Yes, a step was missing. I've updated it to include multiplication by "a" and loop back to step 4.
And yes, this is more complex than basic reasoning. It's an optimization to the original algorithm, and like most optimized algorithms, is less transparent.
Instead of shading in cells, consider a field of discrete, equally spaced points. For instance, mark the intersections on the graph paper instead of the open spaces.
The shapes are not constrained by taxicab geometry. Not only can you have diagonal lines, but you can have curves as well. The only difference from regular geometry is how the length of lines and curves is measured.
Consider creating taxicab shapes on graph paper. If you color in cells that satisfy the definition of a circle or ellipse, you're right that you won't see diagonal lines, only colored squares. If, however, you shrink the size of the grid further and further until it's infinitesimally small, those points will take on the appearance of diagonal lines.
I think it often does feel that way to kids, as most things with rules do. Even as an adult the commitment to taking a weekly break sometimes seems restrictive, but only in the short term. The long term effect is rejuvenating.
It's interesting to see the secular world discover the value of resting and disconnecting. I've long thought it interesting that Stephen Covey chose the seventh habit of highly effective people to be "Sharpen the Saw".
In regard to forcing others, individuals vary, but the SDA church as a whole has long opposed the state forcing citizens to observe a Sabbath. Any members who use physical force over the matter of Sabbath observance would probably use physical force over other things too, and likely says more about the individual's character than the character of the Sabbath, Sabbath-keeping, or sabbatarians.
I've used Clojure on and off but never really learned enough Java to be comfortable with it. Clojure-py has been a lot more fun because I can use the Python libraries I'm already familiar with.
I made an app that puts a feedback form on a website and emails the developer with user feedback. I know there are more sophisticated feedback management tools out there, but I wanted something simple.