Meredith Williams - Senior, Interior Architecture and Design majo

Click to open a larger image in a new window

Materials and Process

  • Pencil
  • Ruler
  • Compass
  • Tracing paper
  • Drawing paper
  • Black marker
  1. Starting with a sheet of tracing paper and pencil, I divided the sheet in half and then created a 2 inch by 2 inch square grid.
  2. In the center of another sheet of tracing paper, I constructed a square lattice pattern of circles.
  3. Then I created a diagonal 2 inch grid.
  4. I overlapped the different grids and found connections between lines.

Artist's Narrative

I found inspiration from J. Bourgoin's Arabic Geometric Pattern and Design. Having begun the process, as stated above, I created larger circles that slightly overlapped, the diameters of which connected with one another. I turned the circles into octagons, with each radius of a circle connected to another circle's radius equaling the length of one circle's diameter.

To create the border pattern I divided the pattern in half, which created half-octagons that interlocked. Then I took my border pattern and overlapped the lines over and under each other to create an interlacing pattern.

Teacher's Comment

The complexity of this pattern is difficult to perceive. The pattern contains seven-pointed stars (!) and pentagons (!), yet it creates a tessellation. A tessellation contains a single shape, which when repeated covers the plane with no gaps and no overlaps. Pentagons don't normally tessellate. The key to this pattern is the underlying square grid (connect the centers of the diamonds, which are created by the adjoining indentations of adjacent pentagons). The arrangement of forms conforms to the symmetry group having parallel and perpendicular reflections and glide reflections. This arrangement, using pentagons and seven-pointed stars allows for a brilliantly complex composition set within the simplicity of a square grid.

more by Meredith Williams || back to other students' practicums

[About Symmetry] [Rug Gallery] [About Carpets] [Ed. Resources] [About This Site]
[Title Page]

© 1997-2012 The Textile Museum & The Math Forum @ Drexel
Viewers' Comments || Contact Us