Marina Toeters and Loe Feijs

The garment is based on a novel fractal. The fractal resembles the classical Mandelbrot fractal, but it has different aesthetic qualities. The classical fractal is an icon of complexity science, aiming at understanding chaos, randomness, complexity, predictability and infinity. This type of fractal has an unbelievable complexity, even though it is the result of a straightforward formula, just a quadratic mapping. Here we present a new interpretation of Mandelbrot's idea, but based on another metric.Whereas the traditional quadratic mapping uses the addition and multiplication of complex numbers, for this work, we define an unconventional multiplication operation, inspired by the Taxicab metric. We explored the visual features of the fractal, aiming to design an attractive fashion item. The shirt, in nude colors, has cut-out neck-opening, corresponding to one of the secondary bulbs of the fractal.

In fashion, the idea of skin color, sometimes called "nude" is a theme of growing interest. The garment is based on a novel fractal, whose colored zones are calculated with the well-known escape-time algorithm. Instead of using the full hue range and saturated colors, as is customary, we developed a range of nude colors, zigzagging step-wise through a selected block in the Hue-Saturation-Brightness color space. The fractal was calculated using Mathematica 10.4 at Eindhoven University of Technology whereas the garment design and construction work was done in the studio of by-wire.net in Utrecht. The garment has a wide neck opening and additional openings, thus making use of the features of the fractal. The overall appearance is romantic and feminine.

One of the features of the traditional Mandelbrot fractal is the appearance of so-called lemniscates, nested lines such as a circle, an ellipse, a pear-form and then more and more complex lines approximating the outline of the fractal. In this novel Taxicab metric based work, the lemniscates become piecewise polynomials. In the trousers shown here, these new lemniscates have been used as cut lines, sewing lines, darts and hemlines. The garment construction responds to this feature of the fractal. One of the effects is the appearance of protruding volumes. Also the pocket design is based on these piecewise polynomial "lemniscates". This garment, like the other pieces of this collection, tells the main message of complexity science, related to chaos, randomness, complexity, predictability and infinity. Namely that a simple formula can give rise to an unexpected complexity.