benoît M vs Fractal Explorer

benoît M is a visual exploration of the Mandelbrot set — one of the most iconic and fascinating shapes in mathematics. Named in homage to Benoît Mandelbrot, who discovered this fractal-set named after him in 1979. The mathematician introduced the world to fractal geometry. This app lets you dive into a universe created from one deceptively simple formula: repeat z² + c, again and again. From that small rule emerge endless spirals, islands, valleys, coastlines, and self-similar structures that continue to reveal new detail as you zoom deeper. With real-time Metal rendering, benoît M turns fractal exploration into a smooth, visual experience. Pinch to zoom, pan to move, and double-tap to dive into interesting regions. Switch between classic Mandelbrot rendering and a beautiful pseudo-3D relief mode that gives the fractal a sculptural, almost metallic depth. Customize the look with image gradients, procedural palettes, inverted or flipped color styles, and adjustable iteration quality. When you find a scene worth keeping, export it as a square high-resolution PNG — up to 8K — directly to your Photo Library. Features: - Explore the Mandelbrot set interactively - Smooth Metal-based rendering - Classic Mandelbrot and pseudo-3D relief modes - Image-based and procedural color gradients - Adjustable iteration depth - Pinch, pan, and double-tap navigation - High-resolution PNG export: 2K and 8K - Saved app state, so you continue where you left off A compact tribute to Benoît Mandelbrot and the beauty of fractal geometry Whether you are fascinated by mathematics, generative art, abstract visuals, or simply beautiful patterns, benoît M invites you to explore infinity — one zoom at a time.

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.