For i = 1,2, let S; R² → R² be the affine transformations defined by Si(t, x) = (t/2+(i − 1)/2, ait +rix + bi). Let F be the attractor of S₁ and S2. (a) Determine values of ai, bi and ri (i = 1,2) for which F is a self-affine curve passing through the points (0,0), (1/4, 7), (1/2,4), (3/4, 11/2), (1, 0). (b) Determine the box dimension of F. (c) Determine whether F can be modified so that it is invariant under reflection in the line t = 1/2 and still passes through the points (0,0), (1/4,7), (1/2,4) and (1,0).

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