Two Lorenz-system paths that start one millionth apart: scrub or replay 30 time units and watch them stay glued together for most of the run, then split onto opposite wings of the butterfly. A small sensitivity demo, not the free-form Lorenz playground the name suggests.
One Millionth (the page's own headline is "One millionth. Two different paths.") is a small interactive experiment about sensitivity to initial conditions, the idea usually called chaos. It computes two paths of the Lorenz system, the three-equation weather model whose plot looks like a butterfly, and draws them on top of each other. Path A starts at x = 1. Path B starts at x = 1.000001. Everything else is identical, including the rules, and you can watch them separate.
It is not what the catalogue's short label, "Interactive Lorenz attractor", might suggest. There are no sliders for sigma, rho or beta, no rotating 3D view and no trail-length setting. The picture is flat (x across, z up), the equations are fixed, and the only thing you choose is how far apart the two starting points are, from three options, and when in time you look. What you get in exchange is a very clear demonstration of one fact: a difference too small to see can end up as a difference as large as the attractor itself.
The page is one route (/chaos) of a small site by Juy, who posts as @juyeam on X. That site is called Tiny Worlds. Its home page turns a name or X handle into a small floating low-poly island of houses, trees and clouds, the same island every time for the same name (juyeam's own is "Apricot Archipelago", with 15 homes and 16 groves). This page is a different kind of thing that sits beside it: a top-left "Tiny Worlds" link goes back to the island page, and "More experiments by @juyeam" leads to Juy's X profile. Both pages say they were built with Astra, and Juy's post says the same about this one.
How to play One Millionth
- The page opens already run to the end, at simulated time 30.00: a butterfly of faint grey lines (the full paths), with bright blue and orange tails showing the last two time units of each path and a dot at the current position of each. Below the paths the page shows the "separation in 3D", the straight-line distance between the two points, which at this moment is 13.619.
- Press Replay and the run starts from t = 0 and plays through to t = 30 in about 20 seconds (the page calls the playback accelerated). The button turns into Pause while it runs and Play once you pause. Or ignore the button and drag the time slider, which goes from 0 to 30 in steps of 0.01; the picture and the separation number follow your hand immediately. Reset returns to t = 0, paused, and Jump to t = 25 takes you to the moment just before the separation takes off (0.199 there).
- The three buttons on the right choose the starting difference in x: 0 (identical), 0.000001 or 0.001. With 0, the separation is exactly 0 for the whole run and only one path is visible, because the second is drawn exactly over the first. With 0.001, the same thing happens faster: by t = 30 the separation is 25.453. A read-out of the separation switches to scientific notation while it is tiny (for example 1.000e-6 at t = 0), so the growth is readable at every scale.
- It works with mouse, touch and keyboard: the slider takes arrow keys (0.01 per press), Page Down (10 back) and Home. On a phone (I tried a 390-pixel-wide iPhone profile) the page stacks into one column, does not scroll sideways, and both the buttons and the time slider respond to taps and finger drags.
Controls: Pick a starting difference (0, 0.000001 or 0.001), drag the time slider or press Replay, Reset returns to t = 0, and Jump to t = 25 skips ahead. Touch or mouse.
Click Fullscreen above the game for the largest play area. If the game does not load, use Open in new tab to play it directly from our copy.
Why it's worth your time
Credit first: the experiment is Juy's (@juyeam). In the X post that announces it, Juy says the Lorenz simulation and its 20-second animation were coded by Astra, and that the rules never change while a tiny difference in the starting x grows. The page itself adds that no AI call runs when you change a control. That last claim matches what I saw: after loading the live page, I switched it offline and it kept computing and responding, and it only ever talked to its own host, with no third-party scripts or trackers.
What I could check about the maths, I checked. The page states sigma = 10, rho = 28, beta = 8/3, fourth-order Runge-Kutta with a step of 0.000125, and both paths starting at y = 1, z = 1. Its own code uses the standard Lorenz equations with exactly those numbers. I then wrote my own independent Runge-Kutta run in Python with the same settings, and it reproduced the figures the page shows: separation 1.758e-6 at t = 10, 9.25e-4 at t = 20, 0.199 at t = 25 and 13.619 at t = 30 for a difference of 0.000001, and 25.453 at t = 30 for 0.001. The page also offers a downloadable Python script that does the same check; it is byte-identical in our mirror. I did not check any claim beyond these numbers.
