Published
Edited
Apr 28, 2019
Importers
20 stars
Chandrupatla’s root-finding methodSidi’s root-finding methodRegular numbersDruidJS workerNatural breaksDistance to a segmentRay out of a convex hullWord Tour: 40k words and their friendsHello, @thi.ng/grid-iteratorsHead/tail breaksPseudo-blue noise shaderHow fast does walk-on-spheres converge?AoC 12: shortest path under constraintsKDE estimationPlot: Correlation heatmapPoisson Finish 2Poisson disk sampling functionsWoS with transportSimple and surprising sortLocal medianTime series topological subsamplingUnion-FindLevel set experiment 1Mean value coordinatesPoisson potentialMiddle-squareWorld of squares (spherical)World of squaresLargest Inscribed SquareHello, PyWaveletsGeothmetic meandianHello, Reorder.jsGeometric MedianImage FFTTransport to a mapDisc TransportTP3: Power Diagram and Semi-Discrete Optimal TransportThe blue waveHello, genetic-jsSliced Optimal TransportDruidJSSelf-Organizing Maps meet DelaunayHello, polygon-clippingseedrandom, minimalWalk on Spheres 2Walk on SpheresHello, AutoencoderKaprekar’s numberVoronoiMap2DHello, ccwt.jsPolygon TriangulationQuantile.invert?Linear congruential generatorHue blurNeedle in a haystackMoving average blurApollo 11 implementation of trigonometric functions, by Margaret H. Hamilton (march 1969)2D curves intersectionThe 2D approximate Newton-Raphson methodInverting Lee’s Tetrahedral projectionLinde–Buzo–Gray stipplingMean shift clustering with kd-tree2D point distributionsShortest pathKahan SummationHello, delatinDijkstra’s algorithm in gpu.jsLloyd’s relaxation on a graphManhattan DiameterManhattan VoronoiMobility landscapes — an introductionDijkstra’s shortest-path treeH3 odditiesProtein MatrixConvex Spectral WeightsSort stuff by similarityKrigingDelaunay.findTrianglen-dimensions binning?UMAP-o-MaticMNIST & UMAP-jsHello UMAP-jsMean shift clusteringLevenshtein transitionRd quasi-random sequencesAutomated label placement (countries)Phyllotaxis explainedMotionrugsPlanar hull (Andrew’s monotone chain algorithm)South Africa’s medial axisTravelling salesperson approximation with t-SNEDistance to shoreWorkerngraph: pagerank, louvain…t-SNE VoronoiCloud ContoursCircular function drawingKruskal MazeMyceliumTravelling salesperson approximation on the globe, with t-SNEtsne.jstsne.js & worker
Travelling with a self-organizing map
points = (replay,
Array.from({ length: 300 }, (_, i) =>
Object.assign([Math.random(), Math.random()], { index: i })
))
order = {
const D = d3.Delaunay.from(som.neurons);
const order = points.map(d => D.find(d[0], d[1]));
// return the new order — if something goes wrong (we receive -1), use the previous value
return order[0] === -1 ? this : order;
/*
// Quadtree version
const D = d3
.quadtree()
.addAll(som.neurons.map((d, i) => Object.assign(d, { index: i })));
const order = points.map(d => D.find(d[0], d[1]).index);
return order[0] === -1 ? this : order;
*/
}
som = {
const tsp = new TravelingSalesman();
tsp.maxCycles = 400;
tsp.createFirstNeuron();
tsp.cities = points.map((d, i) => ({ x: d[0], y: d[1] }));
var done, pos;
do {
done = tsp.surveyRun();
let n = tsp.neurons.start;
pos = [[n.x, n.y]];
for (let i = 0; i < tsp.neurons.length; i++) {
n = n.right;
pos.push([n.x, n.y]);
}
if (tsp.cycle > 3)
yield {
cycle: tsp.cycle,
length: tsp.neurons.tourLength(),
neurons: pos
};
} while (!done && tsp.cycle < tsp.maxCycles);
yield {
cycle: tsp.cycle,
length: tsp.neurons.tourLength(),
neurons: pos
};
}
TravelingSalesman = {
// copy-pasted from github.com/kifj/tsp-js
const $ = "we don't jQuery and a lot of this code is just ignored";
/* Sample of a city */
function Sample() {
this.x = 0.0;
this.y = 0.0;
}
Sample.prototype.draw = function(canvas) {
var centerX = this.x * canvas.width;
var centerY = canvas.height - this.y * canvas.height;
var ctx = canvas.ctx;
ctx.fillStyle = "#C06060";
ctx.beginPath();
ctx.arc(centerX, centerY, 3, 0, Math.PI * 2, true);
ctx.closePath();
ctx.fill();
};
/* a node in the neural network */
function Node(x, y) {
this.x = x;
this.y = y;
this.right = this;
this.left = this;
this.life = 3;
this.inhibitation = 0;
this.isWinner = 0;
}
/* the distance of the euklidian points */
