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// add your points
var points = [
    {
        "type": "Feature",
        "geometry": {
            "type": "Point",
            "coordinates": [0, 0]
        },
        "properties": {}
    },
    {
        "type": "Feature",
        "geometry": {
            "type": "Point",
            "coordinates": [10, -10]
        },
        "properties": {}
    },
    {
        "type": "Feature",
        "geometry": {
            "type": "Point",
            "coordinates": [50, 50]
        },
        "properties": {}
    }
]

// add a variable for keeping track of points
var y = 0;

// Start drawing the polyline.
add();

function add() {

    // add a point on the line for the new marker
    polyline.addLatLng(
        L.latLng(points[y].geometry.coordinates[1],
            points[y].geometry.coordinates[0])
    );


    // Pan the map along with where the line is being added.
    map.setView(points[y].geometry.coordinates, 3);

    // Continue to draw and pan the map by calling `add()`
    // until `y` reaches the number of points
    if (++y < points.length) window.setTimeout(add, 1000);
}

<!DOCTYPE html>
<html>
<head>
    <meta charset='utf-8' />
    <title>Animate a line</title>
    <meta name='viewport' content='initial-scale=1,maximum-scale=1,user-scalable=no' />
    <script src='https://api.tiles.mapbox.com/mapbox-gl-js/v0.50.0/mapbox-gl.js'></script>
    <link href='https://api.tiles.mapbox.com/mapbox-gl-js/v0.50.0/mapbox-gl.css' rel='stylesheet' />
    <style>
        body { margin:0; padding:0; }
        #map { position:absolute; top:0; bottom:0; width:100%; }
    #route {
  stroke-dasharray: 1000;
  stroke-dashoffset: 1000;
  animation: dash 1s linear alternate infinite;
}

@keyframes dash {
  from {
    stroke-dashoffset: 1000;
  }
  to {
    stroke-dashoffset: 0;
  }
}
    </style>
</head>
<body>

<div id='map'></div>
<script>
mapboxgl.accessToken =
  "pk.eyJ1IjoiaHllb25namlua2ltIiwiYSI6ImNpZXh4dXp5eDA2YjFzaGtyOGR2dnBza2oifQ.a5K673tSr0cOcYoX1rpPhg";

var map = new mapboxgl.Map({
    container: 'map',
    style: 'mapbox://styles/mapbox/streets-v9',
    center: [-122.486052, 37.830348],
    zoom: 5
});

map.on('load', function () {

    map.addLayer({
        "id": "route",
        "type": "line",

        "source": {
            "type": "geojson",
            "data": {
                "type": "Feature",
                "properties": {},
                "geometry": {
                    "type": "LineString",
                    "coordinates": [
                        [-122.414, 37.776],
                        [-77.032, 38.913]
                    ]
                }
            }
        }
    });

});
</script>

</body>
</html>