Celtic knot

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

How to create a few basic Celtic knots, illustrated in ASCII

When you draw these knots, they can be done in ASCII or by hand on graph paper; the method is much the same.

A brief warning: if you have difficulty understanding any of these knots, copy them to Notepad and change the font to Lucida Console, size 10. This is the most attractive font I have found so far for displaying Celtic knots. If the size is different, it ceases to be a monospaced font, so be sure you have it right.

In any Celtic knot, the main idea is to be sure that every line alternates going over and under when it overlaps itself. In fact, you can draw the outline of any of these knots on a sheet of paper and then determine whether the line overlaps or underlaps by starting at any intersection and working outward.

This is the most simple Celtic knot to draw. It is in the shape of a heart and is designed to work the same way as an ordinary knot, like you would tie in your shoelaces.

  /\  /\
 /  \/  \
/ /\ \/\ \
\ \/\ \/ /
 \/ /\/ /
 / /\/ /\
  /\  /\ 
    \/

Several of these can be joined together by the trailing ends to make more complex knots. Four of them can be connected in a square, or two opposite each other can be connected. They can be made pointing in any direction, as below.

     /\  /\
    /  \/  \
   / /\ \/\ \
   \ \/\ \/ /
    \/ /\/ /
    / /\/ /\
   / /\  /\ \
  / /  \/  \ \
  \ \  /\  / /
   \ \/  \/ /
    \/ /\/ /
    / /\/ /\
   / /\ \/\ \
   \ \/\ \/ /
    \  /\  /
     \/  \/     

Another simple knot is the loop. This just looks like a diamond, and it can be linked with other loops or other hearts. The larger it is, the more easy to distinguish from the rest of the pattern it becomes; smaller ones can be used together to make a chain.

    /\
   /  \
  / /\ \
  \ \/ /
   \  /
    \/
 
   /\  /\  /\
  /  \/  \/  \
 / /\/ /\/ /\ \ 
/ / / /\/ /\ \ \
\ \ \/ /\/ / / /
 \ \/ /\/ /\/ /
  \  /\  /\  / 
   \/  \/  \/

   /\/\
  / /  \ 
 / / /\ \
 \ \/ / /
  \  / /
   \/\/

Something that looks especially pleasing when done in ASCII, and is also impressive when drawn by hand, is the spiral. Imagine taking two pieces of yarn and winding them around each other, and you understand what the spiral is supposed to look like. It can be made alone, like below,

 \ \/ /
  \/ /
  / /\
  \/ /
  / /\
  \/ /
  / /\
  \/ /
  / /\
 / /\ \

Or combined with other knots, like this knot that combines the loop with the spiral.

   /\
  /  \
 / /\ \
 \ \/ /
  \ \/
  /\ \
  \ \/
  /\ \
  \ \/
  /\ \
 / /\ \
 \ \ \/
 /\ \ \
 \ \/ /
  \ \/
  /\ \
  \ \/
  /\ \
  \ \/
  /\ \
 / /\ \
 \ \/ /
  \  /
   \/

A rather minor category of knot that I am going to discuss is made by combining two heart knots. Personally, I call it the double heart knot; I don't know if there is a specific technical name for it. It looks like this:

    /\    /\
   /  \  /  \
  / /\ \/ /\ \
 / /  \ \/  \ \
/ /   /\ \   \ \
\ \  / /\ \  / /
 \ \/ /  \ \/ /
  \/ /    \/ /
  / /\    / /\
 / /\ \  / /\ \
/ /  \ \/ /  \ \
\ \   \ \/   / /
 \ \  /\ \  / /
  \ \/ /\ \/ /
   \  /  \  /
    \/    \/

These can be made huge or tiny. They can also be made with two sets of lines instead of one to make a very attractive knot, as will be illustrated below.