The shape of the result is the interesting part. For a start difference of one millionth, the distance between the paths is still only about 1.8 millionths at t = 10, under a thousandth at t = 20, and around a fifth at t = 25. Then in five more time units it reaches 13.6, about the width of one wing of the attractor. In practice, through the middle of a Replay (I looked at about t = 16) you see a single orange line with the blue one hidden beneath it, and only later two separate loops. The page is careful about the limits: it says roundoff and integration error also grow, and that these are numerical paths, not exact long-term forecasts.
It computes both paths in your browser when the page loads (a few hundred thousand steps each). On my machine that finished in well under a second from the local copy, and switching the starting difference took about 0.2 seconds. Replay held 60 frames per second. There is no game, score or goal, so we label it a visualization and not a game.
Our copy is a full mirror of the /chaos page and the Tiny Worlds home page it links to, 1.5 MB in total with nothing near the 25 MB limit, and it runs offline. The mirror keeps the Python check and the Lorenz (1963) link, which still leads to the paper on the American Meteorological Society's site. This entry was found through Tripo's GPT-6 Astra prompt collection, where the catalogue lists it as "Interactive Lorenz attractor"; the creator's own page and post are the sources here.
How it was made and where it lives
Published through ChatGPT Sites (chatgpt.site) — the same hosting pipeline GPT-6 Astra uses to ship playable games straight from a prompt. The author publishes as juyeam. Original: https://tiny-worlds-juyeam.juyeam.chatgpt.site/chaos. The Play button above runs our own unmodified copy, so the game keeps working here if that page goes down — which on free hosting usually has nothing to do with the author. Nothing about the game itself is changed, and the original stays linked from every page.
ChatGPT Sites is the hosting side of the workflow OpenAI describes for building games with GPT-6 Astra: the model writes the game, then publishes it to a public address in one step. That is why so many of the newest single-file browser games are appearing on chatgpt.site domains.
The post that led us here
Juy@juyeamA 0.000001 change. Two different paths. Change the starting difference. Scrub through time. Try it in your browser: [link] Astra coded this Lorenz simulation and 20s animation. The rules never change.
If you like One Millionth, try these
For another piece of generative art with no goal, try Orbital Garden, 48,000 points of light you can reshape and photograph. For something in the same spirit of taking a subject apart to see how it works, RB19 Engineering Lab does it with a Formula 1 car.
Frequently asked questions
- Is this a game?
- No. It is a small interactive experiment with nothing to win. You choose a starting difference and move through time.
- Can I change sigma, rho and beta, or rotate the attractor?
- No. The page fixes sigma = 10, rho = 28 and beta = 8/3, draws a flat x-z view and only lets you pick one of three starting differences (0, 0.000001, 0.001) and the point in time.
- Are the numbers right?
- The equations and settings the page states are the standard Lorenz system, and an independent Python run reproduced the separations it shows (13.619 at t = 30 for 0.000001, 25.453 for 0.001). The page itself warns that these are numerical paths and not exact long-term forecasts.
- Does it work on a phone?
- Yes. In a phone-sized window the page becomes one column, and the buttons and the time slider both respond to touch, including a finger drag on the slider.
- Does it need the internet or an AI service?
- No AI runs when you use it, and once loaded it works offline. The maths runs in your browser. Our copy also runs with no network at all.
- Who made it?
- Juy (@juyeam on X), as one page of the Tiny Worlds site on ChatGPT Sites. Juy's post says Astra coded the simulation and the 20-second animation.
- Is One Millionth free to play?
- Yes. Everything on Floating Arcade is free, with no account, ads or downloads.
- Can I embed this game on my own website?
- Yes — copy the snippet below. The embedded player links back here, which is how we ask to be credited.
Embed One Millionth on your site
Paste this where you want the game to appear:
