  A new equation is proposed to explain the curvature of spent sparklers. We
found the state of a segment of the sparkler to depend strongly on the state of
its spent segments. The equation is nearly able to produce the sparkler shape
for a range of lengths and for all elevation angles. The method proposed here
is likely to explain any phenomena in nature related to an evolving length
scale associated with some material that becomes progressively stiff or dry,
such as the growth of resin exuded from trees. The equation can produce a very
rich spectrum of shapes by varying material parameters (density,
temperature-dependent strength), heating temperature, elevation angle, and
gravitational acceleration. This might provide new insights into explaining
many shapes in nature or man-made structures.
