SHORT DESCRIPTION

In mathematical analysis, space-filling curves are defined by intricate geometric patterns and recursive algorithms that traverse and occupy higher-dimensional spaces, ensuring complete coverage of a defined region. The fractal geometry that shapes these curves, simultaneously aesthetic and structural, illustrates how generative algorithms can be used, respecting their rules while enhancing their creative potential. A line that fills space automatically generates an organic, infinite path, guiding the extruder of a robotic arm toward a formal conception that merges form with function. The lines serve as inputs, but the outputs emerge as surfaces - crystalline, organic, or high-tech. The selected recycled material ( Rpetg) follows the formal matrix, exploring its unique substance and giving distinctive physical presence to the design piece. This work, created with 3D-printed robotic arms, employs Gary’s Space-Filling Curves algorithm to generate a looping fractal: an evolving spiral that defines the structure of the table. The creative process maps production paths through a direct human–machine, software-hardware interface. The resulting design evokes a futuristic, high-tech aesthetic, with a glass tabletop ensuring usability while completing the circular flow at the core of the structure. Despite its reliance on algorithmic and biomimetic principles to achieve visual impact, the coffee table does not compromise functionality. It delivers a seamless user experience while contributing decisively to the aesthetic refinement of contemporary environments. By transforming recursive code into matter, the design becomes a manifesto of how machines and creativity can co-author the future of form.