diff --git a/_posts/2017-10-19-tiling-shapes-proofs.md b/_posts/2017-10-19-tiling-shapes-proofs.md
index 68594a5..b06f9de 100644
--- a/_posts/2017-10-19-tiling-shapes-proofs.md
+++ b/_posts/2017-10-19-tiling-shapes-proofs.md
@@ -103,300 +103,4 @@ This procedure can be applied recursively on larger values of $n$ as well, so
this concludes a proof of tiling an equilateral triangle divided into $4^n$
equilateral triangles using trapezoidal tiles after removing a single piece.
-
+
diff --git a/js/tiling-shapes.js b/js/tiling-shapes.js
new file mode 100644
index 0000000..3426fac
--- /dev/null
+++ b/js/tiling-shapes.js
@@ -0,0 +1,295 @@
+(function() {
+ var tilingTriangle = document.getElementById('tiling-triangle');
+ var c = tilingTriangle.getContext('2d');
+
+ function TriangleCanvas(id) {
+ this.element = document.getElementById(id);
+ this.context = this.element.getContext('2d');
+ }
+
+ function modifyColor(c, p) {
+ var e = document.createElement('i');
+ e.style.background = c;
+ var r = getComputedStyle(e).backgroundColor.slice(4, -1).split(',').map(parseFloat);
+ return 'rgb(' + [r[0] + p, r[1] + p, r[2] + p].join(',') + ')';
+ }
+
+ function dedup(list) {
+ return list.reduce(function(newList, item) {
+ if (!newList.some(function(a) { return deepCompare(a, item) })) {
+ return newList.concat(item);
+ }
+ return newList;
+ }, []);
+ }
+
+ function deepCompare () {
+ var i, l, leftChain, rightChain;
+
+ function compare2Objects (x, y) {
+ var p;
+
+ // remember that NaN === NaN returns false
+ // and isNaN(undefined) returns true
+ if (isNaN(x) && isNaN(y) && typeof x === 'number' && typeof y === 'number') {
+ return true;
+ }
+
+ // Compare primitives and functions.
+ // Check if both arguments link to the same object.
+ // Especially useful on the step where we compare prototypes
+ if (x === y) {
+ return true;
+ }
+
+ // Works in case when functions are created in constructor.
+ // Comparing dates is a common scenario. Another built-ins?
+ // We can even handle functions passed across iframes
+ if ((typeof x === 'function' && typeof y === 'function') ||
+ (x instanceof Date && y instanceof Date) ||
+ (x instanceof RegExp && y instanceof RegExp) ||
+ (x instanceof String && y instanceof String) ||
+ (x instanceof Number && y instanceof Number)) {
+ return x.toString() === y.toString();
+ }
+
+ // At last checking prototypes as good as we can
+ if (!(x instanceof Object && y instanceof Object)) {
+ return false;
+ }
+
+ if (x.isPrototypeOf(y) || y.isPrototypeOf(x)) {
+ return false;
+ }
+
+ if (x.constructor !== y.constructor) {
+ return false;
+ }
+
+ if (x.prototype !== y.prototype) {
+ return false;
+ }
+
+ // Check for infinitive linking loops
+ if (leftChain.indexOf(x) > -1 || rightChain.indexOf(y) > -1) {
+ return false;
+ }
+
+ // Quick checking of one object being a subset of another.
+ // todo: cache the structure of arguments[0] for performance
+ for (p in y) {
+ if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
+ return false;
+ }
+ else if (typeof y[p] !== typeof x[p]) {
+ return false;
+ }
+ }
+
+ for (p in x) {
+ if (y.hasOwnProperty(p) !== x.hasOwnProperty(p)) {
+ return false;
+ }
+ else if (typeof y[p] !== typeof x[p]) {
+ return false;
+ }
+
+ switch (typeof (x[p])) {
+ case 'object':
+ case 'function':
+
+ leftChain.push(x);
+ rightChain.push(y);
+
+ if (!compare2Objects (x[p], y[p])) {
+ return false;
+ }
+
+ leftChain.pop();
+ rightChain.pop();
+ break;
+
+ default:
+ if (x[p] !== y[p]) {
+ return false;
+ }
+ break;
+ }
+ }
+
+ return true;
+ }
+
+ if (arguments.length < 1) {
+ return true; //Die silently? Don't know how to handle such case, please help...
