In the depot of the museum of Avenches (Switzerland) lies this interesting fragment of a large roman mosaic :You see immediately that this is a rosette with rotational symmetry, except for the fruit at the center. Looking closer we see an additional symmetry. The black and white shapes are all similar. They grow exponentially in size, going away from the center.
An inverse transformation of this image with the complex exponential function exp(x+i*y)=exp(x)*(cos(y)+i*sin(y)) results in :The rosette becomes now a vertical strip with a periodic image. The periodicities in x- and y-direction correspond to radial and azimutal motions in the rosette. The rosette is thus an exponential transform of a periodic tiling. Note the high precision of the design of the mosaic.