Section: New Results

Fractal Geometry

Participant : Dmitry Sokolov.

This is a collaboration with Christian Gentil (LE2I), Gilles Gouatay (LSIS), Anton Mishkinis (LE2I).

Additive manufacturing enables for the first time the physical realization of objects having complex geometries. Good approximations of fractals, in particular, can now be manufactured in a variety of materials, including metals. The application domains of fabricated fractal geometries are vast, from the be design of “fractal” micro-strip antennas, to the creation of meta-materials.

The main challenge with traditional fractals is the control of the resulting geometry. For example, it is quite challenging to get the desired shape using the system of fractal homeomorphisms proposed by Barnsley  [29] . We elaborate here a new type of modeling system, using the facilities of existing CAGD software, while extending their capabilities and their application areas. This new type of modeling system will offer designers (engineers in industry) and creators (visual artists, stylists, designers, architects, etc.) new opportunities to design and produce a quick mock-up, a prototype or a single object. Our approach is to expand the possibilities of a standard CAD system by including fractal shapes while preserving ease of use for end users.

This year we published two papers on the subject [20] , [16] .