[quote:]
To save this state do I then add an action to the click event that saves a local storage variable - in this case imagex 'visible'. Then on page load add an event that retrieves the local storage variable imagex 'visible' ?
[/quote]
Yes
[quote:]
Just wondering if I can test this in the web browser or whether I would need to move it to the mobile environment?
[/quote]
Yes, you can easily test in any browser.
[quote:]
Although I haven't added any user-specific data that would remember that a particular user had made the particular change - I guess that is where parse.com would come in to create login credentials?
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Yes, one option is to use Parse. But maybe you don't have to, if it's one user per browser.