This comment by Matt Kelly seems to be the most pertinent

Regarding the similarity to a double slit interference pattern, what I found in my investigation (see my previous comment) is it was solely the result of the sorting algorithm used for the X coordinates of each possible outcome/weight. Ordering by the average X location results in a binomial distribution, but there are still ties to deal with. Applying secondary sorting to those based on the position of the left or rightmost X creates secondary binomial distributions within the main binomial distribution, similar to what Jonathan showed, except without all the spikiness because his example wasn’t consistently sorted in this manner.

You can see the sorting I’m talking about by looking at the sorting of Xs in the output of weights in Jonathan’s double-slit examples. The bottom half is sorted as I stated, but the top half is somewhat out of order, corresponding to the spikes in the tallest curve in the center of the graphs.

Maxime C, I had the same question as you – Why choose this sorting method for encoding the photon positions? My conclusion is that it doesn’t work however. Each additional step run with a large string produces an additional secondary binomial distribution. To get a smooth curve, we’d need to run billions of steps on a large string, but then we we’d also see billions of peaks, which no longer compares well with the expected diffraction pattern.