  For all positive integers $t$ exceeding one, a matroid has the cyclic
$(t-1,t)$-property if its ground set has a cyclic ordering $\sigma$ such that
every set of $t-1$ consecutive elements in $\sigma$ is contained in a
$t$-element circuit and $t$-element cocircuit. We show that if $M$ has the
cyclic $(t-1,t)$-property and $|E(M)|$ is sufficiently large, then these
$t$-element circuits and $t$-element cocircuits are arranged in a prescribed
way in $\sigma$, which, for odd $t$, is analogous to how 3-element circuits and
cocircuits appear in wheels and whirls, and, for even $t$, is analogous to how
4-element circuits and cocircuits appear in swirls. Furthermore, we show that
any appropriate concatenation $\Phi$ of $\sigma$ is a flower. If $t$ is odd,
then $\Phi$ is a daisy, but if $t$ is even, then, depending on $M$, it is
possible for $\Phi$ to be either an anemone or a daisy.
