Leonardo's Patterns
Pattern 1: Small Square and 3 to 1 Rectangle
The largest sketch (and two other smaller sketches) shows a pattern that alternates one-unit squares with one-unit by three-unit rectangles. This seems to be the one he thought would be the most practical for covering a rectangular area. Nearby on the page he shows ideas for using this pattern as a continuous bridge-like structure. Start the pattern by building a one-unit square. From the free end of one of the sticks build a square going the opposite direction. If the original square has been built with sticks added in the counterclockwise direction, build the second square be adding sticks in the clockwise direction. Do the same on all four sticks of the original square, and continue by adding small squares
Pattern 2: Small Square and Large Square
Hidden under a stain on Leonardo's page is a variation on Pattern 1 which replaces the one-unit by three-unit rectangle with a two-unit square. Start from a small square and build new squares off the ends of the first square in the same direction as the original square. Just changing the direction of the new squares produces a new pattern of alternating one unitand two-unit squares.
It is a pattern found in Arabic tiles, especially in Spain, where a large tile alternates with a small decorated tile.
Because this pattern is not symmetrical, it can also be built going in the other direction.
Pattern 3: Large Triangle and Small Hexagon
The third pattern Leonardo develops is based on a two-unit triangle. Start from that triangle and place ends of new sticks on the free notches parallel to the stick on the other notch. Place a new stick end on the second notch on the new stick, and swing it under the free end of the original triangle to create a new two-unit triangle. Do the other two triangles, and then begin a third ring of triangles in the same way by adding new sticks to the free notches parallel to the sticks on the other notches of the same sticks. When you complete this third row you will see that one-unit hexagons have formed. This pattern can also be started by building a one-unit hexagon and then adding two-unit triangles around it. It is exciting to see that just by starting with patterns of one geometric shape other geometric shapes can automatically be created!
Leonardo's Unfinished Sketches
He also drew unfinished sketches for a variation of Pattern 3. Instead of a two-unit triangle and a one-unit hexagon, start with a one-unit triangle and create two-unit hexagons around it. Add sticks to the free notches parallel to the sticks on the other notches, and then add sticks to the first notches of the new sticks and swing them under the ends of the original stick to make new small triangles. Repeat the same process for each of the two free ends of the new triangles, and the hexagons will be completed. Continue with more small triangles.
Leonardo also sketched a variation on Pattern 3 with some odd shaped quadrilaterals, but it's not clear.
Beyond Leonardo
Rinus Roelofs explored many other patterns, and we have included a few of them for you to try.
More patterns he found can be seen at his site. The diagrams do not show the overlaps, but they all follow the one Rule. Once you have mastered these, try creating your own. As long as the sticks overlap properly, the structure will support itself. Always keep the spacing as even as possible, by making sure the ends of the sticks overlap the ones below by about half a unit. Each stick you place can wiggle all the others, and if even one or two collapse, you may not be able to put them back.
Some of Rinus' Other Patterns
Braided ring Woven cane Trapezoids Diamonds
Rinus also introduced the ides of using sticks of different colors. Try making patterns of colors in addition to patterns of shapes. Have a look the gallery.