Maki Furukado

Discovered Tilings

Preview Nautilus
Nautilus

This is the dual partner of Conch, which has more details. The scaaling factor of this rule is either of the (complex conjugate) expanding roots of $x^4 - x^3 + 1 = 0$.

Finite Rotations Euclidean Windowed Tiling Polytopal Tiles

Preview Conch (Volume Hierarchic)
Conch (Volume Hierarchic)

A volume hierarchic version of Conch.

Finite Rotations Euclidean Windowed Tiling Self Similar Substitution

Preview Conch
Conch

This tiling and Nautilus are dual tilings generated by non-PV morphisms. As such they are the first step in a generalisation of the work of G. Rauzy, P. Arnoux, S. Ito and others for PV substitution rules. The work that developed out of G. Rauzy’s seminal paper [Rau82] .

The inflation factor for …

Finite Rotations Euclidean Windowed Tiling

Preview Nautilus (Volume Hierarchic)
Nautilus (Volume Hierarchic)

A volume hierarchic version of Nautilus

Finite Rotations Euclidean Windowed Tiling Self Similar Substitution