+ // throw "Need two or more arguments to compare";
+ }
+
+ for (i = 1, l = arguments.length; i < l; i++) {
+
+ leftChain = []; //Todo: this can be cached
+ rightChain = [];
+
+ if (!compare2Objects(arguments[0], arguments[i])) {
+ return false;
+ }
+ }
+
+ return true;
+ }
+
+ TriangleCanvas.prototype.drawTriangle = function(x, y, size, fill, reversed) {
+ var c = this.context;
+ var corners = [{
+ x: x,
+ y: y,
+ }, {
+ x: x - size / 2,
+ y: y + size,
+ }, {
+ x: x + size / 2,
+ y: y + size,
+ }];
+
+ if (reversed) {
+ corners = [{
+ x: x + size / 2,
+ y: y,
+ }, {
+ x: x - size / 2,
+ y: y,
+ }, {
+ x: x,
+ y: y + size
+ }];
+ }
+
+ if (fill) {
+ this.drawShape(corners, modifyColor(fill, 20), fill);
+ } else {
+ this.drawShape(corners);
+ }
+ }
+
+ TriangleCanvas.prototype.drawTrapezoid = function(tiles, size, strokeStyle, fillStyle) {
+ var corners = tiles
+ .map(function(o) {
+ return { x: o[0] * size, y: o[1] * size };
+ });
+
+ console.log(corners);
+
+ this.drawShape(corners, strokeStyle, fillStyle);
+ }
+
+ TriangleCanvas.prototype.drawShape = function(corners, strokeStyle, fillStyle) {
+ var c = this.context;
+ c.beginPath();
+
+ c.moveTo(corners[0].x, corners[0].y);
+ corners.slice(1).concat([corners[0]]).forEach(function(object, index) {
+ c.lineTo(object.x, object.y);
+ });
+
+ c.closePath();
+ if (fillStyle) {
+ c.fillStyle = fillStyle;
+ c.fill();
+ }
+ if (strokeStyle) c.strokeStyle = strokeStyle;
+ c.stroke();
+ }
+
+ TriangleCanvas.prototype.drawSplittedTriangle = function(x, y, size, split, blocks, rest) {
+ var c = this.context;
+
+ var rows = Math.sqrt(split);
+ var rowHeight = size / rows;
+ var triangleSize = size / rows;
+
+ for (var i = 0; i < rows * 2; i += 2) {
+ var row = Math.floor(i / 2);
+
+ for (var j = 0; j < i + 1; j++) {
+ var position = {
+ x: x + triangleSize * j / 2 - (row * triangleSize / 2),
+ y: y + row * rowHeight,
+ };
+
+ var block = blocks.reduce(function(c, a) {
+ return (a[0] === row && a[1] === j) ? (a[2] || 'black') : c;
+ }, null);
+
+ this.drawTriangle(position.x, position.y, triangleSize, block || rest, j % 2 == 1);
+ }
+ }
+ }
+
+ var c1 = new TriangleCanvas('tiling-triangle');
+ c1.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, '#435062']], '#92afd7');
+
+ var c2 = new TriangleCanvas('base-case');
+ c2.drawSplittedTriangle(50, 0, 100, 4, [[0, 0, '#435062']], '#92afd7');
+
+ var c3 = new TriangleCanvas('n-2');
+ c3.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), [[0, 0, '#435062']], '#92afd7');
+
+ var c4 = new TriangleCanvas('n-2-grouped');
+ var groups = [
+ [0, 0, '#809bce'], [1, 0, '#809bce'], [1, 1, '#809bce'], [1, 2, '#809bce'],
+ [2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'],
+ [2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'],
+ [2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
+ ];
+ c4.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+
+ var c5 = new TriangleCanvas('n-2-grouped-removed');
+ var groups = [
+ [0, 0, 'rgb(90, 90, 90)'], [1, 0, '#809bce'], [1, 1, '#809bce'], [1, 2, '#809bce'],
+ [2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'],
+ [2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'],
+ [2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
+ ];
+ c5.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+ c5.context.strokeStyle = '#ff7777';
+ c5.context.lineWidth = 3;
+ c5.drawTriangle(100, 0, 100);
+
+ var c6 = new TriangleCanvas('n-2-grouped-neighbours');
+ var groups = [
+ [0, 0, '#e7ecf6'], [1, 0, '#e7ecf6'], [1, 1, '#e7ecf6'], [1, 2, '#e7ecf6'],
+ [2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#6d8699'],
+ [2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#657b73'],
+ [2, 4, '#d6eadf'], [3, 4, '#89958e'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
+ ];
+ c6.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+
+ var trapezoids = [
+ [[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
+ [[1, 2], [1.5, 3], [1, 4], [0, 4]],
+ [[3, 2], [4, 4], [3, 4], [2.5, 3]],
+ ];
+ c6.drawTrapezoid(trapezoids[0], 200 / 4, '#ff7777');
+ c6.drawTrapezoid(trapezoids[1], 200 / 4, '#ff7777');
+ c6.drawTrapezoid(trapezoids[2], 200 / 4, '#ff7777');
+
+ var c7 = new TriangleCanvas('final');
+ var groups = [
+ [0, 0, '#435062'], [1, 0, '#92afd7'], [1, 1, '#92afd7'], [1, 2, '#92afd7'],
+ [2, 0, '#95b8d1'], [3, 0, '#95b8d1'], [3, 1, '#95b8d1'], [3, 2, '#95b8d1'],
+ [2, 1, '#b8e0d2'], [2, 2, '#b8e0d2'], [2, 3, '#b8e0d2'], [3, 3, '#b8e0d2'],
+ [2, 4, '#d6eadf'], [3, 4, '#d6eadf'], [3, 5, '#d6eadf'], [3, 6, '#d6eadf'],
+ ];
+ c7.drawSplittedTriangle(100, 0, 200, Math.pow(4, 2), groups);
+
+ var trapezoids = [
+ [[1.5, 1], [2.5, 1], [3, 2], [1, 2]],
+ [[1, 2], [3, 2], [2.5, 3], [1.5, 3]],
+ [[1, 2], [1.5, 3], [1, 4], [0, 4]],
+ [[3, 2], [4, 4], [3, 4], [2.5, 3]],
+ [[1.5, 3], [1, 4], [3, 4], [2.5, 3]],
+ ];
+ trapezoids.forEach(function(el) {
+ c7.drawTrapezoid(el, 200 / 4, '#ff7777');
+ });
+}());