  A circle pattern is a configuration of circles in the plane whose
combinatorics is given by a planar graph G such that to each vertex of G
corresponds a circle. If two vertices are connected by an edge in G, the
corresponding circles intersect with an intersection angle in $(0,\pi)$.
  Two sequences of circle patterns are employed to approximate a given
conformal map $g$ and its first derivative. For the domain of $g$ we use
embedded circle patterns where all circles have the same radius decreasing to 0
and which have uniformly bounded intersection angles. The image circle patterns
have the same combinatorics and intersection angles and are determined from
boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$
or $\arg g'$). For quasicrystallic circle patterns the convergence result is
strengthened to $C^\infty$-convergence on compact subsets.
