  Magnetic reconnection may be the fundamental process allowing energy stored
in magnetic fields to be released abruptly, solar flares and coronal mass
ejection (CME) being archetypal natural plasma examples. Magnetic reconnection
is much too slow a process to be efficient on the large scales, but accelerates
once small enough scales are formed in the system. For this reason, the fractal
reconnection scenario was introduced (Shibata and Tanuma 2001) to explain
explosive events in the solar atmosphere: it was based on the recursive
triggering and collapse via tearing instability of a current sheet originally
thinned during the rise of a filament in the solar corona. Here we compare the
different fractal reconnection scenarios that have been proposed, and derive
generalized scaling relations for the recursive triggering of fast, `ideal' -
i.e. Lundquist number independent - tearing in collapsing current sheet
configurations with arbitrary current profile shapes. An important result is
that the Sweet-Parker scaling with Lundquist number, if interpreted as the
aspect ratio of the singular layer in an ideally unstable sheet, is universal
and does not depend on the details of the current profile in the sheet. Such a
scaling however must not be interpreted in terms of stationary reconnection,
rather it defines a step in the accelerating sequence of events of the ideal
tearing mediated fractal cascade. We calculate scalings for the expected number
of plasmoids for such generic profiles and realistic Lundquist numbers.
