# Roberto Luis Giardili

The motivation for my work comes from the idea that mathematical methods and concepts can be used as a source of art. In particular, I focus on the design and construction of sculptures inspired by fractal geometry through traditional methods.

For this purpose, I develop my own computer programs, a 3D version of L-systems that allows me to combine a starting shape (initiator) with a rule for modifying it (generator) and, from an aesthetic perspective, conceive the sculpture.

The design of the sculpture constitutes the first part of the process. Complexity arises with the construction. This requires both developing the hardware tools to cut and weld the tubing’s, and monitoring to minimize error accumulation.

“Missing Tetrahedron” is based on an L system. I use as initiator the edges of the tetrahedron resting on one of them, in an unstable equilibrium. Each edge, except for the support, is replaced by a generator formed by two equal segments longer than half of the edge of the tetrahedron. These two segments constitute a plane which can be rotated at will around each edge of the tetrahedron. The lower support edge is replaced by three segments of the same length.

In a second step, the result on the previous stage is taken as an initiator and a similar Koch generator is applied, but in 3D. Again each generator can be rotated independently for each segment of the initiator. This rotation allows aesthetically modify the set.