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PI Monte Carlo Pi Approximation in Vega
Raw
.block
license: bsd-3-clause
Raw
index.html
<!DOCTYPE html>
<head>
<meta charset="utf-8">
<script src="https://cdn.jsdelivr.net/npm/vega@3"></script>
<script src="https://cdn.jsdelivr.net/npm/vega-embed@3"></script>
<style>
body {
font-family: sans-serif;
}
.vega-actions a {
padding: 0.2em;
}
</style>
</head>
<body>
<div id="vis"></div>
<script>
const spec = "pi.vg.json";
vegaEmbed('#vis', spec, {actions: false, renderer: 'canvas'});
</script>
</body>
Raw
pi.vg.json
{
"$schema": "https://vega.github.io/schema/vega/v3.0.json",
"autosize": "pad",
"padding": 5,
"height": 380,
"data": [
{
"name": "random_data",
"transform": [
{"type": "sequence", "start": 1, "stop": 4000},
{"type": "formula", "as": "x", "expr": "random()"},
{"type": "formula", "as": "y", "expr": "random()"},
{"type": "filter", "expr": "datum.data <= num_points"}
]
},
{
"name": "pi_estimates",
"source": "random_data",
"transform": [
{"type": "formula", "as": "is_inside", "expr": "(datum.x * datum.x + datum.y * datum.y) < 1"},
{"type": "window", "fields": ["is_inside"], "ops": ["sum"], "as": ["num_inside"]},
{"type": "formula", "as": "estimate", "expr": "4 * datum.num_inside / datum.data"}
]
},
{
"name": "pi_estimate",
"source": "pi_estimates",
"transform": [
{"type": "filter", "expr": "datum.data == num_points"},
{"type": "formula", "as": "value", "expr": "datum.estimate"}
]
},
{
"name": "pi",
"values": [{ "value": 3.141592653589793 }]
}
],
"signals": [
{
"name": "num_points",
"value": 1000,
"bind": {
"input": "range",
"min": 1,
"max": 4000,
"debounce": 10
}
}
],
"layout": {
"padding": {
"row": 10,
"column": 10
},
"offset": 20,
"bounds": "full",
"align": "all"
},
"marks": [
{
"type": "group",
"title": {
"text": "In Points and Out Points"
},
"style": "cell",
"encode": {
"update": {
"width": {
"signal": "height"
},
"height": {
"signal": "height"
}
}
},
"marks": [
{
"type": "symbol",
"style": [
"circle"
],
"from": {
"data": "random_data"
},
"encode": {
"update": {
"opacity": {
"value": 0.6
},
"fill": [
{
"test": "sqrt(datum['x'] * datum['x'] + datum['y'] * datum['y']) <= 1",
"value": "#003f5c"
},
{
"value": "#ffa600"
}
],
"x": {
"scale": "x_scale",
"field": "x"
},
"y": {
"scale": "y_scale",
"field": "y"
},
"shape": {
"value": "circle"
}
}
}
}
],
"axes": [
{
"scale": "x_scale",
"orient": "bottom",
"title": "x",
"labelFlush": true,
"labelOverlap": true,
"zindex": 1
},
{
"scale": "x_scale",
"orient": "bottom",
"grid": true,
"gridScale": "y_scale",
"domain": false,
"labels": false,
"maxExtent": 0,
"minExtent": 0,
"ticks": false,
"zindex": 0
},
{
"scale": "y_scale",
"orient": "left",
"title": "y",
"labelOverlap": true,
"zindex": 1
},
{
"scale": "y_scale",
"orient": "left",
"grid": true,
"gridScale": "x_scale",
"domain": false,
"labels": false,
"maxExtent": 0,
"minExtent": 0,
"ticks": false,
"zindex": 0
}
]
},
{
"type": "group",
"name": "concat_1_group",
"title": {
"text": "Pi Estimation"
},
"style": "cell",
"encode": {
"update": {
"width": {
"signal": "height"
},
"height": {
"signal": "height"
}
}
},
"marks": [
{
"type": "symbol",
"style": [
"circle"
],
"from": {
"data": "pi_estimates"
},
"encode": {
"update": {
"opacity": {
"value": 0.7
},
"fill": {
"value": "#4c78a8"
},
"x": {
"scale": "data_point_scale",
"field": "data"
},
"y": {
"scale": "pi_scale",
"field": "estimate"
},
"size": {
"value": 8
},
"shape": {
"value": "circle"
}
}
}
},
{
"type": "rule",
"from": {
"data": "pi"
},
"encode": {
"update": {
"stroke": {
"value": "darkgrey"
},
"x": {
"value": 0
},
"y": {
"scale": "pi_scale",
"field": "value"
},
"x2": {
"field": {
"group": "width"
}
}
}
}
},
{
"type": "text",
"from": {
"data": "pi"
},
"encode": {
"update": {
"align": {
"value": "left"
},
"x": {
"value": 10
},
"fill": {
"value": "black"
},
"y": {
"scale": "pi_scale",
"field": "value",
"offset": -5
},
"text": {
"value": "Real PI: 3.1415..."
}
}
}
},
{
"type": "text",
"from": {
"data": "pi_estimate"
},
"encode": {
"update": {
"align": {
"value": "right"
},
"x": {
"signal": "height",
"offset": -5
},
"dy": {
"value": -5
},
"fill": {
"value": "black"
},
"y": {
"scale": "pi_scale",
"field": "value"
},
"text": {
"signal": "'Estimate: ' + format(datum.estimate, ',.3f')"
}
}
}
}
],
"axes": [
{
"scale": "data_point_scale",
"orient": "bottom",
"title": "Number of Points",
"labelFlush": true,
"labelOverlap": true,
"zindex": 1
},
{
"scale": "data_point_scale",
"orient": "bottom",
"grid": true,
"gridScale": "pi_scale",
"domain": false,
"labels": false,
"maxExtent": 0,
"minExtent": 0,
"ticks": false,
"zindex": 0
},
{
"scale": "pi_scale",
"orient": "left",
"title": "Estimated Pi Value",
"labelOverlap": true,
"zindex": 1
},
{
"scale": "pi_scale",
"orient": "left",
"grid": true,
"gridScale": "data_point_scale",
"domain": false,
"labels": false,
"maxExtent": 0,
"minExtent": 0,
"ticks": false,
"zindex": 0
}
]
}
],
"scales": [
{
"name": "x_scale",
"type": "linear",
"domain": [0,1],
"range": "height",
"reverse": true,
"nice": true,
"zero": true
},
{
"name": "y_scale",
"type": "linear",
"domain": [0,1],
"range": "height",
"nice": true,
"zero": true
},
{
"name": "data_point_scale",
"type": "linear",
"domain": {
"data": "pi_estimates",
"field": "data"
},
"range": "height",
"reverse": true,
"nice": false,
"zero": true
},
{
"name": "pi_scale",
"type": "linear",
"domain": {
"fields": [
[2, 4],
{
"data": "pi",
"field": "value"
},
{
"data": "pi_estimates",
"field": "estimate"
}
]
},
"range": "height",
"nice": true,
"zero": false
}
],
"config": {
"axisY": {
"minExtent": 30
}
}
}
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