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.

The Collatz orbit of 27: 111 steps, peaking at 9232, on a log scale.

Collatz trajectory explorer Numbers & structure

Follow any starting number, exactly, with BigInt

$T(x) = \\dfrac{3x+1}{2^{v_2(3x+1)}}$

Same accelerated map as above — but here you choose the starting number (any size, exact BigInt arithmetic, not limited by floating-point precision) and see the whole trajectory. Type a positive whole number below and press Trace trajectory.

Math: the accelerated (odd-only) Collatz map, the same v₂ step as the live histogram above — every trajectory you trace here builds its own v₂ distribution behind the scenes, from exactly the number you typed, not a random sample. Dev: the path is drawn with self-hosted Paper.js (vector art, not a raster canvas trail) — the turn angle above controls how the same trajectory data gets rendered, it never changes the actual sequence of numbers.

steps to list art turn angle: 11°

collatz-explorer — output

trajectory, drawn as a path

Not decoration: one real segment per step, drawn with Paper.js (self-hosted, MIT). Segment length ∝ v₂ for that step; the path turns a fixed angle left or right, alternating — so the shape is a direct trace of your own number's trajectory, not generated from randomness.

trajectory (first 60 steps)

raw output, click to copy

← Previous toolThe calculator that never rounds Next tool →Miller-Rabin, step by step

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