What the fractal screensaver is
The rule generating all of this is short enough to fit on one line. Pick a point on the plane, square it, add the original point, and keep going. Some points shoot off to infinity and some never do. Colour each one by how many steps it took to escape, and the boundary between the two turns out to hold infinite detail.
The escape count is smoothed rather than used as a whole number. A plain count produces hard concentric bands, so the fractional part is recovered from how far past the escape circle the point landed, which is what turns those bands into continuous gradients.
- An ambient screen for an office, a lab or a classroom
- A live demonstration of what a two-line equation can produce
- A background that is genuinely never the same twice
Mandelbrot zoom as a screensaver
The descent runs into a fixed point on the boundary, deep in what is known as the seahorse valley, and covers about a thousandfold in magnification before it fades out and begins the same descent again. Both ends of that range were chosen by measuring rather than guessing. Come out much further and the frame is mostly the flat interior of the set; go much deeper and every pixel needs thousands of steps before it resolves, which no browser can do sixty times a second.
Detail raises the resolution the fractal is computed at, at the cost of frame rate — turn it up on a desktop and down on a phone. The palette scrolls independently of the zoom, which is what gives the colour its own slow motion through the image while the shapes hold still.
How to run the fractal screensaver full screen
Press the fullscreen button on the player, or the F key. Escape brings you back to the page. On a desktop browser F11 does the same job and hides the browser’s own toolbars as well, which is what you want on a display that is going to be left running.
Everything you change in the settings is written into the address bar as you change it, so the version you have set up is a link. Bookmark it, or send it to whoever is running the screen. Space pauses and resumes at any time.