I wrote a program to visualize binary expansions of fractions in the form of a grid. Each row is one fraction; for instance the third row is 1/3 = 0.010101... The digits are color-coded, gray for 1 and blue for 0.
When I made a big version of the grid (below) with many more fractions and one pixel per digit, I was surprised at how many patterns I saw. It's not shocking that there are prominent horizontal stripes around powers of 2, but there are also diagonal "stripes" and near-vertical structures. I can even convince myself there are various thick horizontal bands with different proportions of ones and zeros.
This feels like a pretty natural construction, so it must have been done before. Regardless, I'd be interested in any pointers or explanations of the stripes I'm seeing.