Before we start:

The method described in this article involves a lot of duplicating and arranging of shapes.  I want to highlight the method I use to do this quickly.

1. Identify the shape we want to arrange into a pattern
2. With snapping on, grab the shape from the corner
3. Snap the shape to itself.  Press the right mouse button once to put the move in duplicate mode (the cursor will have a '+' box under it)
4. Press ctrl+d several times (if you have never used ctrl+d, the first time will pop up a dialog box, press ok, undo to step 2. and continue with step 3.)
5. Select all of the shapes, snap to the top corner of any of the triangles and move. Click the right mouse to put in duplicate mode.  Snap to the original.
6. Select all shapes and repeat once more.  At this point you can press ctrl+d to make a pattern as large as you like. 

Depending on the pattern we're creating, the steps may vary a bit.  If you become familiar with this method, you should be able to create these types of patterns in seconds.

Escher patterns

A favourite artist of mine is M.C, Escher.  I suppose his mixture of art and mathematics is what attracts me to his work.  One of the things he is well known for is creating amazing interlocking patterns, otherwise known as tessellation.  The concept behind tessellation is simple, any space can be divided up into triangles, rectangles or hexagons.  This article will focus on the triangle configuration and depending on interest, I'll go into rectangles and hexagon configurations in a separate article.

While Escher only had his pen and paper, you have something that will give you a huge advantage -- the clone.  We are going to set up the document so that you can edit the entire pattern by editing one tiny line segment. 

1. Create a horizontal line segment

This segment will be the master object, and the driving force of the final pattern.

2. Clone it (edit menu->clone)

The selected shape is the clone, the first of many.  We don't want to mix the clone and master up, so move the clone away from the master (and remember which is which).  From this point on, any duplications will be made on the clone.  A duplicated clone is also a clone.

3. Duplicate the clone once.  Move the new clone so that the centers are snapped together and rotate it 120 degrees (e.g. via the property bar). 

4. Duplicate again.  The duplicate will be rotated an additional 120 degrees, which is what we want.

5. Move the rotated clones with the pick tool, snapping the ends together to form a triangle (do not node edit them, this will break a link with the master).

6. Follow the steps in the "Before we start" section to create a grid of triangles.

We're done!  Now for the fun part.  Go back to the master line and enter node edit mode.  Double click the middle of the line segment to add a new node.  Move the node slightly.  

There is one rule to follow: do not change the start or end node of the master.  Doing so will break the triangle.  Everything else is fair game.  You can insert as many nodes as you like, convert them to curves, and anything else you like.  

Hmmmm, while this is cool, and could be useful for certain types of patterns, we seem to have a problem.  We have two different shapes forming the pattern, seen here in green and blue.  What we're after is true tessellation where every shape is an exact duplicate.  As it turns out, this isn't very hard to accomplish.

1. Create a new document, make another horizontal line and clone it.  This time, give the master an arrowhead so that we can clearly see the arrangement of the clones.  We can remove the arrowhead from the master later

.

2. Duplicate the clone and rotate the clone 180 degrees.  Using the pick tool, snap the clones end to end.

3. Treat these clones as one line, and create the triangle we created in the previous pattern

4. Create the grid pattern

At this point, you can remove the arrowhead from the master.  Again, we're done and it's time for some fun.  Start node editing the master curve.  Be careful not to move the start and end point of the curve.

There are endless patterns you can create using this method, and it's a lot of fun trying to come up with interesting shapes.

Where to go from here?

Here are some ideas:

• Try using the smart fill tool to create fillable shapes
• Patterns can be powerclipped into other shapes
• It is possible to create a real pattern fill (though a bit tricky since the pattern doesn't exactly align to a square grid)
• See if you can figure out how to extend this to squares and hexagons.  There are several configurations for both.
• Create a .CDR of the finished grid before the node edit stage so that you can quickly start creating new patterns without the setup time
• Check out Part 2 

I created the following image using this technique:

This was created using a hexagonal grid, but the concept is similar.  It will take some experimenting to create this type of pattern, but that's part of the fun, right?

Have Fun!

[Edit: I just finished another image which uses the triangle grid]