H-Fractal machine embroidered antenna swatch H

The miniaturization of electronic devices has led to the development of what is known as fractal antennas - miniaturized antennas that use an iterative function system to create a fractal element at a reduced size. The term "fractal" was first used by mathematician Benoit Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus meaning "broken" or "fractured", and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature. One of the properties of fractals geometry is that it can have an infinite length while fitting in a finite volume. The radiation characteristic of any electromagnetic radiator depends on electrical length of the structure. By using the property of fractal geometry in antenna design one can increase the electrical length, keeping the volume of the antenna the same. The fractal concept can be used to reduce antenna size, such as the Koch dipole, Koch monopole, Koch loop, and Minkowski loop. Or, it can be used to achieve multiple bandwidth and increase bandwidth of each single band due to the self-similarity in the geometry, such as the Sierpinski triangle, Cantor slot patch, and fractal tree dipole.

process photos
To create this antenna I used an L-systems fractal, specifically the H-Fractal in its fourth iteration:
https://onlinefractaltools.com/draw-hausdorff-fractal

After vectorizing the image I used a Brother Persona embroidery machine and Madeira HC-12 the silver-plated nylon conductive thread and made four different variations on different fabrics (cotton, polyester, mesh, jersey).

This antenna was created in the context of my artistic research projects Fractal Antennae and Embodied RF Ecologies and paired with a sound amplifier circuit it acts like an EMF detector, or paired with an amp and a downconverter as an RF sensing and decoding device. It can also be used with software-defined radio to pick up RF transmissions. Its resonant frequency will depend on the placement of the SMA connector and its corresponding GND, and can be experimentally tested and measured with a vector analyzer.

material list

• Brother Persona embroidery / machine Brother Persona
• Madeira HC-12 silver-plated nylon conductive thread / HC-12
• cotton, polyester, mesh, jersey