  Non-periodic folding of periodic crease patterns paves the way to novel
nonlinear phenomena that cannot be feasible through periodic folding. This
paper focuses on the non-periodic folding of recursive crease patterns
generalized from Spidron. Although it is known that the Spidron has a $1$-DOF
isotropic rigid folding motion, its general kinematics and dependence on the
crease pattern remain unclear. Using the kinematics of a single unit cell of
the Spidron and the recursive construction of the folded state of multiple unit
cells, we consider the folding of the Spidron that is not necessarily
isotropic. We found that as the number of unit cells increases, the
non-periodic folding is restricted and the isotropic folding becomes dominant.
Then, we analyze the three kinds of isotropic folding modes by constructing
$1$-dimensional dynamical systems governing each of them. We show that these
systems can possess different recursive natures depending on folding modes even
in an identical crease pattern. Furthermore, we show their novel nonlinear
nature, including the period-doubling cascade leading to the emergence of
chaos.
