Golden Ratio as Pisot Number Generates Quasicrystal Diffraction Patterns — E8 Intelligence Research

Andrew Stewart Caldin

doi:10.5281/zenodo.21503491

July 23, 2026Open Access

Golden Ratio as Pisot Number Generates Quasicrystal Diffraction Patterns — E8 Intelligence Research

View Full Paper

Ask AI

Bookmark

Share

Key Points

This research investigates how the golden ratio, as a Pisot number, influences quasicrystal diffraction patterns.
Analyzed the golden ratio's properties as a quadratic irrational Pisot number.
Explored the generation of self-similar diffraction patterns using algebraic integers.
Examined the connections between geometry and quasicrystal structures.
The golden ratio generates self-similar quasicrystal diffraction patterns indexed by ℤ[φ].
5-fold rotational symmetry was observed in quasicrystals, which is forbidden in periodic crystals.
Connections were established between number theory and condensed matter physics through the properties of φ.

No abstract yet

We only have this paper's title and publication details.

Read it at the source

Implication

Finding reveals quasicrystal diffraction patterns generated by the golden ratio in condensed matter physics, implying deeper connections in algebraic structures.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a65a6b5d3aea3239cd77d5a https://doi.org/10.5281/zenodo.21503491

View Full Paper

Ask AI

Bookmark

Share

Golden Ratio as Pisot Number Generates Quasicrystal Diffraction Patterns — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

Golden Ratio as Pisot Number Generates Quasicrystal Diffraction Patterns — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

Keep reading

Keep reading