How did Bresenham represented pixel grids to derive his line drawing algorithm?

How did Bresenham represented pixel grids to derive his line drawing algorithm?
3 by shivajikobardan | 0 comments on Hacker News.
I am seeking for a succinct source regarding how did Bresenham's imagined the pixel grids. Because different APIs have different implementations of pixel grid. Without the fundamental understanding of a pixel grid, it is impossible to understand the derivation of line drawing algorithm and circle drawing algorithm. I hope to get some valuable input from hackers.