The Girih tile patterns from 1453, which resemble those discovered by Penrose in 1973 and published by Penrose in 1974, are aperiodic tile patterns of order 5. Alain Connes analyzed these in his work “Noncommutative Geometry” dated June 30, 1994, as follows: «In order to get some intuitive idea of what the generic leaf of a foliation can be like, as well as its space X of leaves (at this level of measure theory) one can consider the space of Penrose tilings of the plane (or Penrose universes). After the discovery of aperiodic tilings of the plane, the number of required tiles was gradually reduced to two. Given the two basic tiles: the Penrose kites and darts, one can tile the plane with these two tiles (with a matching condition on the colors of the vertices) but no such tiling is periodic. Two tilings are called identical if they are carried into each other by an isometry of the plane. Examples of non-identical tilings are given by the star tiling and the cartwheel tiling. The set X of all nonidentical tilings of the plane by the above two tiles is a very strange set because of the following: “Every finite patch of tiles in a tiling by kites and darts does occur, and infinitely many times, in any other tiling by the same tiles”.»

These patterns were included in the acoustic optimization of the base in order to find one that, in its irregular regularity, could be designed to absorb critical surfaces. The Penrose pattern is a very special, mathematically strictly defined aperiodic tiling with exactly two shapes and 5-fold symmetry. On the other hand, a pattern that would have a very general geometric construction, arising from arbitrary point distributions - and which occurs extremely frequently in nature - could be more acoustically effective. A mostly non-aperiodic pattern with no fixed number of tile shapes is required.

The Delaunay triangulation and the Voronoi diagram are dual structures: each edge of the Delaunay triangulation connects exactly two points whose Voronoi cells are adjacent - and conversely, each Voronoi edge lies exactly halfway between two neighboring Delaunay triangles. The Delaunay triangulation is the dual of the Voronoi diagram - and the Voronoi diagram is the dual of the Delaunay triangulation.

The SUBGRAPH base, derived from the METAGRAPH, has a more minimal static cross-section and is therefore more acoustically challenging. Its upper and lower sides feature differentiated patterns in depth, which acoustically trim the non-retaining support base (no fixation). This design optimizes the spectral balance, contrasting finely detailed highs with an immediate, deeper bass.

The SUBGRAPH is available in three versions, each of which, compared to the standard version (pure copper), influences its sonic characteristics in two extreme directions through the use of different materials. Pure Grade 2 titanium produces shorter and faster transients than pure copper, while pure tungsten has the opposite effect of titanium and, in particular, shapes the bass range differently - significantly extending it downward. GRAND ANALOG ELECTRICS takes a critical view of hybrid materials such as Exium AM in terms of sustainability, as true closed-loop-recycling is generally not possible here; instead, only downcycling occurs.