These docs are for an old release. Info on upgrading to v4
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now

Explicitly sets the “today” date of the calendar. This is the day that is normally highlighted in yellow.

Moment, function

Normally, the local browser’s current date is used.

You can override the current date by providing a Moment-like value, such as an ISO8601 date string like "2013-12-01T00:00:00".

You can also provide a function that returns a Moment-like value.

Overriding the current date is particularly useful when your calendar is using a custom timezone parameter. The current year/month/date in the custom timezone might be different than the local computer’s current date.

You’ll most likely want to calculate this with a server-side script and inject it into the settings of the calendar. Here is an example in PHP:

<?php
  $datetime = new DateTime('now', 'America/Chicago');
  $datetime_string = $datetime->format('c');
?>

$('#calendar').fullCalendar({
  now: <?php echo json_encode($datetime_string) ?>
});