Node.prototype.potential = function(sample) {
return (
(sample.x - this.x) * (sample.x - this.x) +
(sample.y - this.y) * (sample.y - this.y)
);
};
/* moves a single node in direction to the sample */
Node.prototype.move = function(city, value) {
this.x += value * (city.x - this.x);
this.y += value * (city.y - this.y);
};
/* computes the number of nodes between the to nodes on the ring */
Node.prototype.distance = function(other, length) {
var right = 0;
var left = 0;
var current = other;
while (current != this) {
current = current.left;
left++;
}
right = length - left;
return left < right ? left : right;
};
Node.prototype.draw = function(canvas) {
var centerX = this.x * canvas.width + 0.5;
var centerY = canvas.height - this.y * canvas.height + 0.5;
var ctx = canvas.ctx;
ctx.fillStyle = "#208020";
ctx.fillRect(centerX, centerY, 1, 1);
if (this.right != null) {
ctx.lineTo(
this.right.x * canvas.width + 0.5,
canvas.height - this.right.y * canvas.height + 0.5
);
}
};
/* the neural network as a ring of neurons */
function Ring(start) {
this.start = start;
this.length = 1;
}
/* moves all nodes to in direction of the sample */
Ring.prototype.moveAllNodes = function(city, gain) {
var current = this.start;
var best = this.findMinimum(city);
for (var i = 0; i < this.length; i++) {
current.move(city, this.f(gain, best.distance(current, this.length)));
current = current.right;
}
};
/* finds the node with the least distance to the sample */
Ring.prototype.findMinimum = function(city) {
var actual;
var node = this.start;
var best = node;
var min = node.potential(city);
for (var i = 1; i < this.length; i++) {
node = node.right;
actual = node.potential(city);
if (actual < min) {
min = actual;
best = node;
}
}
best.isWinner++;
return best;
};
/* deletes a node */
Ring.prototype.deleteNode = function(node) {
var previous = node.left;
var next = node.right;
if (previous != null) {
previous.right = next;
}
if (next != null) {
next.left = previous;
}
if (next == node) {
next = null;
}
if (this.start == node) {
this.start = next;
}
this.length--;
};
/* a node is duplicated & inserted into the ring */
Ring.prototype.duplicateNode = function(node) {
var newNode = new Node(node.x, node.y);
var next = node.left;
next.right = newNode;
node.left = newNode;
node.inhibitation = 1;
newNode.left = next;
newNode.right = node;
newNode.inhibitation = 1;
this.length++;
};
/* length of tour */
Ring.prototype.tourLength = function() {
var dist = 0.0;
var current = this.start;
var previous = current.left;
for (var i = 0; i < this.length; i++) {
dist += Math.sqrt(
(current.x - previous.x) * (current.x - previous.x) +
(current.y - previous.y) * (current.y - previous.y)
);
current = previous;
previous = previous.left;
}
return dist;
};
Ring.prototype.f = function(gain, n) {
return 0.70710678 * Math.exp(-(n * n) / (gain * gain));
};
/* the simulator containing all the data */
function TravelingSalesman() {
this.N = 100; /* Number of cities. */
this.cycle = 0; /* Number of complete survey done */
this.maxCycles = 1000; /* Number of complete suerveys */
this.cities = null; /* the samples */
this.neurons = null; /* the neurons */
this.alpha = 0.05; /* learning rate */
this.gain = 50.0; /* gain */
this.lastLength = null; /* length of tour */
this.isRunning = false;
this.update = 5; /* screen update */
}
/* creates the first node (ring) */
TravelingSalesman.prototype.createFirstNeuron = function() {
var start = new Node(0.5, 0.5);
this.neurons = new Ring(start);
};
/* deletes all nodes */
TravelingSalesman.prototype.deleteAllNeurons = function() {
if (this.neurons != null) {
while (this.neurons.start != null) {
this.neurons.deleteNode(this.neurons.start);
}
this.neurons = null;
}
};
/* prints positions of cities & nodes */
TravelingSalesman.prototype.print = function() {
console.log(
"TSP: N= " +
this.N +
", cycle=" +
this.cycle +
", lastLength=" +
this.lastLength
);
for (var i = 0; i < this.cities.length; i++) {
var c = this.cities[i];
console.log("City: " + i + " (" + c.x + "," + c.y + ")");
}
var n = this.neurons.start;
for (i = 0; i < this.neurons.length; i++) {
console.log("Node: " + i + "(" + n.x + "," + n.y + ")");
n = n.right;
}
};
