Quillwheel

Here a Turing machine is a brass copyist. Its quill rides a scroll of cells, reads one glyph, writes another and steps left or right by a rubric of lines that you write yourself. Run it slowly or at full pace, step back through any move, or tap a line so the run stops just before the quill uses it, while a trace under the scroll keeps the whole history of the run. Fifteen lessons in five folios begin with a single stroke and end with a machine that imitates other machines, and each folio also brings back to life Brother Tiquin, an old brass scribe found seized at his desk in a sandstone tower. Thirty copy orders give real work: erase a merchant tally, write the next binary number, put every A flag before every B, double a tally of sacks. The Judge tries your rubric on every example and awards up to three seals, for a correct result, for no more lines than the reference and for no more steps. On the shelf wait forty ready machines in six families, from adders and bracket checkers to the four-hour busy beaver and a loom that weaves rule 30. Five chronicles tell how the idea was found, starting with the 1936 paper by Alan Turing. Your best machines go into a codex with notes and a photo, and any of them can be saved to Photos as a card. Three bindings to choose from, works offline, no account.