Here is my take.
- The rising smoke makes a line that carries the viewer up to our hapless hero who is about to pay for his heresy. Actually, he would have said the heretics are burning him. He was a 17th century Russian clergyman who opposed the changes meant to modernize the church. He wrote a series of letters that are evidently classics of Russian literature.
- The guy in the fur coat is juxtaposed in front of dark figures and leans backwards at such an angle that the straight line of the front of his coat counteracts and balances the line of the rising smoke. There is a clear unobstructed alley of light snow from the bottom of the painting leading up to the base of the figure. That draws more attention to him. He must be in charge of the burning. The figure of this official and our hero at the stake are the balanced protagonists about which this picture revolves. They are the two whose faces are most distinctly shown. Everyone else is either turned away from the viewer or small and in the background.
- The spear on the right points us up to Avvakum, it also is a reminder of the spear that was used to pierce the side of Christ. The man holding the spear is restraining a woman who is objecting to the burning, and both their figures close off the exit from that corner and lean inwards directing our view to the figures on the stakes..
- Over and over dark figures have been laid over light backgrounds and light figures set against dark backgrounds.
- The line of the rifle is a balance to the line of the rising smoke. They are opposites and relieve one another. I find the rifle crossing the head of the man behind it a little uncomfortable. That seems a little clunky to me.
- The men burning at the stake have the churches on their side of the painting and the official and the rabble have the town, or the secular world on their side. The smoke from a tiny chimney on the right echos the larger smoke cloud from the burning pyre. The smoke of the burning pyre is the largest shape on the canvas and that draws our attention to the dark shapes of the men tied to the stakes awaiting immolation.
- Each of the figures in green across the foreground is arrayed in front of either a red coat or the fire. So besides "stacking" opposite values he is also "stacking" compliments on top of one another.
This is a design system called the golden section. I never quite see the placement of the paintings under these lines, I wonder if other lines wouldn't serves as well. There are obviously relationships between the lines and the image, but I think that artistic placement could account for that as well as a geometric scheme. But there were classical artists who used the geometric armatures on which to hang their pictures. What do you think?