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<!DOCTYPE html>
<html>
<head>
  <link rel="stylesheet" type="text/css" href="asciinema-player.css" />
</head>
<body>
  <div id="player"></div>
  <script src="asciinema-player.min.js"></script>
  <script>
    AsciinemaPlayer.create(
      '/assets/314833.cast',
      document.getElementById('player'),
      { cols: 68, rows: 16 }
    );
  </script>
</body>
</html>

See asciinema player quick-start guide for full usage instructions.

While this site doesn't provide GIF conversion at the moment, you can still do it yourself with the help of asciinema GIF generator utility - agg.

Once you have it installed, generate a GIF with the following command:

agg https://asciinema.org/a/314833 demo.gif

Or, if you already downloaded the recording file:

agg demo.cast demo.gif

Check agg --help for all available options. You can change font family and size, select color theme, adjust speed and more.

See agg manual for full usage instructions.