(p ∧ q) ∨ (¬p ∧ r) on the 2-by-4 map
karnaugh is one function. Everything below came out of it during this
build, at parameters taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and if the generator changes, this page
changes with it.
At its defaults
show: "gray"
show: "cover"
What it checks while it draws
Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.
- consecutive entries of the Gray code differ in exactly one bit ×1
- every cell of a prime implicant is one the function makes true ×1
- every leaf of the formula is a variable ×1
- every opening bracket in the formula is closed ×1
- squares next to each other on the map differ in one variable ×1
- the covering rectangles and the formula agree on every assignment ×1
- the formula and its disjunctive normal form agree on every row ×1
- the formula has between one and five variables ×1
- the formula is a non-empty string ×1
- the map is drawn for three or four variables ×1
- the table has one row per assignment ×1
- the whole formula is consumed by the parser ×1
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.
A formula is a corner of a cube
A formula about three letters is a set of eight rows. Written as a table that is a list; drawn on a cube it is a shape — and the shape is what almost every later question in this field turns out to be about.
LogicA proof with one rule
Two clauses that disagree about exactly one variable can be combined into a third that forgets it; repeat, and if the clauses cannot all be true the empty clause eventually appears — a complete proof system with a single move.
DiscreteA walk that changes one thing at a time
Counting from nothing to fifteen in binary changes four digits at once somewhere in the middle. There is another order through the same sixteen words in which every step changes exactly one — and it is a closed walk on a four-dimensional cube.
LogicThe map that puts neighbours side by side
Reorder the rows of a truth table so that neighbouring squares differ in one letter, and finding a short formula stops being algebra and becomes the problem of covering a shape with rectangles.