9x.cl

About

What this is

9x is a cabinet of nine small machines. Each one takes a rule simple enough to write on a napkin and runs it until something appears that the rule does not obviously contain — a cardioid, a fractal, a road, π.

They are not illustrations. Every plate computes its picture in your browser from the rule itself, at whatever size your window happens to be, while you watch. The controls are not garnish; they are the whole argument. A claim like the golden angle is the only one that never lines up means very little as a sentence and is completely obvious after ten seconds of dragging a slider past it.

The through-line is emergence, and specifically the cheap kind: not "complicated things are complicated" but "here is a rule you can hold in your head, and here is the thing it does that nobody would have guessed." That gap is the most interesting object in mathematics, and it is very hard to photograph. It has to run.

How to use it

  • Every plate has a panel of controls. Changing one restarts the figure — except the speed and display settings, which take effect without interrupting it.
  • Every setting is written into the address bar. A figure you like has its own link — copy it, bookmark it, send it. Copy link does exactly that.
  • Save PNG exports the canvas at the resolution it is being drawn, which on a high-density screen is larger than it looks.
  • Plates run wider on a wide window. Several of them are worth resizing.
  • The theme follows your system setting until you press the switch in the header, after which it remembers what you chose.

The nine

  1. Plate I MultiplyJoin every number on a circle to its multiple. The threads pile up into a cardioid.
  2. Plate II SpiralWind the whole numbers into a square spiral and mark the primes. Diagonals appear.
  3. Plate III AntTwo rules on a grid. Ten thousand steps of chaos, and then, abruptly, a highway.
  4. Plate IV RuleEight bits of rule, one row of cells, and a complete catalogue of what can happen.
  5. Plate V NeedleDrop needles on a lined floor. Count the ones that cross a line. Out comes π.
  6. Plate VI HailHalve it or triple it and add one. Everything falls to 1, and nobody knows why.
  7. Plate VII SwingFour pendulums, two axes, and a pen that runs down. Ratios you can see.
  8. Plate VIII SeedTurn 137.5° between seeds and nothing ever lines up. Turn 137.4° and everything does.
  9. Plate IX FoldRoll a die, jump halfway to that corner, mark the spot. Repeat. Order from noise.

Honesty notes

Where a plate makes a claim, the claim is either proved, cited to a named result, or explicitly flagged as unproved. Three of the nine are built around open problems — the Collatz conjecture, the behaviour of Langton's ant, and the distribution of primes along quadratics — and in each case the page says so rather than implying the picture settles anything.

The one place a figure could mislead you is Plate V, and it does so on purpose: Buffon's needle looks like it is converging on π long before it has earned any of the digits it is showing. The shaded band is drawn precisely so you can see how much of the estimate is noise.

Privacy

There is no analytics, no cookie, no font service, no CDN, no embedded anything. The site makes no network requests at all after its own files have loaded. Nothing is stored about you except your theme choice, which lives in your own browser and never leaves it.

Accessibility

Every control is a real, labelled form element and the whole site is operable from the keyboard. Each canvas carries a text description of what it draws. Machines that would otherwise animate indefinitely stop on their own if your system asks for reduced motion, and every plate can be paused. Colour is never the only carrier of meaning: the readouts panel states in words whatever the picture is showing.

Reuse

The code is MIT-licensed and the prose is CC BY 4.0. Take the machines apart. That is more or less what they are for.

Colophon — how this was made →