blog photo / icon

I’m looking for a plug in that will create the same type of blog photo /icon that I have playing on a wordpress hosted blog — on a wordpress blog hosted on my own servers.

I’ve looked all over in plugins but all I’m finding is scores and scores of favicons which is not what I am looking for. I figure there’s got to be a plug in, since the wordpress sites have this feature automatically. It’s just buried?

Any help appreciated.

The site that has the blog photo /icon is here: http://celluloidblonde.wordpress.com

If you share the site on social media sites, an icon is attached to the site. That’s what I want to recreate in a wordpress blog that’s not hosted on wordpress.