We consider a class of planar self-affine tiles T that are generated by the lower triangular expanding matrices and the product-form digit sets. We give necessary and sufficient conditions for T to be connected and disk-like. Also for the disconnect case, we give a condition that enumerates the number of connected components of T .

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For a conformal iterated function system satisfying the bounded distortion property and the weak separation condition, we prove a formula for the Hausdorff dimension of the attractor, and establish the equality between the Hausdorff dimension and the growth dimension. Furthermore, a relation between the open set condition and the weak separation condition is given.

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