"Directrix" (1998, 2025) is a long-form generative artwork and interactive drawing environment, in which animated "pseudo-parabolas" are created autonomously or in collaboration with a participant. These complex curves are the result of an interplay between a set of dynamic and static gestures. Depending on how they are structured and layered, the results can vary from sparse and delicate constructions of gently curved lines, to violently twitching, thatchy masses.

Directrix creates images from a generalized model of parabolas — the set of points which are equidistant from a special point called the focus, and an (ordinarily) straight line called the directrix. This interactive environment was designed to explore the implications of two premises: firstly, that the shape of a parabola's directrix could be an idiosyncratically drawn or generated line, and secondly, that its focus could be a moving point, animated along the trace of a viewer's recorded gesture. Directrix is interesting, in my opinion, because of the interplay it establishes between a strictly spatial specification (the directrix) and a spatio-temporal one (the path of the focus). 

A discussion of Directrix appears in section 3.1.4 (pages 69-71) of my masters thesis, "Painterly Interfaces for Audiovisual Performance" (2000), produced in the Aesthetics and Computation Group at the MIT Media Laboratory. The original project was developed in C++; this port to p5.js is the first time the project has been made available to the public, and includes expanded features for autonomous play and generative variation. 
  
There are five possible drawing targets: the white directrix line, and the focal paths of four different pseudo-parabolas. You can select the drawing target by pressing keys 1-5, or you may cycle through them by clicking the right mouse button.
  
Key commands:
• H - display Help
• P - export a PNG screenshot
• N - generate a Novel variation
• R/Return/Space/Escape - Restore to original
• 1,2,3,4 - select Parabola # for editing
• 5/D - select Directrix for editing