JavaScript is off, so the live parts of this page are not running. Everything written below is complete on its own and says what each computation does and what it produced — the empty rectangles are where it would have run in front of you. Nothing here needs an account, and nothing is hidden behind the scripts; they compute, they do not reveal.

Moving visuals on this page — measured at 0.26% brightness change per frame and zero flashes per second; your reduce motion setting stops them. What moves, and how it was measured

Mathematical plates that draw themselves — prime counts, orbits and lattices rendered live rather than shipped as pictures. It runs continuously while on screen, and it pauses on its own whenever it scrolls out of view.

We measured it rather than guessing: the largest frame-to-frame change in average brightness is 0.26%, and it produces zero flashes per second against the threshold of three set by WCAG 2.3.1. That is well under the limit, and it is not a promise about any individual: if moving images are a problem for you, you should not have to assess ours.

Everything animated on this site honours your system’s reduce motion setting — turn it on in your operating system or browser and these pages stop moving, with nothing else lost. All the mathematics is in the text and the still figures.

Entry 2 of 2 in Machines Run itMeasured

Why we never use floating point Machines

n! computed two ways, live — watch them agree, then quietly stop agreeing

Math: n! grows fast enough to leave IEEE-754 double precision's exact-integer range ( $2^{53}$ ) at a fixed, known n — not a rare edge case, a certainty. Dev: this site's own internal rule (never floats, only BigInt/exact fractions) exists precisely because of what's about to happen to the float column below.

Both cells compute the same n! as n counts up, live, right now — one in BigInt (unlimited precision), one in an ordinary JavaScript Number, the same IEEE 754 double most languages use for floating-point numbers. They agree exactly through 18!. From 19! on, Number is no longer guaranteed exact — it stays exact through 22! because the factors of two in n! cost no mantissa bits, and at 23! the odd part outgrows 2⁵³: from there it is provably wrong for every n after.

exact

float

← Previous in this roomOrbits, photons & ODE integrators

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Name	Type	Set by	Purpose	Duration
`ksec_theme`	localStorage	This site	Remembers your light/dark mode choice	Until you clear it
`ksec_cookie_ack_v1`	localStorage	This site	Remembers you've seen this notice	Until you clear it
`ksec_cookie_choice`	localStorage	This site	Remembers whether you accepted or rejected, so we do not ask again	Until you clear it
`ksec_build_notice_v1`	localStorage	This site	Remembers that you collapsed the build notice in the corner	Until you clear it
`ksec_notice_rev_v1`	localStorage	This site	The site revision you last loaded, so a page left open across a deploy can tell you it is stale	Until you clear it
`ksec_catalog_seen`	localStorage	This site	How many entries the shared catalogue had the last time you looked at it, so the nav can tell you when it has grown and stay quiet when it has not. One number. It says nothing about you — only about how much of a public list you have already seen	Until you clear it
`ksec_findings_seen`	localStorage	This site	The measurements of Life objects this browser has already sent to the shared catalogue, so it does not send the same one twice. A short list of numbers such as `p6:d0-0:n14` — period, displacement, population. It describes what the background drew, not you, and it never leaves your browser: what goes to the catalogue is the pattern itself, and the server measures it there	Until you clear it
`ksec_notebook`	localStorage	This site	The mascot’s research notebook on /mascot: the claims it tested in this browser, the seed, and the verdict, at most 40 entries. Never sent anywhere.	Until you clear it (there is a button on the page)
`ksec_last_visit`	localStorage	This site	When you were last here, so the mascot can tell you the site was rebuilt while you were away — and stay quiet when it was not. A timestamp, nothing else, and it never leaves your browser	Until you clear it
`ksec_tool_uses_…`	localStorage	This site	A per-tool daily-use counter for the free tools, one key per tool (a fair-use nudge, not an enforced limit, never sent anywhere) — set only if you actually use one of those tools	Resets daily; until you clear it
`__cf_bm` and similar	HTTP cookie	Cloudflare, Inc. (our security & CDN provider)	Distinguishes legitimate traffic from automated abuse — the same security gate described in Methodology	Session, typically under 30 minutes