Here's an easy to understand guide to calculating and plotting the Mandelbrot set by hand.
http://www.wikihow.com/Plot-the-Mandelbrot-Set-By-Hand
It's a laborious process but if you're really struggling to understand what's going on with all the mathematics underlying the set, doing it by hand is an excellent way to get a feel for it.
It reminds me of learning to program by typing in listings back in the 90s. Although not ideal, sometimes when you're struggling just applying practical action can help breakthroughs in understanding.
