Fourier Epicycles
circles on circles drawing a curve that never repeats

What you see on every new tab

Fourier Epicycles draws the classic mathematical animation on the New Tab page: a chain of circles, each riding on the one before it, tracing a slowly changing curve. It is the picture behind every Fourier-series explainer, running live.

• Sixteen circles from big and slow to tiny and fast, each turning at its own rate.
• A trailing pen line that draws the resulting curve and fades as it goes.
• Breathing radii: without music, a slow synthetic spectrum keeps the circles growing and shrinking so the curve keeps evolving.

Nothing is a video. The scene is generated live on your graphics card with WebGL, so it never loops and never looks the same twice.

What it reacts to

• Music: bass drives the big low-order circles, mids the middle, treble the tiny fast ones. While synced, the drawing is literally the song's spectrum.
• Mouse: x sets the tempo, y skews the phases so the curve leans. The pointer never grabs anything, so a passing cursor only nudges the drawing.
• Night: darkens after dusk, following the sun at your location.

Free or Pro?Pro

Ambient New Tab is free to install, with three free themes. Fourier Epicycles is a Pro theme. Pro is a one-time $19 purchase, no subscription, and it unlocks every Pro theme, music sync, and every theme we release in the future. You can preview Fourier Epicycles full screen before you buy: open the Themes panel and rest your mouse on it. Changed your mind? 14-day refund, no questions.

How to get it

1. Add Ambient New Tab to Chrome (or Edge, Brave, Arc, Vivaldi, Opera).
2. Open a new tab and click the Themes pill in the bottom-right corner.
3. Pick Fourier Epicycles. Done.

Questions

What is an epicycle?

A circle whose centre rides on another circle. Chain enough of them at the right sizes and speeds and the end point can draw any closed curve; that is what a Fourier series says.

Is Fourier Epicycles free?

It is a Pro theme. Pro is a one-time $19 purchase, no subscription, that unlocks every Pro theme, music sync, and every future theme.

Is it light on the machine?

Yes. It is a 2-D drawing at a capped resolution and one of the lightest themes.

Does it work on my phone?

No. It's a desktop browser extension for Chrome and Edge on Windows, macOS, Linux and ChromeOS. If you're reading this on a phone, send yourself the link.

More themes

See every theme →