How to construct a Celtic knot using a grid
Step 1:
Start with a grid with an even number of squares in each direction. Place dots at each (x,y) where x and y are odd. These dots indicate where splittings will later be placed.
Step 2:
Place splittings on all the dots along the outside border of the grid a splitting is a line through which the knot cannot pass. Such lines are drawn slightly shorter than two grid units long and centered on the dots.
Step 3:
Inner splitting should be chosen, which determine the eventual form of the knot. They are drawn directly over the dots. Symmetric patterns are generally more pleasing. All splittings are either horizontal or vertical, and only one splitting may be placed at each dot
Step 4:
All remaining dots represent where the dot will intersect itself. Connect the remaining diagonally adjacent dots, but not all the way. Stop just before reaching each dot.
Step 5:
Going diagonally outwards from each dot, if the dot is approaching a splitting, draw a short curve out from just past the dot to the edge of the grid square. The curve should go straight towards the dot. Once again, the curve should not quite reach the dot.
Step 6:
Wherever a horizontal and vertical splitting meet in a corner, the knot will also have a sharp corner. Draw these at the same level as the short curves, so they smoothly meet.
Step 7:
Wherever there are thin stretches going in the same direction, the knot will basically be flat, these should be filled in with straight line segments.
Step 8:
Wherever there is a dot left, the centers must now be filled in. On odd rows, connect the lower right piece to the upper left piece. On even rows, connect the lower left piece to the upper right piece.
The knot is now complete