To make a more complex knot, you may want to consider making one of the basic knots, but using two sets of lines to make it. To do this, simply pay close attention to where the lines intersect. An intersection in one of these knots will consist of four lines, rather than two and will look like this:

  \ \ \  / / /
   \ \ \/ / /
    \ \ \/ /
     \/\/ /
     / /\/\
    / /\ \ \
   / / /\ \ \
  / / /  \ \ \

A heart knot using two sets of lines will look like this:

     /\    /\
    /  \  /  \
   / /\ \/ /\ \
  / /  \/ /  \ \
 / / /\ \/\/\ \ \
 \ \ \/\/\ \/ / /
  \ \/ / /\/ / /
   \ \/\/\ \/\/
   /\/\ \/\/\ \
  / / /\  / /\ \
 / / /\ \/ /\ \ \
/ / /  \  /  \ \ \
        \/    

Note how each of the intersections follows the pattern shown above. Almost any knot can be made this way, provided that it is large enough.

Almost all knots are a combination or variation of one of these, with added loops, twists and spirals to make them pretty. Just use your intuition and you will soon be creating knots like these, that can be used for design and on web pages. Try to identify the different simple componenents used in each one:

            /\/\
           /  \ \
          / /\ \ \
          \/ /\/ /
          / /\/ /\
         / /\ \/\ \
        / / /\ \ \ \
     /\/ / / /\ \ \ \/\
    /  \/ / /  \ \ \ \ \
   / /\ \/ /    \ \/\ \ \
   \/ /\/ /      \/ /\/ /
   / /\/ /\      / /\/ /\
   \ \ \/\ \    / /\ \/ /
    \ \ \ \ \  / / /\  /
     \/\ \ \ \/ / / /\/
        \ \ \ \/ / /
         \ \/\ \/ /
          \/ /\/ /
          / /\/ /\
          \ \ \/ /
           \ \  /
            \/\/



           /\  /\
          /  \/  \
          \ \ \/ /
           \/\/ /
           / /\/\
          / /\ \ \
         / / /\ \ \
	/ / /  \ \ \ 
        \ \ \  / / /
         \ \ \/ / /
          \ \ \/ /
           \/\/ /
           / /\/\
          / /\ \ \
         / / /\ \ \
        / / /  \ \ \
       / / /    \ \ \
      / / / /\/\ \ \ \
     / / / /  \ \ \ \ \
    / / / / /\ \ \ \ \ \
    \ \ \ \/ /\/ / / / /
     \ \ \/ /\/ /\/ / /
      \ \ \/\ \/\ \/ /
       \/\ \/\ \/\/ /
     /\/ /\/ /\/ / /\/\
    /  \/\ \/\/ /\/\ \ \
   / /\ \/\ \ \/\ \/\ \ \
   \/ /\/ /\/\/ /\/ /\/ /
   / /\/ /\/ /\/\/ /\/ /\
   \ \ \/\ \/\ \ \/\ \/ /
    \ \ \/\/ /\/\ \/\  /
     \/\/ / /\/ /\/ /\/
       / /\/\ \/\ \/\
      / /\ \/\ \/\ \ \
     / / /\/ /\/ /\ \ \
    / / / / /\/ /\ \ \ \
    \ \ \ \ \ \/ / / / /
     \ \ \ \ \  / / / /
      \ \ \ \/\/ / / /
       \ \ \    / / /
        \ \ \  / / /
         \ \ \/ / /
          \ \ \/ /
           \/\/ /
           / /\/\
          / /\ \ \
          \  /\  /
           \/  \/

     /\    /\
    /  \  /  \
   / /\ \/ /\ \
  / /  \/ /  \ \
 / / /\ \/\/\ \ \
 \ \ \/\/\ \/ / /
  \ \/ / /\/ / /
   \ \/\/\ \/\/
   /\/\ \/\/\ \
  / / /\  / /\ \
 / / /\ \/ /\ \ \
 \ \/  \  /  \ \/
 /\ \   \/   /\ \
 \ \/        \ \/
 /\ \        /\ \
 \ \/        \ \/
 /\ \        /\ \
 \ \/   /\   \ \/
 /\ \  /  \  /\ \
 \ \ \/ /\ \/ / /
  \ \/ /  \/ / /
   \ \/\/\ \/\/
   /\/\ \/\/\ \
  / / /\/ / /\ \
 / / /\ \/\/\ \ \
 \ \ \/\/\ \/ / /
  \ \  / /\  / /
   \ \/ /\ \/ /
    \  /  \  /
     \/    \/