Sunflower hard disk graphs

Carl P Dettmann *, Orestis Georgiou

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review


The random geometric graph consists of a random point set with links between points with mutual distance below a fixed threshold. Here, we use the same geometric connection rule (“hard disk graph”) but for a deterministic point set, the sunflower spiral. At large distances, the local structure is asymptotically a lattice where for each lattice vector, there is another of length a factor√5 greater, and the angle between these varies log-periodically with distance from the origin. Graph properties including node degrees, stretch factor, clique and chromatic numbers are considered, as well as link formation, connectivity and planarity transitions. Properties depend on a combination of the central region and the perturbed distant lattices, in a rich and varied manner.
Original languageEnglish
Article number129180
Number of pages15
JournalPhysica A: Statistical Mechanics and its Applications
Early online date3 Sept 2023
Publication statusPublished - 1 Nov 2023

Bibliographical note

Funding Information:
This work was supported by the Engineering and Physical Sciences Research Council [ EP/N002458/1 ]. All underlying data is included in full within the paper.

Publisher Copyright:
© 2023 The University of Bristol


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