Cells Tiling

Fractal dimension: 2

Visualization

Open in IFStile ↗

AIFS program

@
$dim=4
$subspace=[s,1]
g=1+s
s=$companion([1,0,-1,0])
r=$exchange()
h0=s^11*[-1,0,1,1]
h1=r*[0,0,0,0]
h2=s^4*[0,0,-1,-1]
h3=r*s*[0,1,0,-1]
h4=r*[0,0,0,0]
h5=s^3*r*[-1,-1,0,1]
h6=s^7*[-1,-1,-1,0]
h7=s^10*[-1,-1,0,1]
h8=s^2*r*[-1,0,1,0]
h9=s^10*[0,0,0,0]
h10=r*s^6*[0,0,-1,-1]
h11=s^5*r*[0,-1,-2,-1]
h12=s^3*r*[-1,-1,-1,0]
h13=s*[0,0,-1,-1]
h14=s^2*r*[-2,-2,0,1]
h15=s^2*[0,-1,-2,-1]
h16=s^9*[-1,0,1,1]
h17=r*s^2*[-1,0,1,1]
h18=s^5*[-2,-2,0,1]
h19=s^3*[-1,-1,-1,-1]
h20=s^11*[0,1,0,-1]
h21=s^4*r*[-1,-1,-1,-1]
A0=h9^-1*g*A3|h10^-1*g*A3|h11^-1*g*A3|h12^-1*g*A3|h13^-1*g*A3|h14^-1*g*A3|h15^-1*g*A3|h4^-1*g*A2|h5^-1*g*A2|h6^-1*g*A2|h7^-1*g*A2
A1=h16^-1*g*A3|h17^-1*g*A3|h18^-1*g*A3|h1^-1*g*A1|h2^-1*g*A1
A2=h19^-1*g*A3|h20^-1*g*A3|h21^-1*g*A3|h8^-1*g*A2|h3^-1*g*A1
A3=h0^-1*g*A0

Overview

The Cells tiling is the dual of the Shield tiling, obtained by projecting the same 4D rational space onto the second eigenplane ($subspace=[s,1]) instead of the first. In the cut-and-project scheme, this is equivalent to swapping the roles of direct space and internal space.

The tiling shares the 12-fold rotational symmetry and the same inflation factor $|g|^2 = 2+\sqrt{3}$ as the Shield tiling. The algebraic description uses inverse maps: $h_k^{-1}g$ instead of $g^{-1}h_k$ .