Why are there these patterns in these pathtraced images?

Question

I've written a path tracing renderer for a technology class, and, while examining the histograms of the resulting images, I found a weird wavy pattern. The resultant image is the average of many passes, and my program can also store values above 255 internally, but clips them to 255 before writing the file. Why does this happen? 1 pass:

2 passes:

25 passes:

50 passes:

100 passes:

5000 passes:

Answer 1

To simplify matters assume that you generate a sequence of random images (noise) but all with a fixed given histogram (e.g. the histogram of your first image). Then averaging a number of these images will result in an image with a histogram that is (approximately) a convolution power of the given fixed histogram. My guess is that something like that is happening here as well. Since now the image has a strong spatial correlation the result will not simply be a convolution but something similar. The bins in the histogram will smooth out with the number of samples.