This interactive companion accompanies a manuscript on explicit interpolations among the Sierpinski, Rauzy, and Apollonian gaskets. The parameterized views display finite-level approximants of the maps defined in the paper.

The affine-projective family connects the Sierpinski gasket with the Rauzy gasket. The conformal family connects the Sierpinski gasket with the equilateral Apollonian gasket. The Boundary view implements the side-fixed normalization suggested by the boundary model: the base side is the segment $[0,1]$, and the Apollonian endpoint is generated by $G_0(z)=z/(z+1)$, $G_1(z)=1/(2-z)$, and $G_*(z)=(z-i)/(2z-1-2i)$.

In that side-fixed view the positive half of the stack uses the auxiliary maps $H_{0,s}(z)=z/(2-s+sz)$, $H_{1,s}(z)=1-(1-z)/(2-s+s(1-z))$, and $H_{*,s}(z)=p+(z-p)/(2-s+2is(z-p))$, where $p=(1+i)/2$.