Expansion of a Triangle

For this project, I decided to look at the ways a triangle could be transformed by one changing its dimensions one square of the grid at a time. I began with this red 4 by 4 triangle in the upper right hand corner, and then following the rules (which I explain later), form this progression of triangles modeling Sol Lewitt's work.

The initial pattern continues on to form this trio of blue triangles:

The project actually would have worked better if we had one large grid to work on like a wall in Sol Lewitt's art, but since I was constrained to the paper, I had to make adjustments. I will begin with the instructions for a large continuous grid, then tell how I made adjustments after.

1. Begin with 4 x 4 right triangle in upper left hand corner, calling the top point of the triangle the pivot point, because the rotation of the triangle hinges on this point. The other points that do rotate are called the left point and the right angle point, respectively.

2. The movement of the entire triangle from one triangle to the next is (in theory) always the same. The pivot point of the new triangle is two squares down and two squares to the left of the left point of the previous triangle.

3. The rotation of the triangle is controlled by the successive movement across the grid and how many grid squares the right angle point and the left point move. Moving from one triangle to the next is essentially a copy of the last triangle in its new position (as determined by the movement rule). This copy is then rotated and expanded, so that the right angle point is moved down and left one square, and the left point is moved right and up one square.

4. You continue this pattern until you develop the sloping triangle as represented by my project.

5. For the color scheme, I decided to begin with red, and moved through the range of colors until the last triangle. The color changes quickly in the beginning, as the triangle rotates rapidly, but then slows down with different shades of dark blue and purple as the triangle gets bigger, and its rotation is less noticeable. I decided to end with pink because I felt this showed the continuum of the color spectrum, and how this pattern could be continued eternally, eventually producing a very large upright triangle.

I had to modify some of the rules for my project, such as the movement rule, so that the triangles could fit neatly on the pages. Also, if the pattern was done on a large grid, the triangles would be moving downward continuously, instead of me restarting the pattern at the top right of the paper after it reached the bottom of the previous page.

Here is the final product after ten pages of the progression: