Brian Eno is well-represented in iOS. His other apps like Bloom, Trope and Air invite listeners to touch the screen to make their own composition. Reflection ($30.99) is different, there is no interaction for the listener. The interface has three buttons: a pause button, a sleep timer, and AirPlay. Reflection produces endless permutations of Eno’s 2017 album, an hour and five minute long title track.
“Just calling it an app is akin to saying Falling Water is just a building,” writes one app store reviewer. “I would not call this an app,” agrees another, “Between the music and visuals it’s more like sonic architecture.” The visuals consist of slowly morphing rectangles that only seem to change in the split second you look away from the screen.
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.