On an iPhone running iOS8 Safari, when you save a bookmark to your home screen, Safari queries the web server for an apple-touch-icon.png file, and uses that as the icon. This is similar to a favicon used for bookmarks and URL bars in desktop browsers. Tableau Server ships with a 16x16 pixel file called apple-touch-icon-precomposed.png in its root web directory (C:\Program Files\Tableau\Tableau Server\8.x\wgserver\public\v_BUILDNUMBER). That naming convention has been superseded by apple-touch-icon.png but when I add such a file I can't get Safari to recognize it, but I think the problem is that Tableau Server is not serving it when requested. So the icon I get is a white box that changes with the latest contents of the web page which is not what I want.
If you point your iPhone at a standard website, like cnn.com, and save a bookmark to your home screen, you will get a custom icon. But I can't get this to work with our Tableau 8.1 Server running SSL. It won't use either the 150x150 apple-touch-icon.png file I added or the apple-touch-icon-precomposed.png that comes from Tableau. Interestingly, if I manually enter [tableau server]/apple-touch-icon-precomposed.png I will see the tiny icon in the browser, but if I request [tableau server]/apple-touch-icon.png I get a "No route matches" error. This suggests there may be special handling of these files. Any advice appreciated. Tableau tech support is out of ideas.
Here's a link to Apple's instructions and some other links.