**Figure 1:** Densely branched growth in quasi-2D electrochemical
deposition. (a) Radial geometry. Zinc deposited from
0.05M at 10V, with mm and *R*=4.2 cm.
(b) Flat geometry. Copper deposited from 0.1M
at 5V with *R*=4 mm.

**Figure 2:** Dimensionless growth rate of the th harmonic
in the three-dimensional radial geometry.
Conductivity anisotropy = 0.01, , and .
Lines are plotted for
.
As the branches become increasingly resistive, the critical
mode number below which all modes are stable increases.
The dependence on *R* is very weak provided .

**Figure 3:** Plot of the critical perturbation harmonic as a function
of the amount of dissipation and degree of
anisotropy
in the three-dimensional radial geometry model, with
, and . Dissipation and anisotropy
both help stabilize the DBM.

**Figure 4:** Plot of the critical perturbation harmonic as a function
of the size of the pattern, , in the three-dimensional
radial geometry model, with and .
Lines are plotted for
, , , and .
Predictions for the size-dependent crossover to stable growth in
the anisotropic limit given by Eq. (18),
, 8, 10.5, and 13 for the four values respectively,
agree well with the jump in for the full solution.

Mon May 20 13:07:47 CDT 1996