JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="http://cdn.leafletjs.com/leaflet-0.6.4/leaflet.css">
<script src="http://cdn.leafletjs.com/leaflet-0.6.4/leaflet.js"></script>
<div id="map-tiles" class="map-tiles"></div>

CSS

.map-tiles {
    width: 500px;
    height: 500px;
    position: absolute;
    top: 0;
    left: 0;
}

.leaflet-marker-icon.animated {
    -webkit-transition: -webkit-transform 0.2s;
            transition: transform 0.2s;
}

JavaScript

(function () {
    var map = L.map('map-tiles', {
        zoom: 16,
        center: [59.913031, 10.741367]
    });

    var tiles = L.tileLayer('http://{s}.tiles.mapbox.com/v3/examples.map-zq0f1vuc/{z}/{x}/{y}.png', {
        tileSize: 256,
        maxZoom: 17,
        minZoom: 6,
        reuseTiles: true,
        detectRetina: true,
        unloadInvisibleTiles: true,
        updateWhenIdle: true
    });

    tiles.addTo(map);
    
    var divIcon = L.divIcon({
        iconSize: [39, 42]
    });

    var marker = L.marker([59.913031, 10.741367], { icon: divIcon});

    marker.addTo(map);

    window.setInterval(function () {
        var lat = 59.913031 + (0.0005 * Math.random()),
            lng = 10.741367 + (0.0005 * Math.random());
        marker.setLatLng([lat, lng]);
    }, 500);
    
    marker._icon.classList.add('animated')
})();