  In this article we apply an L-system to prove a recurrence formula for the
length of the boundary of iterands of the well known Harter-Heighway dragon
curve, a space filling curve with fractal boundary. This leads to finding
formulas for related sequences of certain binary strings and ternary matrices.
This proves some long standing conjectures for the recurrence relation for the
number of terms in the boundary of the dragon curve, first stated in
unpublished work Daykin and Tucker in 1975.
