Blockly

This really is very cool.  Below is a screen shot of my solution to the non simply connected maze where your algorithm allows for no 'memory'.

You need a memory because just 'follow-the-left/right-hand-wall' will result in you getting 'stuck-in-the-loops'.

The Blockly demo does allow for a 'random-turn' and that was what saved the day.  On the downside; there is a non zero probability that it will take an arbitrary amount of time to solve a maze with loops using the algorithm I give.

And here is the link to the site "http://blockly-demo.appspot.com/blockly/demos/maze/index.html"

From