2d:null 2e:["$","title",null,{"children":"Game of Life | John C | Observable"}] 33:T45b,viewof opts2D = { //ref to https://observablehq.com/@s-haensch/multiple-inputs-in-a-cell const form = html` ` ; form.oninput = () => { form.value = [form.El.value, form.Eu.value,form.Fl.value, form.Fu.value, form.density.value]; } form.value = [form.El.value, form.Eu.value,form.Fl.value, form.Fu.value, form.density.value]; return form; } 34:T965,p5(s => { let rule = opts2D.map(n => parseInt(n)); rule.pop(); rule[4] = parseFloat(opts2D[4]) let cols = 120,rows = 80; let grid = (() => { let tem = new Array(cols); for (let i = 0; i < tem.length; i++) { tem[i] = new Array(rows); } return tem; })() let size = 5; s.setup = function () { s.createCanvas(600,400); for (let i = 0; i < grid.length; i++) { for (let j = 0; j < grid[i].length; j++){ let coin = s.random(1); if (coin < rule[4]) { grid[i][j] = 1; } else { grid[i][j] = 0; } } } s.frameRate(8); } s.draw = function () { s.background(255); grid.forEach((col,x) => { col.forEach((c,y) => { if (c) { s.fill(0); s.noStroke(); s.rect(size * x, size * y, size, size); } else { s.noFill(); s.stroke(140,150); s.rect(size * x, size * y, size, size); } }); }); updateGrid(); } const updateGrid = function () { let next = (() => { let tem = new Array(cols); for (let i = 0; i < tem.length; i++) { tem[i] = new Array(rows); } return tem; })() for (let i = 0; i < cols; i++) { for (let j = 0; j < rows; j++){ let pre = grid[i][j]; let sum = count(grid, i, j); if (pre) sum--; let nxt; if (pre) { if (sum >= rule[0] && sum <= rule[1]) { nxt = 1; } else { nxt = 0; } } else { if (sum >= rule[2] && sum <= rule[3]) { nxt = 1; } else { nxt = 0; } } next[i][j] = nxt; } } grid = next; } const count = function (grid, i, j) { let sum = 0; for (let k = -1; k < 2; k++) { for (let l = -1; l < 2; l++){ let x = (i + k + cols) % cols; let y = (j + l + rows) % rows; sum += grid[x][y]; } } return sum; } s.mouseClicked = function () { if (s.mouseX > s.width || s.mouseX < 0 || s.mouseY > s.height || s.mouseY < 0) return; for (let i = 0; i < grid.length; i++) { for (let j = 0; j < grid[i].length; j++){ let coin = s.random(1); if (coin < rule[4]) { grid[i][j] = 1; } else { grid[i][j] = 0; } } } } })35:T45b,viewof opts3D = { //ref to https://observablehq.com/@s-haensch/multiple-inputs-in-a-cell const form = html` ` ; form.oninput = () => { form.value = [form.El.value, form.Eu.value,form.Fl.value, form.Fu.value, form.density.value]; } form.value = [form.El.value, form.Eu.value,form.Fl.value, form.Fu.value, form.density.value]; return form; }36:Tc59,p5(s => { let rule = opts3D.map(n => parseInt(n)); rule.pop(); rule[4] = parseFloat(opts3D[4]); let xNo = 40, yNo = 40, zNo = 40; let grid = (() => { let tem = new Array(xNo); for (let i = 0; i < tem.length; i++) { tem[i] = new Array(yNo); for (let j = 0; j < tem[i].length; j++) { tem[i][j] = new Array(zNo); } } return tem; })() let size = 10; s.setup = function () { s.createCanvas(400,400,s.WEBGL); for (let i = 0; i < grid.length; i++) { for (let j = 0; j < grid[i].length; j++){ for (let k = 0; k < grid[i][j].length; k++) { let coin = s.random(1); if (coin < rule[4]) { grid[i][j][k] = 1; } else { grid[i][j][k] = 0; } } } } s.frameRate(2); } s.draw = function () { s.background(255); s.push(); s.translate(-s.height/2, -s.height/2, -300) s.rotateY(s.PI/4); grid.forEach((xa,x) => { xa.forEach((ya,y) => { ya.forEach((c,z) => { if (c) { s.fill(0,150); s.noStroke(); s.push(); s.translate(size/2 + size * x,size/2 + size * y,size/2 + size * z); s.box(size); s.pop(); } }); }); }); s.pop(); updateGrid(); } const updateGrid = function () { let next = (() => { let tem = new Array(xNo); for (let i = 0; i < tem.length; i++) { tem[i] = new Array(yNo); for (let j = 0; j < tem[i].length; j++) { tem[i][j] = new Array(zNo); } } return tem; })() for (let i = 0; i < xNo; i++) { for (let j = 0; j < yNo; j++) { for (let k = 0; k < xNo; k++) { let pre = grid[i][j][k]; let sum = count(grid, i, j, k); //if (sum!