Dendrites are the typical patterns for many anisotropic growth process
es. A detailed understanding of their dynamics appears to be crucial f
or a proper classification of various growth morphologies. In particul
ar the morphology transitions occurring for varying anisotropy were pr
edicted to depend upon fluctuations. In the present investigation we c
ompare analytical and numerical results on the stability of dendrites
under influence of external fluctuations. In particular we confirm the
previous ideas that the dendrites are linearly stable under influence
of noise even in the limit of extremely small but nonzero anisotropy.
This supports the concept of a smooth change-over from compact to fra
ctal dendrites and finally to fractal seaweed whose internal length sc
ale was predicted to depend on noise.