  We consider the escaping parameters in the family $\beta\wp_\Lambda$, i.e.
these parameters for which the orbits of critical values of $\beta\wp_\Lambda$
approach infinity, where $\wp_\Lambda$ is the Weierstrass function. Unlike to
the exponential map the considered functions are ergodic. They admit a
non-atomic, $\sigma$-finite, ergodic, conservative and invariant measure $\mu$
absolutely continuous with respect to the Lebesgue measure. Under additional
assumptions on the $\wp_\Lambda$-function we estimate from below the Hausdorff
dimension of the set of escaping parameters in the family $\beta\wp_\Lambda$,
and compare it with the Hausdorff dimension of escaping set in dynamical space,
proving a similarity between parameter plane and dynamical space.