=0) console.log(sum); if (pre) sum --; let nxt; if (pre) { if (sum >= rule[0] && sum <= rule[1]) { nxt = 1; } else { nxt = 0; } } else { if (sum >= rule[2] && sum <= rule[3]) { nxt = 1; } else { nxt = 0; } } next[i][j][k] = nxt; } } } grid = next; //console.log(grid) } const count = function (g, i, j, k) { let sum = 0; for (let l = -1; l < 2; l++) { for (let m = -1; m < 2; m++) { for (let n = -1; n < 2; n++) { let x = (i + l + xNo) % xNo; let y = (j + m + yNo) % yNo; let z = (k + n + zNo) % zNo; sum += g[x][y][z]; } } } return sum; } s.mouseClicked = function () { if (s.mouseX > s.width || s.mouseX < 0 || s.mouseY > s.height || s.mouseY < 0) return; for (let i = 0; i < grid.length; i++) { for (let j = 0; j < grid[i].length; j++){ for (let k = 0; k < grid[i][j].length; k++) { let coin = s.random(1); if (coin < rule[4]) { grid[i][j][k] = 1; } else { grid[i][j][k] = 0; } } } } } })37:[] 31:{"id":"f9e075e3c69ce260","slug":"game-of-life","title":"Game of Life","thumbnail":"e9d871f5b2f7ca81fc57153a5dc27d6ef518162803f5696993d96a799e3df255","access_level":"public","create_time":"$D2021-10-23T08:58:50.977Z","update_time":"$D2021-10-23T09:01:33.976Z","view_time":null,"first_public_time":"$D2021-10-23T09:01:49.517Z","has_unpublished_edits":null,"fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"b2e9840be7b1b607","login":"real-john-cheung","name":"John C","avatar_url":"https://avatars-next.observableusercontent.com/1d9ef6121a0bbd1a75fab479f9891fe1d78cc65f76c394585ae1a7dad0d3abf6","tier":"starter_2024"},"version":32,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"e8e99acdbe3aebfb","login":"real-john-cheung","name":"John C","avatar_url":"https://avatars-next.observableusercontent.com/1d9ef6121a0bbd1a75fab479f9891fe1d78cc65f76c394585ae1a7dad0d3abf6","tier":null}],"members":[{"type":"individual","id":"e8e99acdbe3aebfb","login":"real-john-cheung","name":"John C","avatar_url":"https://avatars-next.observableusercontent.com/1d9ef6121a0bbd1a75fab479f9891fe1d78cc65f76c394585ae1a7dad0d3abf6","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":{"id":"aac27ce630a2ebd4","slug":"posts","title":"Posts","owner":{"id":"b2e9840be7b1b607","login":"real-john-cheung","name":"John C"}},"type":"notebook","body":{"title":"Game of Life","cells":[{"id":0,"value":"# Game of Life","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"

Based on: Candidates for the Game of Life in Three Dimentions by Cater Bays, Complex System. Vol 1, 1987

E: environment, the # of neibours alive to keep a cell alive.
\nF:fertility, the # of neibours alive to create a new alive cell.
\nfor E_l≤E≤E_u and F_l≤F≤F_u, we can define rule R=(E_lE_uF_lF_u).
Conway's Game of Life will be rule R=(2333)

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Philosophical questions: As you can see when you try to play with the above sketch, the pre-set R(3434) and Conway's Game of Life R(2333) are two of the few rules that create interesting (or \"alive\") behaviours in the all 1296 possible rules. Now the questions are: Why these two? And who choose them?
\nIf we expand the grid into 3D, we can see this rareness more clearly. With totally 123201 possible rules, only less than 1% of them creates \"alive\" behaviours. And also, they are more demanding for the initial status.

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