/* creates & displaces randomly a given number of cities, returns the first */
TravelingSalesman.prototype.createRandomCities = function() {
this.cities = new Array(this.N);
for (var i = 0; i < this.N; i++) {
var c = new Sample();
c.x = Math.random();
c.y = Math.random();
this.cities[i] = c;
}
};
TravelingSalesman.prototype.stop = function() {
this.isRunning = false;
this.repaint();
this.cities = null;
this.deleteAllNeurons();
};
TravelingSalesman.prototype.start = function() {
this.stop();
this.init();
this.isRunning = true;
this.run();
};
TravelingSalesman.prototype.init = function() {
this.cycle = 0;
this.lastLength = null;
this.createFirstNeuron();
this.createRandomCities();
this.canvas = new Canvas(document.getElementById("canvas"));
this.repaint();
};
TravelingSalesman.prototype.run = function() {
if (this.neurons != null) {
if (this.cycle < this.maxCycles && this.isRunning) {
var done = this.surveyRun();
if (!done) {
var self = this;
window.setInterval(function() {
self.run();
}, 100);
return;
}
}
if (this.isRunning) {
//this.print();
this.isRunning = false;
this.repaint();
}
}
};
/* one cycle in the simulation */
TravelingSalesman.prototype.surveyRun = function() {
var done = false;
if (this.neurons != null) {
for (var i = 0; i < this.cities.length; i++) {
this.neurons.moveAllNodes(this.cities[i], this.gain);
}
}
this.surveyFinish();
this.gain = this.gain * (1 - this.alpha);
if (this.cycle++ % this.update == 0) {
var length = this.neurons.tourLength();
//this.print();
this.repaint();
if (length == this.lastLength) {
done = true;
} else {
this.lastLength = length;
}
}
return done;
};
/* after moving creating & deleting is done */
TravelingSalesman.prototype.surveyFinish = function() {
if (this.neurons == null) {
return;
}
var node = this.neurons.start;
for (var i = 0; i < this.neurons.length; i++) {
node.inhibitation = 0;
switch (node.isWinner) {
case 0:
node.life--;
if (node.life == 0) {
this.neurons.deleteNode(node);
}
break;
case 1:
node.life = 3;
break;
default:
node.life = 3;
this.neurons.duplicateNode(node);
break;
}
node.isWinner = 0;
node = node.right;
}
};
TravelingSalesman.prototype.repaint = function() {
if (!this.canvas) {
return;
}
this.canvas.ctx.clearRect(0, 0, this.canvas.width, this.canvas.height);
if (this.cities) {
for (var i = 0; i < this.cities.length; i++) {
var c = this.cities[i];
c.draw(this.canvas);
}
}
if (this.neurons) {
this.canvas.ctx.strokeStyle = "#80D080";
this.canvas.ctx.beginPath();
var n = this.neurons.start;
this.canvas.ctx.moveTo(
n.x * this.canvas.width + 0.5,
this.canvas.height - n.y * this.canvas.height + 0.5
);
for (i = 0; i < this.neurons.length; i++) {
n.draw(this.canvas);
n = n.right;
}
this.canvas.ctx.lineWidth = 1;
this.canvas.ctx.stroke();
this.canvas.ctx.closePath();
}
$("#cycle").val(this.cycle);
$("#length").val(this.lastLength);
$("#done").prop("checked", !this.isRunning);
if (this.isRunning) {
$("#run").attr("disabled", "disabled");
$("#stop").removeAttr("disabled");
} else {
$("#stop").attr("disabled", "disabled");
$("#run").removeAttr("disabled");
}
};
TravelingSalesman.prototype.setupForm = function() {
var self = this;
$("#cities").val(this.N);
$("#maxCycles").val(this.maxCycles);
$("#alpha").val(this.alpha);
$("#gain").val(this.gain);
$("#run").bind("click", function(event) {
self.N = $("#cities").val();
self.maxCycles = $("#maxCycles").val();
self.alpha = $("#alpha").val();
self.gain = $("#gain").val();
self.start();
});
$("#stop").bind("click", function(event) {
self.stop();
});
};
function Canvas(elem) {
this.elem = elem;
this.ctx = elem.getContext("2d");
this.height = elem.height;
this.width = elem.width;
}
return TravelingSalesman;
}
d3 = require("d3-scale@2", "d3-geo@1", "d3-delaunay@4")
One platform to build and deploy the best data apps
Experiment and prototype by building visualizations in live JavaScript notebooks. Collaborate with your team and decide which concepts to build out.
Use Observable Framework to build data apps locally. Use data loaders to build in any language or library, including Python, SQL, and R.
Seamlessly deploy to Observable. Test before you ship, use automatic deploy-on-commit, and ensure your projects are always up-to-date.