I usually mock visualizations on paper! I'm interested in using WYSIWIG interactive diagram tools like http://aprt.us/ but I never seem to get into them. When I started, making the visualizations was the largest part of the work, but now I've gotten better at it, and making the explanation is now the part that takes the most time.
After paper, I often use SVG to make a non interactive diagram, either by hand, or in inkscape. One of my guiding principles is that the page should be usable without interaction, so the static diagram is a test of that. If it looks promising I can then gradually transform it into an interactive diagram. For example if I had the circle above, and I am using vue.js, I can change it to <circle :cx=x :cy=y r=100 fill=red/> (note the ":" before attributes), and then vue will fill those values in from the object I give it. I can give it {x: 300, y: 400}, and any time I change x or y, it will automatically redraw. I can then hook up x or y to a slider to try out the interactivity. This allows me to start with a static diagram, gradually add interactivity, and then build reusable abstractions that I can apply to multiple diagrams. ObservableHQ and React/JSX allow something similar, with slightly different syntax.
I'd love to see an article about regexes with interactive diagrams. There's a standalone diagram tool https://regexper.com/ and an interactive tutorial https://regexone.com/ but neither is an essay in the style of the Gears article. If you're pursuing this, let me know at redblobgames@gmail.com and I can send over more resources.