Penrose Null-Band Scaling: A Programme Note (INDYNA Research Note 22)

Abstract

On Penrose vertex sets (de Bruijn pentagrid, $\mathbb{Z}^5\!\to\!\mathbb{R}^2$) the two-shell operator with the conjugate rhomb-diagonal pair exhibits a macroscopic null band whose weight is conjectured to obey a golden scaling law in the patch size. This note fixes the construction, the shell pair, and the scaling protocol (patch radii in Fibonacci steps; observable: null-band fraction and its $\varphi$-ladder). The production run is executing on the author's workstation; results will appear as v2 of this record. Related: the tan$^2$ rung law and the "only gold dwells finitely" theorem (Note 26). Licence CC-BY-4.0. Continues: Note 21. Supplement to: INDYNA Law Register. Part of the INDYNA Notes series (Notes 16–34). All numbers reproduce from the INDYNA law register (master data record, doi:10.5281/zenodo.21891088). Licence CC-BY-4.0.