Juan J. G. Escudero

"… lines of flight, movements of deterritorialization and destratification…orchid and wasp: aparallel evolution of two beings that have absolutely nothing to do with each other…the two becomings interlink and form relays in a circulation of intensities pushing the deterritorialization even further…transversal communications between different lines scramble the genealogical trees…"

(from "A Thousand Plateaus" by Gilles Deleuze and Félix Guattari.)

25 x 40 cm
Digital Print

The images under h of periodic billiard trajectories inside F are particular cases of curves known as hypotrochoids and configurations of lines in the plane. The configurations of lines have been used recently to solve a problem posed by Paul Erdös in 1982 ("Gallai triangles in configurations of lines in the projective plane".C. R. Math. Acad. Sci. Paris, Vol. 354, pp.551-554, 2016). They are associated to a one-parameter family of polynomials which are related with eigenvectors of diffusion operators. This work is based on a polynomial associated with the union of the deltoid, the trifolium and an arrangement of six lines.