30:T439,// toTheLimit // returns an array of every number min...max that can be found using only cartesian products of min...limit // requires plusOne, multiplyArray // to-do: maybe implement d3.cross toTheLimit = (min,limit,max) => { var baseset = plusOne(limit) // starts with 1, filtered later var fullset = [] var uniqueset = [] var hardstop = 5 // realistic performance hard stop function checkMin(num){return (num >= min)} function checkMax(num){return (num <= max)} function compareNumbers (a,b) {return a-b} // filters out numbers below min var baliset = baseset.filter(checkMin) for (var i=0; i <= hardstop; i++){ // break if went over var highest = baliset[baliset.length - 1] if (baliset[highest] > max){break} // multiply each element in the array by itself fullset = multiplyArray(baseset,baliset) // only keep unique values at or equal max uniqueset = [...new Set(fullset)] baliset = uniqueset.filter(checkMax) } // sort ascending, or 10 comes before 9 baliset.sort(compareNumbers) return baliset }31:[] 2e:{"title":"Cartesian Limits","cells":[{"id":0,"value":"# Cartesian Limits\n\nProvides an array of every whole number min...max that can be found using only prime numbers between min...limit\n\nFor example, a five-limit set would only include multiples of 1 through 5, and excludes 7, 11, 13, 14... as so:
\n${multiplyArray(plusOne(5),plusOne(5)).toString()},...\n\nThis is useful for math on musical intervals, among others.","pinned":false,"hidden":false,"mode":"md"},{"id":6,"value":"

This work by Alessandro G. Magnasco is licensed under CC BY-NC-SA 4.0

","pinned":false,"hidden":false,"mode":"html"},{"id":24,"value":"## Try it out!\nMaking a ${limitInput}-limit set of whole numbers between ${minInput}-${maxInput}, of which there are ${demo.length}.\n
The limit removed ${leftovers.length} numbers.","pinned":false,"hidden":false,"mode":"md"},{"id":56,"value":"viewof minInput = Inputs.range([1, 30], {label: \"Minimum:\", step: 1, value: 1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":53,"value":"viewof limitInput = Inputs.range([minInput, maxInput], {label: \"Limit:\", step: 1, value: 5})","pinned":false,"hidden":false,"mode":"ojs"},{"id":58,"value":"viewof maxInput = Inputs.range([minInput, 100], {label: \"Maximum:\", step: 1, value: 30})","pinned":false,"hidden":false,"mode":"ojs"},{"id":243,"value":"This set includes: \n
${demo.toString()}.\n\nThis set excludes:\n
${leftovers.toString()}.","pinned":false,"hidden":false,"mode":"md"},{"id":127,"value":"### (WIP) -- Visualized as a Sierpiński sieve (through Al-Karaji's triangle)\nRender by https://observablehq.com/@jonsadka/sierpinski-triangle","pinned":false,"hidden":false,"mode":"md"},{"id":130,"value":"// by Jon Sadka 2020\n// https://observablehq.com/@jonsadka/sierpinski-triangle\n{\n const svg = d3.select(DOM.svg(width, height));\n \n const pascal = svg.append(\"g\");\n const rows = pascal.selectAll(\".row\")\n\t .data(pascals)\n .enter().append(\"g\")\n .attr(\"class\", \"row\");\n\n rows.selectAll(\"rect\")\n .data(d => d)\n .enter().append(\"rect\")\n .attr(\"x\", (d, index) => x(index + d.offset) - dimension / 2)\n .attr(\"y\", (d, index) => y(d.rowNumber))\n .attr(\"width\", dimension)\n .attr(\"height\", dimension) \n .attr(\"fill\", color); \n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"## Preliminary math","pinned":false,"hidden":false,"mode":"md"},{"id":12,"value":"// multiplies every element in one array by every element in another one\n// heavy modification from original python by Sheshank S. 2019\n// https://stackoverflow.com/questions/57258804/divide-each-element-of-an-array-by-each-element-of-an-other-array\n\nmultiplyArray = (array1, array2) => {\n var newArray = []\n function compareNumbers (a,b) {return a-b}\n \n for (var i1=0; i1 < array1.length; i1++){\n for (var i2=0; i2 < array2.length; i2++){\n newArray.push(array1[i1]*array2[i2])\n newArray = [...new