It's theorized that curliness can be a inheritable trait in koa. There's different kinds of curl. The large, flame type curl comes from the crotch of big branches. Fiddleback or tiger striping will normally come from large branches or the trunk. I would assume that the weight of the tree is what causes the curliness. Although, I have seen very small branches with tight curl in them. I believe UH has done a few studies on the characteristics of koa and genetic inheritance.
Koa can also come in a quilted pattern, but unlike maple, the figure is shown when quarter sawn. I have a few really nice pieces that I'm saving for that special build. I have no idea what causes that kind of figuring, but I certainly can appreciate it.