {\n const x = particles.x[i];\n let y = particles.y[i];\n \n while (y < height-1 && !field[(y+1)*width + x]) ++y;\n particles.y[i] = y;\n particles.stuck[i] = 1;\n field[y*width + x] = 1;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"updateParticleKPZ = (particles,field,i) => {\n const x = particles.x[i];\n let y = particles.y[i];\n \n while (y < height-1 && !(field[(y+1)*width + x] || (x < width-1 && field[y*width + x+1]) || \n (x > 0 && field[y*width + x-1]) )) ++y;\n particles.y[i] = y;\n particles.stuck[i] = 1;\n field[y*width + x] = 1;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":114,"value":"updateParticleKPZQ = (strength) => {\n // begin with equal probability for each column\n const xcache = Array(width).fill(0).map((d,i) => i);\n return (particles,field,i) => {\n // select a random column from xcache\n const x = xcache[Math.floor(xcache.length*Math.random())];\n particles.x[i] = x;\n let y = particles.y[i];\n\n while (y < height-1 && !(field[(y+1)*width + x] || (x < width-1 && field[y*width + x+1]) || \n (x > 0 && field[y*width + x-1]) )) ++y;\n \n particles.y[i] = y;\n particles.stuck[i] = 1;\n field[y*width + x] = 1;\n \n while (Math.random() < strength) // strength had better be less than 1 or this will hang!\n xcache.push(x);\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":219,"value":"md`## Variables`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":81,"value":"width = Math.floor(window.innerWidth)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"height = Math.floor(width*3/4)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"count = height*width","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"particlesPoisson = {\n resetPoisson;\n const particles = ({\n x: new Uint16Array(count),\n y: new Uint16Array(count),\n stuck: new Uint8Array(count)\n});\n for (let i = 0; i < count; i++) {\n startParticle(particles, i);\n }\n return particles;\n};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":99,"value":"particlesKPZ = {\n resetKPZ;\n const particles = ({\n x: new Uint16Array(count),\n y: new Uint16Array(count),\n stuck: new Uint8Array(count)\n});\n for (let i = 0; i < count; i++) {\n startParticle(particles, i);\n }\n return particles;\n};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":128,"value":"particlesKPZQ = {\n resetKPZQ;\n const particles = ({\n x: new Uint16Array(count),\n y: new Uint16Array(count),\n stuck: new Uint8Array(count)\n});\n return particles;\n};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"fieldPoisson = {\n resetPoisson;\n return new Uint8Array(width * height);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":107,"value":"fieldKPZ = {\n resetKPZ;\n return new Uint8Array(width * height);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":130,"value":"fieldKPZQ = {\n resetKPZQ;\n return new Uint8Array(width * height);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":214,"value":"md`## Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":74,"value":"hsl2rgb = require(await FileAttachment(\"hsl-rgb-1.0.0.js\").url())","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"import {slider} from \"@lemonnish/nonlinear-slider\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 33:"$32:body"