These are Petoskey stones, a rock and a fossil of a coral called Hexagonaria percarinata which flourished during the Devonian period. They are found in the Gravel Point Formation of Michigan. The rounded stones formed as glaciers grabbed them from the bedrock of complete fossilized coral colonies. As the glaciers moved the rocks were smoothed and moved to just one area on the shore of Lake Michigan.
When it's picked up as a dry stone it resembles ordinary limestone but when wet or polished by a lapidary, the mottled pattern of the six-sided coral fossils emerge.
The name comes from an Ottawa Indian Chief Pet-O-Sega. The city of Petoskey, Michigan is also named after him and is the centre of the area where the stones are found. The movement of the frozen lake ice against the shore of Lake Michigan turns over the buried stones exposing new deposits to be found each spring. They can also be found on the beaches and in sand dunes but only in this northwestern portion of Michigan's lower peninsula. In 1965, it was named the state stone of Michigan.
This is a living coral colony in the sea today. The same six sided polyps show up in lovely colour but they are the same as the fossil shapes in the second image.
Anyone travelling to Michigan in spring is welcome to send me a pretty Petoskey, doesn't have to be large but must be pretty.