Space-Filling Curves

In the late 19th century, the Italian mathematician Giuseppe Peano astounded the world of mathematics when he constructed a remarkable curve. Infinitely long and always changing direction no matter how closely you look at it, the curve systematically reaches every point inside a simple square. As a result, even the definition of a curve had to be changed. These constructions are now called space-filling curves. They are a special kind of fractal tiling pattern.

Our Designs

Doug McKenna is an award-winning software designer, a fractal pioneer, a mathematical artist, and an expert in constructing space-filling curves. He has played with and studied these fascinating patterns for nearly 40 years. Using sophisticated computer techniques, he fashions his fabric patterns using unique space-filling curves that he discovers and devises to be both elegant and eye-catching.

Each pattern is repeated and drawn using custom layout algorithms so that everything tiles and threads seamlessly without self-intersection. Remarkably, you could cut any of these designs into two identically shaped jigsaw pieces: just follow the border between color and white. But the cut would be several hundred feet long, because the border is approximately space-filling. (Try tracing the pattern with your finger, if you’re not convinced!)

DMCK Silk Chiffon Scarves

There is a reason our fabric patterns please and fascinate the eye. When you look closely at any part, you can never tell what the foreground or background is: they look the same. Is it color on white, or is it white on color? Well, it’s both! Turn the design upside down and everything reverses. This Escher-like quality is also true of individual parts of the overall pattern. Even the smallest overlapping constituent patterns will be the reverse of one another. So the pattern is both self-similar, like a fractal, and self-reverse.

Like mathematics, the elegance of these designs is mysterious and timeless.