The cat, layer by layer

The cat from the cat map, now in grey, is written as a 96 × 96 table of numbers, each the brightness of one square. The singular value decomposition splits it into layers of plaid: each layer is a row pattern times a column pattern, weighted by one singular value σ. The slider adds up the first k layers, largest first: one layer gives a plaid-like pattern; by ten or so the face, the eyes and the ears are there; by forty it cannot be told from the original. The sum can dip below 0 in places, and those squares are tinted ice blue: none with one layer, some from two, most at three or four, and almost none by twenty. The bars on the left are the first 48 singular values on a log scale, gold once taken; from the 42nd on they are less than a ten-millionth of the first, too short to show, and adding them changes nothing you can see. The corner reads the relative error twice, once measured square by square on the table drawn and once from the singular values left out, and the two agree; with each layer added, the picture is the closest that many layers can get to the original. Under the bars is the count of numbers the first k layers take to store: at 48 layers it is more than the picture's own 9216.