An optimal model for a quiddity sequence, drawn from Frieze patterns, with respect to their relation to cluster algebra is explored.
A frieze pattern which grows and shrinks is understood to represent a finite pattern.
The study focuses on exploring growth which varies between arithmetic and exponential sequences, with infinite pattern growths in rubber geometry typologies.
By focusing on the limitations imposed by patterns formed when working with triangulations (where each unit has a maximum of 3 vertices), where the model has no superfluous points, a constrained environment is used to find architectures where non-convergence of form is optimised. By combining the patterns of growth – represented by the “diamond rule” where (ab – 1 = cd), a formal constraint is used to generate finding a loft form within the rubber geometries – where the curved-line-of-thought process for the mathematician is used as a a defined NURBS (non-uniform rational B-spline) curve, containing an inherent new geometric quality for an architectural form.
The link above is the score written for a’capella SSATB and flute, derived from the research in Quiddity Sequences.