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#fractals

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Branching Dendrites

This award-winning aerial image by photographer Stuart Chape shows a tidal creek in Lake Cakora, New South Wales, Australia. At first glance, it looks much like any river delta, with branching dendritic paths that split into smaller and smaller waterways. That’s deceptive, though, because very different forces shape this creek. Because tides move in and out, a tidal creek is home to flows that move both directions — toward and away from the branches. That also means that flow speeds can change rapidly as the tides shift, which in turn changes which sediments get lifted, dropped, and moved around the creek bed. (Image credit: S. Chape/IAPOTY; via Colossal)

Fractal Fingers

As bizarre as the branching fractal fingers of the Saffman-Taylor instability look, they’re quite a common phenomenon. In his video, Steve Mould demonstrates how to make them by sandwiching a viscous liquid like school glue between two acrylic sheets and then pulling them apart. The more formal lab-version of this is the Hele-Shaw cell, which he also demonstrates. But you may have come across the effect when pealing up a screen protector or in dealing with a cracked phone screen. In all of these cases, a less viscous fluid — specifically air — is forcing its way into a more viscous fluid, something that it cannot manage without the fluid interface fracturing. (Video and image credit: S. Mould)

Vintage-Style Map of the Mandelbrot Set via Kottke [Shared]

Bill Tavis designed this lovely vintage-style map of the familiar fractal shape, the Mandelbrot set. He is selling a poster version of the map, starting at the very reasonable price of $24. I don’t usually highlight the price on this sort of thing, but an unauthorized seller on Amazon was selling poor-quality counterfeits of the map and even though it wasn’t his fault, Tavis offered to replace any of the crappy maps for free. Great map, and apparently a great human who made it.

welchwrite.com/blog/2025/04/26