The circle outlining one seems interesting to me. I definitely didn't read the algorithm ahead of time, and I'm probably not as smart as a revolutionary genius computer scientist, but I thought of 2 basic algorithms in a few minutes.

You could iterate over the degrees 0 to 360, use trig functions to figure out where the point at that angle is, and plot the closest point. Might need to be a bit tricky about the step size, but I bet you could compute a decent guess from the radius using more trig functions. Of course that probably doesn't work if you don't have floating point and trig functions.

You could also split it into four quadrants. Plot each of the top, bottom, right, and left points by direct computation of adding/subtracting the radius, then for each quadrant, you start from the computed point, check 3 specific points in the appropriate direction for which way you're going in that quadrant, plot whichever one is closest to the radius away from the center, then repeat from that plotted point until you reach the computed point for the next quadrant. It would be tedious and repetitive, but should be doable. You could probably also avoid computing square roots by comparing the squares instead. So I guess you'd want something based on that idea to do it fast on 90s hardware.

An optimal algorithm is shockingly simple

https://en.wikipedia.org/wiki/Midpoint_circle_algorithm

Spoiler: https://gist.github.com/denkspuren/df24bf57ae3a44310631