Moving north-east A times produces:
Moving north-east A times produces: .
How to construct:
Start with any h-line: four squares along a horizontal line with , e.g. :
Extend the arithmetic progressions along the diagonals:
Then fill in a diagonal next to one of these 2, with any arithmetic progression. e.g:
Then all the empty squares have been determined and can be filled in, making the sums equal across all line segments (the h-lines and v-lines).
Then when drawing the squaring, draw the squares of negative size on the other side of the line from where they ‘should’ be, e.g. :
It seems that any grid of numbers constructed this way makes a tesselation of the plane.
Also, it seems that all the -sized squares (I mark them with a small circle on the squaring) lie in a straight line, no matter what sequences are used. I’m sure there’s an obvious reason for that!
Unfortunately TikZ has too many bugs with barycentric plotting. ARGGHH! Unusable. Not slight – massive and weird errors.
Nonregular CFs can also be represented as squares in a rectangle.
Picture of : 1/(1+1/(1+1/(1+etc