Fractal Embroidery is the application of fractal geometry to generate embroidery patterns.

Traditionally embroidery is classified into blackwork embroidery where embroidery stitches only decorate the fabric, and canvas work where the fabric is mostly covered by embroidery. This distinction parallels the difference between drawing and painting, or more generally line-based vs. surface-based, or 1D- vs. 2D-design.

Since fractals are of fractal dimension they question the divide between 1D- and 2D, thus challenging the distinction between blackwork and canvas work.

The very same embroidery plan may be considered blackwork or canvas work depending only on the thread count used in the actual execution, or the number of iterations used in the generation of the fractal.

Depending on its origin, fractal embroidery may be classified into folk art fractals, and computer fractals.

Fractal folk art embroidery can be the result of an actual fractal craft process, predating contemporary fractal geometry by centuries.

Fractal computer embroidery on the other hand is the application of mathematics to the field of embroidery where the embroidery design is generated by a computer program, and then turned into a fractal textile, usually by an embroidery machine rather than a human crafter.

The so called cross-stitch-curve obtained its name from Martin Gardener, because it resembles blackwork embroidery on the edge of a square blanket. He also used the term anti-cross-stitch-curve to refer to the closely related box-fractal. This box-fractal can be found in indian and armenian folk art.

An example for fractal folk art embroidery is provided in the Kutch embroidery tutorial.

Though many folk art practices may be considered prior art, Pulse Microsystems has been granted software patents for using fundamental fractal algorihms in the field of embroidery:

• US5430658: embroidery of fractal shapes
• US6968255: spacefilling curves to fill polygon shapes

• Fractal Kutch Embroidery

• Cross-Stitch-Curve
• Anti-Cross-Stitch-Curve aka Box Fractal.

• US5430658 - Method for creating self-generating embroidery pattern, Pulse Microsystems, 1985
• US6968255 - Method and system for automatically deriving stippling stitch designs in embroidery patterns, Pulse Microsystems, 2005

• Fractal Machine Embroidery
• Fractal Embroidery Image
• Hilbert Curve Pillow
• Embroidered Turtle Pillow

• Kutchwork Tutorial by Bhavani Harikrishnan
• Armenian Embroidery
• Shipibo Indians