Recently, I had a chat with a friend of mine about planning, understanding, and overview. Somehow, we both ended up agreeing on how amazing draw.io is. In my own case, I'd used it for mind maps/spider diagrams to help me further understand where automata comes from. My friend had simply asked me why I hadn't put it on my website yet, so here it is!
You may have to right-click the image above and select "Open Image in New Tab" (on Chrome) to be able to zoom into it.
Properties are green and definitions are blue/purple. At the very bottom of the image you'll see four green boxes: "Closure", "Associativity", "Identity", and "Inverse". These summarise the four axioms of group theory and are essentially the only things I understood when I first started trying to learn about how automata was constructed. You'll see how all four of these green properties are connected to the blue/purple definition of a group.
Next thing you may notice is the definition of a "monoid" next to that of a group. It's got all the same properties except that of the property "inverse". And so on, by learning about definitions and what properties they did or did not have, from bottom to top, I eventually learned how automata and rational language are constructed from my basic understanding.
LOVE talking about this stuff, so if anyone has any questions, please email me and I'll provide more clarity on here.
Draw.io for the win.