Set(newArray)] // only keep unique values\n }\n }\n // sort results before returning\n newArray.sort(compareNumbers)\n return newArray\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":16,"value":"// creates an array 1...limit\n// modified from Niko Ruotsalainen 2015 \n// https://stackoverflow.com/questions/3746725/how-to-create-an-array-containing-1-n\nplusOne = (limit) => {var list = Array.from({length: limit}, (_, i) => i + 1); return list}","pinned":false,"hidden":false,"mode":"ojs"},{"id":22,"value":"## toTheLimit and Unlimited\n\nInputs:\n- min: lowest number in set\n- limit: highest common divisor for set (usually a prime number)\n- max: highest number in set\n\ntoTheLimit creates an array of integers min...max with only the cartesian products of the set min...limit
\nUnlimited creates an array of integers limit...max with only the leftover multiples of primes excluded by the limit","pinned":false,"hidden":false,"mode":"md"},{"id":10,"value":"$30","pinned":true,"hidden":false,"mode":"ojs"},{"id":258,"value":"// Unlimited \n// finds all numbers excluded by a limit\n// requires plusOne, toTheLimit\n\nunlimited = (min, limit, max) => {\n // generate a list of every number min...max\n var baseset = plusOne(max)\n var fullset = baseset.filter(x => x >= min)\n // get the array with limit\n var limited = toTheLimit(min,limit,max)\n // filter out the limited set\n var unlimited = fullset.filter(x=> !limited.includes(x))\n\n return unlimited\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":132,"value":"## For the visualization","pinned":false,"hidden":false,"mode":"md"},{"id":61,"value":"demo = toTheLimit(minInput,limitInput,maxInput)","pinned":false,"hidden":false,"mode":"ojs"},{"id":256,"value":"leftovers = unlimited(minInput,limitInput,maxInput)","pinned":false,"hidden":false,"mode":"ojs"},{"id":170,"value":"import {dimension, generatePascalsTriangle, x, y, largeAdd, pascals} from \"@jonsadka/sierpinski-triangle\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"BigNumber = require(\"https://cdnjs.cloudflare.com/ajax/libs/bignumber.js/7.2.1/bignumber.min.js\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":211,"value":"// couldn't get it to pull local values with an import, so just copied over the code\n// by Jon Sadka 2020\n// https://observablehq.com/@jonsadka/sierpinski-triangle#color\n\nfunction color(d, i) {\n for (let mod = 2; mod < numberOfDivisors + 2; mod++){\n if (selectedMod.includes(`${mod}`) && largeMod(d.value, mod)) {\n return chromaColors(mod);\n }\n }\n return \"#F1F2F5\";\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":237,"value":"// idem, by Jon Sadka 2020\nfunction largeMod(number, mod) {\n return Number(BigNumber(number).modulo(mod).valueOf());\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":214,"value":"// idem, by Jon Sadka 2020\nchromaColors = function(mod) {\n const value = reverseColors === 'Yes' ? Math.abs(1 - (mod - 2) / (numberOfDivisors - 1)) : (mod - 2) / (numberOfDivisors - 1)\n return d3[colorScheme](value)\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":164,"value":"// using the base set min...limit to color the triangle\nselectedMod = demo.slice(\n // if demo starts at 1, start at 2 instead\n demo.findIndex(x=>x>=2),\n // end at limit\n demo.findIndex(x=>x==limitInput)+1\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":205,"value":"// using the entire limited set as divisors\nnumberOfDivisors = demo.length","pinned":false,"hidden":false,"mode":"ojs"},{"id":188,"value":"reverseColors = \"Yes\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":134,"value":"colorScheme = \"interpolateSpectral\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":154,"value":"depth = 128","pinned":false,"hidden":false,"mode":"ojs"},{"id":141,"value":"height = 400","pinned":false,"hidden":false,"mode":"ojs"},{"id":233,"value":"d3 = import('d3')","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}