Eucalyptocrinites is one the most common and familiar mid‐Palaeozoic crinoids and is the exemplar of a form with dendritic radicular holdfasts. American museums have hundreds of specimens of Eucalyptocrinites holdfasts from the Silurian Waldron Shale of Indiana and Kentucky, USA. The radix (‘root’) system of Eucalyptocrinites can be described as comprised of links (branches) that meet at nodes. Measured values include the x‐ and y‐coordinates of the nodes, the distances of the nodes from the stem, the angles between branches, branch length and branch width. Rose diagrams show clearly that the root systems are not isotropic but have preferred orientations. Branch angles are highly variable, but cluster around 60 degrees. Branch lengths and distal branch widths are relatively constant, but branch width increases variably towards the column. The branching pattern can be modelled as a self‐similar (‘fractal’) structure. Several specimens labelled as Eucalyptocrinites show a distinct fivefold symmetry without branching and very likely represent a different taxon. The Eucalyptocrinites radix system, along with the probably stiff dististele, most likely functioned as a rigid plate that resisted rotational forces due to currents acting on the crown. Upstream radicles experienced tension, whereas downstream roots were compressed. This force distribution may explain the observed anisotropies in radix morphology. The ‘roots’ of Eucalyptocrinites and other crinoids have long been compared with the root systems of plants. Although there are superficial similarities, there are fundamental differences.

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