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July 23, 2026Open Access

Chiral Aperiodic Spectre Monotile from Hexagonal Golden Ratio Inflation — E8 Intelligence Research

Andrew Stewart Caldin

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Key Points

The aim is to construct a chiral aperiodic monotile and prove its aperiodicity through mathematical rules.
Developed a chiral aperiodic monotile derived from Tile(a,b) using hexagonal inflation rules.
Utilized a hexagonal supertile composed of 12 smaller tiles scaled by the golden ratio.
Established a proof of aperiodicity through combinatorial inflation rules.
Demonstrated a successful construction of the Spectre monotile with specific edge ratios.
Found that the hierarchical tiling exhibits no translational symmetry.
Confirmed the chiral nature through the lack of reflections in the constructed tile.

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Implication

Reveals unique aperiodic tiling properties in geometric configurations, indicating new mathematical concepts.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a65a5bad3aea3239cd7793a https://doi.org/10.5281/zenodo.21503827

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