Analysis of Randomly Shaped Puzzle Fragments: Punch‐Matrix/Particle Puzzles

The fitting‐together‐ability of a Punch‐Matrix/Particle puzzle (PMP‐puzzle) can be automatically investigated, based on two independent scattering experiments. A PMP‐puzzle consists of a large homogeneous matrix piece (the punch‐matrix) and N single homogeneous fragment particles. The well‐investigated ‘Dead Leaves’ puzzle is a special case of a PMP‐puzzle. On the one hand, a Fourier transformation of the scattering curve of this ensemble (matrix piece and fragment particles) yields the function $g1N(r).$ On the other hand, the chord length distribution density $φ(r)$ of the separate fragment pieces, $φ(r),$ is assumed to be known, at least near the origin $r→0.$ The ratio between both terms yields a function $Φ1N(r) = g1N(r)/φ(r),$ the behavior of which is discussed for $r→0.$ The fitting ability is designed by $Φ1N(0+) = 1.$ Examples of $Φ1N(r)$ are discussed. A numerical approach for determining the terms $g(0+)$ in question and two examples are explained.