http://gosper.org/islands.png shows four triadic dragons sharing an endpoint, and fanned out at angular intervals π/6, π/3, and π/2. If we suppose each has unit area, it is a minor puzzle to compute the distance between endpoints (12^(1/4)), and the (slightly greater) diameter, which I haven't bothered to rederive. Perhaps the easiest area derivation is to note that the dragons tile the (infinite) plane in a triangular grid, with 3/2 dragons/triangle. This is a case of using infinity to answer a finite question, and is unrelated to the dragon's infinite perimeter, e.g. Small constant #1: What is the diameter minus endpoint span. Notice the purple Hawaiianoid chain of apparently similar islands formed by the purple dragon minus the blue one, and the (necessarily) congruent white chain between the green and gold dragons. While trying to characterize these Islands, Corey & Julian noticed something peculiar. Define A(ø) := the area of intersection of two coterminous unit area tdragons fanned at angle ø. A(π/3)=0 by virtue of the plane tiling. A(π/6) appears to be some simple function of the area of an island chain. But maybe not an island! On very close inspection, A(π/2) is very slightly positive. This is not a positioning artifact--in the fractal limit, coterminous dragons infinitely entwine, and cannot be slid apart without rotation. This is not visually obvious because they are based on a log spiral with a scale gain of 729 per turn. (kth order dragon ~ (rt3 e^(i pi/6))^k. k=12 makes one turn.) It thus appears that the islands are very slightly dissimilar! Small constant #2: What is A(π/2)? Small constant #3: What is the least positive ϵ for which A(π/2+ϵ)=0? --rwg