restart;
Arithmetisation of the Half-Coil Variant of the Peano Curve
Definition of the operators P0 to P8 (compare chapter 4.5):
P[0] := (x,y) -> (y/3,x/3);
P[1] := (x,y) -> (-x/3+1/3,y/3+1/3);
P[2] := (x,y) -> (y/3, x/3+2/3);
P[3] := (x,y) -> (x/3+1/3,-y/3+1);
P[4] := (x,y) -> (2/3-y/3,2/3-x/3);
P[5] := (x,y) -> (1/3+x/3,1/3-y/3);
P[6] := (x,y) -> (y/3+2/3, x/3);
P[7] := (x,y) -> (-x/3+1, y/3+1/3);
P[8] := (x,y) -> (y/3+2/3, x/3+2/3);