A self-inverse fractal patchwork. We begin with four tangent circles with centers at the vertices of a rhombus, and four lines, each of which is perpendicular to a diagonal at a vertex. (This collection is shown faintly in the background.) We then construct six circles, each of which is orthogonal to a triple of circles (the blue and green circles) or a pair of circles and a line (the red, yellow, orange, and purple circles). This figure is then repeatedly reflected across the four original circles and four lines, producing a cloth whose pattern is invariant under the group generated by the eight transformations.