Fractal Explorer: Deep Zoom

Fractal Explorer draws the Mandelbrot set, and four of its stranger relatives, with the whole power of your device behind it. Pinch, drag and rotate the way you would a photo. The image sharpens as you hold still and keeps up while you move.

Zoom until the arithmetic runs out

Ordinary fractal apps stop at about a million times magnification, where simple math gives up and the picture turns to mush. This one keeps going, past a million trillion trillion times: a grain of sand held against the visible universe. You can keep going down, and there is always more.

Fly

Press Fly and the view falls for as long as you let it. Drag to steer while it goes: you are looking for somewhere, not watching a video. Or choose a bookmark and fly there instead, and the app takes you from the widest view down to a location thirty digits deep, through every scale on the way.

Somewhere to start

Eleven landmarks come with the app, and they are the places the pictures come from: Seahorse Valley, Elephant Valley, the Misiurewicz point at the tip of the antenna, a satellite copy of the whole set buried in its own filaments, Douady's Rabbit, the Dendrite, the San Marco Dragon. Two are deep enough to be worth the trip on their own. Fly to any of them and watch how far down it is.

Five families, both directions

Mandelbrot, Burning Ship, Tricorn, Celtic and Perpendicular, at powers 2 through 6. Every one of them can be read the other way round as a Julia set, and the way to find a good one is to press and hold on a spot in the main image. The Julia that belongs to that point appears in place. The interesting constants sit on a boundary nobody can recite from memory, so pointing at it is the feature.

Color is a separate question from shape

Nine palettes and four coloring modes: smooth iteration, distance estimate, binary decomposition, and a shaded blend of the first two. Changing any of them recolors what is already on screen instantly, even thirty digits deep, so you can try every look at a location without waiting for it to be computed again. Gamma, contrast, palette repeat, the interior color and a slow automatic cycle are all there to be pushed around.

Bookmarks that follow you

Bookmark anything worth returning to. The location is saved at full precision, along with the colors you were using when you found it, and your bookmarks turn up on your other devices through your own iCloud account. The app reopens where you left it.

No accounts, no subscription, no ads, no tracking. Every pixel is computed on your device.