  Recently Ricca and Maggione [MHD (2008)] have presented a very simple and
interesting model of stretch-twist-fold dynamo in diffusive media based on
numerical simulations of Riemannian flux tubes. In this paper we present a yet
simpler way of analytically obtaining fast and slow dynamo, generated by by the
curvature energy of magnetic filaments in diffusive media. geometrical model
for the galactic or accretion disk dynamo in shear flows is presented. In the
fast dynamo case it is shown that the absence of stretching leads to the
absence of fast dynamos and when torsion of filaments vanishes the dynamo
action cannot be support as well. This is the Cowling-Zeldovich theorem for
planar flows. Isotropy of the magnetic fields hypothesis is used to compute the
fast nature of dynamo. A similar result using non-holonomic Frenet frame has
been recently obtained for filamentary dynamos [Garcia de Andrade, AN (2008)].
The stretch-twist-fold (STF) filamented models discussed here may serve to
formulate future experiments in the Madison Dynamo Experiment (MDE) facility
[Nornberg et al, Phys Plasmas (2008)]. Though their running experiments deal
with magnetic fields that are orthogonal to the flow, other topologies are also
used here, with an eye in future experiments. Unstretched filaments in MDE
shows Vishik anti-fast dynamo action applies [Garcia de Andrade[Phys Plasmas
(2008)].
