Matpic
mathematics, in pictures
How this site is made

The figure library

Every picture here is generated from code. This is the list of generators, grouped by the field each was written for, with how many placements call it — which is both the reuse this collection lives on and the blast radius of changing one.

No figure on this site is a drawing that was made once and saved. Each one is a function: it takes parameters and returns SVG, so the same generator produces the four-rectangle version and the thirty-rectangle version of a picture without either being redrawn. There are 116 of them, called 6712 times across 1122 essays.

That indirection is the reason the collection can keep growing without the illustrations drifting apart. A generator is written once, checked once, and every essay that calls it inherits the same line weights, the same colour roles and the same behaviour in dark mode.

The count beside each name is the reuse ratio made visible — a generator called by one essay is a drawing wearing a function's clothes, and reusecheck fails the build over it. It is also the blast radius: changing a generator changes every figure in its list at once, which is worth knowing before the edit rather than after the rebuild. A bad shared helper once broke a hundred and eighty-one figures across four of these sites, and was caught only because somebody rebuilt immediately and knew where to look.

What each one proves is a different question, and it has a page of its own.

Geometry

13 generators · Shapes, and the arguments that can be made by rearranging them.

Analysis

9 generators · Limits, curves, and what happens when the going does not stop.

Algebra

8 generators · Structure — what stays true when the numbers change.

Discrete

12 generators · Counting, graphs, and things that come in whole pieces.

Topology

9 generators · What survives bending, and what does not.

Probability

10 generators · Randomness with a shape.

Number

11 generators · The whole numbers, and how much structure they turn out to have.

Dynamics

11 generators · One rule, applied over and over, and what the sequence does in the end.

Logic

15 generators · What can be said in a system, what follows from it, and what it cannot settle about itself.

Computation

11 generators · A fixed set of operations, and the exact question of what it can and cannot build.

Applied

7 generators · A rule for choosing, stated exactly, and what it forces on whoever adopts it.

What the figures prove · All essays